NCERT Solutions for Class 11 Chemistry Chapter 7 Equilibrium

 

NCERT Solutions for Class 11 Chemistry Chapter 7 Equilibrium- In this chapter, you will get the NCERT solutions for class 11 chemistry chapter 7 Equilibrium of chemical and physical processes and details about equilibrium's dynamic nature. There are some insights about the equilibrium constant, the law of mass action and what are the factors affecting the equilibrium state. It is a lengthy and also an important chapter of class 11 chemistry. In NCERT solutions for class 11 chemistry chapter 7 Equilibrium, there are 73 questions in the exercise. The solutions of NCERT class 11 chemistry chapter 7 Equilibrium are prepared and solved by chemistry experts. These NCERT solutions will help you in the preparation of your class 11 final examination as well as in the various competitive exams like JEE Mains, NEET, BITSAT, etc. 

After studying NCERT solutions for class 11 chemistry chapter 7 Equilibrium, you will be able to identify equilibrium's dynamic nature involved in chemical and physical processes; explain the law of equilibrium; explain characteristics of equilibria involved in chemical and physical processes; write expressions for equilibrium constants; explain factors affecting the equilibrium state of a reaction; classify substances as bases or acids according to Bronsted-Lowry, Arrhenius and Lewis concepts; also able to classify bases and acids as weak or strong in terms of their ionization constants and calculate solubility product constant.

Exercise Questions

 

What is the Equilibrium?

Equilibrium is the state of a process in which the properties like the concentration of the system, pressure, and temperature do not change with the passage of time. It can be established for both chemical and physical processes. At the stage of equilibrium, the rate of forwarding and reverse reactions are equal. The state of equilibrium can only be achieved if the reversible reaction is taking place in a closed system.

Important formulas of NCERT class 11 chemistry chapter 7 Equilibrium  

 1.Equilibrium constant, K

             K=\frac{K_f}{K_b}

2. Concentration quotient, Q

         Q=\frac{[C]^c[D]^d}{[A]^a[B]^b}

3. \Delta G^o=-2.303RT\:logK

4. K_w=[H^+][OH^-]

5. pH = -log[H^+]

 

NCERT solutions for class 11 chemistry chapter 7 Equilibrium

Exercise Questions

 

Question 7.1(a)        A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

What is the initial effect of the change on vapour pressure?

Answer:

By increasing the volume of the container suddenly, initially, the vapour pressure would decrease. It is due to, the amount of vapour has remained the same but it is distributed in a larger volume.

Question 7.1(b)     A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

How do rates of evaporation and condensation change initially?

Answer:

Here the temperature is constant so that the rate of evaporation is also the same as before. On increasing the volume of the container, the density of vapour decreases due to which the rate of collision between vapour particles decreases. Hence the condensation rate also decreases initially.

Question 7.1(c)      A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased .

What happens when equilibrium is restored finally and what will be the final vapour pressure?

Answer:

When equilibrium is restored, the rate of evaporation is equal to the rate of condensation. The temperature is constant and the volume is changed. The vapour pressure is temperature-dependent, not volumes. So, that final vapour pressure is equal to the initial vapour pressure.

Question 7.2     What is Kc for the following equilibrium when the equilibrium concentration of each substance is: [SO2]= 0.60M, [O2] = 0.82M and [SO3] = 1.90M ? 

               2SO_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2SO_{3}_{(g)}

Answer:

Followings are the given information values to solve the above problems-
\\{[SO_{2}]}= 0.60 M\\ {[O_{2}]}=0.82M\\ {[SO_{3}]}=1.90M
The given chemical equation is -

2SO_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2SO_{3}_{(g)}

The equilibrium constant for this reaction is expressed as;
K_c=\frac{[SO_{3}]^2}{[SO_{2}]^2[O_{2}]}
        
       \\=\frac{[1.90]^2}{[0.60]^2[0.82]}\\ =12.22 M^{-1}(approx)

 

Question 7.3     At a certain temperature and total pressure of 105Pa, iodine vapour contains 40% by volume of I atoms

 I_{(g)}\rightleftharpoons 2I_{(g)}

 Calculate Kp for the equilibrium.

Answer:

It is given that total pressure (PT)is 10^5\ Pa and partial pressure of I atom = 40 % of PT
So, the partial pressure of I atom = \frac{40}{100}\times 10^5 = 4\times 10^4Pascal

The partial pressure of I_2 = 60% of PT

So, the partial pressure of I_2 = \frac{60}{100}\times 10^5=6\times 10^4Pascal

Now, for the reaction  I_{(g)}\rightleftharpoons 2I_{(g)}
K_p = \frac{(p_I)^2}{p_{I_2}} = \frac{(4\times 10^4)^2}{6\times 10^4}\ Pa
                           =2.67\times 10^4\ Pa

Question 7.4      Write the expression for the equilibrium constant, Kc for each of the following reactions:

      (i)      2NOCl_{(g)}\rightleftharpoons 2NO_{(g)}+Cl_{2}_{(g)}
       (ii)    2Cu(NO_{3})_{2}_{(s)}\rightleftharpoons 2CuO_{(s)}+4NO_{2}_{(g)}+O_{2}_{(g)} 
      (iii)     CH_{3}COOC_{2}H_{5}_{(aq)}+H_{2}O_{(l)}\rightleftharpoons CH_{3}COOH_{(aq)}+C_{2}H_{5}OH_{(aq)}
       (iv)     Fe^{3+}_{(aq)}+3OH^{-}_{(aq)}\rightleftharpoons Fe(OH)_{3}_{(s)}
       (v)       I_{2}_{(s)}+5F_{2}\rightleftharpoons 2IF_{5}

Answer:

The equilibrium constant for any reaction can be written as (concentration of products) / (concentration of reactants). And we considered constant values for the solids and liquids because their density per unit volume or mass per unit volume does not change.
Thus,
(i) 
K_c = \frac{[NO]^2[Cl_2]}{[NOCl]^2}
(ii) 
  K_c = \frac{[CuO]^2[NO_2]^4[O_2]}{[Cu(NO_3)_2]^2}
(iii)
                                                                          
 K_c = \frac{[CH_3COOH][C_2H_5OH]}{[CH_3COOC_2H5]}       

(iv)
  K_c = \frac{1}{[Fe^{3+}][OH^-]}

(v)
K_c = \frac{[IF_5]^2}{[F_2]^5}                                                                                 

Question  7.5     Find out the value of Kc for each of the following equilibria from the value of Kp:

       (i)     2NOCl _{(g)}\rightleftharpoons 2NO_{(g)}+Cl_{2}_{(g)};K_{p}=1.8 \times 10^{-2} at 500K  

        (ii)     CaCO_{3}_{(s)}\rightleftharpoons CaO_{(s)}+CO_{2}_{(g)};K_{p}=167 at 1073K

Answer:

We know that the relation between K_p and K_c is expressed as;

K_p=K_c(RT)^{\Delta n}............................(i)
here {\Delta n} = (no. of moles of product) - (no. of moles of reactants)

R = 0.0831 bar L /mol/K, and

For (i) 
K_p = 1.8\times 10^{-2} and Temp (T) = 500K

{\Delta n} = 3 - 2 = 1
By putting the all values in eq (i) we get

K_c = \frac{1.8\times 10^{-2}}{0.0831\times 500} = 4.33\times 10^{-4}

For (ii)
K_p = 167 and temp(T) = 1073 K
{\Delta n} = 2 - 1 = 1
Now, by putting all values in eq (i) we get,

K_c = \frac{167}{0.0831\times 1073} = 1.87

Question 7.6     For the following equilibrium, Kc = 6.3 × 1014 at 1000 K

               NO_{(g)}+O_{3}_{(g)}\rightleftharpoons NO_{2}_{(g)}+O_{2}_{(g)}

Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is Kc, for the reverse reaction?

Answer:

It is given that,
K_c=6.3\times 10^{14}
we know that K'_c for the reverse reaction is the inverse of the forward equilibrium constant. Thus it can be calculated as:

K'_c=\frac{1}{K_c}
         =\frac{1}{6.3\times 10^{14}}
          =1.58\times 10^{-15}

Question 7.7     Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression?

Answer:

For the pure liquids and solids, the molecular mass and the density at a particular temperature is always fixed and it is considered as a constant. Thus they can be ignored while writing the equilibrium constant expression

Question  7.8      Reaction between N2 and O2-takes place as follows:

                2N_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2N_{2}O_{(g)} 

If a mixture of 0.482 mol N2 and 0.933 mol of O2 is placed in a 10 L reaction vessel and allowed to form N2O at a temperature for which Kc = 2.0 ×10-37, determine the composition of equilibrium mixture. 

Answer:

It is given that,
K_c = 2.0\times 10^{-37}
Let the concentration of N_2O at equilibrium be x. So,

                                2N_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2N_{2}O_{(g)}
initial conc                  0.482        0.933                     0          (in moles)
at equilibrium             0.482-x   0.933 -  x              x           (in moles)

The equilibrium constant is very small. So, we can assume   0.482-x = 0.482 and 0.933 -  x = 0.933

We know that,
 

K_c = \frac{[N_2O]^2}{[N_2]^2[O_2]}
2\times 10^{-37}=\frac{(x/10)^2}{(0.0482)^2(0.0933)}       {dividing the moles by 10 to get concentration of ions)

\\\frac{x^2}{100}= 2\times 10^{-37}\times (0.0482)^2\times (0.0933)\\ x^2 = 43.35\times 10^{-40}\\ x = \sqrt{43.35\times 10^{-40}}\\ x=6.6\times 10^{-20}

So, the concentration of [N_2O]= \frac{x}{10}=6.6\times 10^{-20}

Question 7.9     Nitric oxide reacts with Br2 and gives nitrosyl bromide as per reaction given below:

              2NO_{(g)}+Br_{2}_{(g)}\rightleftharpoons 2NOBr_{(g)}

When 0.087 mol of NO and 0.0437 mol of Br2 are mixed in a closed container at a constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate the equilibrium amount of NO and Br2  .

Answer:

The initial concentration of NO and Br_2  is  0.087 mol and 0.0437 mol resp.

The given chemical reaction is-
2NO_{(g)}+Br_{2}_{(g)}\rightleftharpoons 2NOBr_{(g)}

Here, 2 mol of NOBr produces from 2 mol of NO. So, 0.0518 mol of NOBr  is obtained from 0.518 mol of NO.

Again, From 1 mol of Br_2  two mol of NOBr produced. So, to produce 0.518 mol of NOBr we need \frac{0.518}{2} = 0.0259 mol of Br_2.

Thus, the amount of NO present at equilibrium = 0.087 - 0.0518 = 0.0352 mol

and the amount of Br_2 present at the equilibrium = 0.0437-0.0259 = 0.0178 mol

Question 7.10     At 450K, Kp= 2.0 × 1010 /bar for the given reaction at equilibrium.

                2SO_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2SO_{3}_{(g)} 

               What is Kc at this temperature?

Answer:

We have,
K_p= 2\times 10^{10}/bar
We know that the relation between K_p and K_c;

K_p=K_c(RT)^{\Delta n} 
Here \Delta n = ( moles of product) - (moles of  reactants)

2SO_{2}_{(g)}+O_{2}_{(g)}\rightleftharpoons 2SO_{3}_{(g)}

So. here \Delta n = 2-3 = -1

By applying the formula we get;

2\times 10^{10} =K_c(0.0831 L\ bar/K/mol)\times 450K
K_c= \frac{2\times 10^{10}}{(0.0831 L\ bar/K/mol)\times 450K}

        =74.79 \times 10^{10}L mol^{-1}
         =  7.48\times 10^{10}L mol^{-1}

Question 7.11     A sample of HI(g) is placed in flask at a pressure of 0.2 atm. At equilibrium the partial pressure of HI(g) is 0.04 atm. What is Kp for the given equilibrium?

                2HI_{(g)}\rightleftharpoons H_{2}_{(g)}+I_{2}_{(g)}

Answer:

The initial pressure of HI is 0.2 atm . At equilibrium, it has a partial pressure of 0.04 atm. Therefore, a decrease in the pressure of HI  is 0.2 - 0.04 = 0.16.

The given reaction is:

2HI_{(g)}\rightleftharpoons H_{2}_{(g)}+I_{2}_{(g)}

HI_{(g)}\rightleftharpoons 1/2H_{2}_{(g)}+1/2I_{2}_{(g)}

At equilibrium,
\\pHI = 0.04\\ pH_2 = \frac{0.16}{2}=0.08\\ pI_2 = \frac{0.16}{2}=0.08

Therefore, 
K_p = \frac{pH_2\times pI_2}{p^2HI}
         \\=\frac{0.08 \times 0.08}{(0.04)^2}\\ =4

Question 7.12     A mixture of 1.57 mol of N2, 1.92 mol of H2 and 8.13 mol of NH3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, Kc for the reaction N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}  is 1.7 × 102. Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?

Answer:

We have,
N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}

K_c = 1.7 \times 10^{2}

The concentration of species are-
[N_2] = 1.57/20 mol L^{-1}\\ {[H_2]}=1.92/20mol L^{-1}\\ {[NH_3]}=8.13/20mol L^{-1}

We know the formula of 

Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3}
      \\=\frac{(8.13/20)^2}{(1.57/20)(1.92/20)^3}\\ =2.4\times 10^{-3}
The reaction is not in equilibrium. Since Qc>K_c, the equilibrium proceeds in reverse direction.

Question 7.14     One mole of H2O and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium 40% of water (by mass) reacts with CO according to the equation,

                H_{2}O_{(g)}+CO_{(g)}\rightleftharpoons H_{2}_{(g)}+CO_{2}_{(g)}

               Calculate the equilibrium constant for the reaction.  

Answer:

The given reaction is-

                               H_{2}O_{(g)}+CO_{(g)}\rightleftharpoons H_{2}_{(g)}+CO_{2}_{(g)}
initial conc                   1/10            1/10              0               0
At equilibrium             0.6/10           0.6/10          0.04          0.04

Now, the equilibrium constant for the reaction can be calculated as;

K_c = \frac{[H_2][CO_2]}{[H_{2}O][CO]}
         = \frac{.04 \times.04}{(.06)^2}

           = 0.44 (approx)

Question 7.15     At 700 K, equilibrium constant for the reaction:

                H_{2}_{(g)}+I_{2}_{(g)}\rightleftharpoons 2HI_{(g)}

                is 54.8. If 0.5 mol L-1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H2(g) and I2(g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700K?

Answer:

We have,

The equilibrium constant of the reaction = 54.8

moles of HI = 0.5 mol/L

The given reaction is-

H_{2}_{(g)}+I_{2}_{(g)}\rightleftharpoons 2HI_{(g)}

So, the reverse equilibrium constant is K'_c = 1/K_c

Suppose the concentration of hydrogen and iodine at equilibrium be x

[I_2]=[H_2]=x

Therefore,

K'_c = \frac{[H_2][I_2]}{[HI]} = \frac{x^2}{(.5)^2}
 So, the value of x = \sqrt{\frac{0.25}{54.8}}=0.0675(approx)\ mol/ L  

Question 7.16     What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M ?

               2ICl _{(g)}\rightleftharpoons I_{2}_{(g)}+Cl_{2}_{(g)}; K_{c}=0.14

Answer:

The given reaction is:
                                2ICl (g) \rightleftharpoons I_2 (g) + Cl_2 (g)
Initial conc.                0.78 M           0           0
At equilibrium         (0.78 - 2x) M     x M        x M

The value of K_c = 0.14

Now we can write,
K_c = \frac{[I_2][Cl_2]}{[ICl]^2}
\\0.14 = \frac{x^2}{(.78-x)^2}\\ 0.374 = \frac{x}{(.78-x)}

By solving this we can get the value of x = 0.167

Question 7.17     Kp = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C2H6 when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium? 

                C_{2}H_{6}_{(g)}\rightleftharpoons C_{2}H_{4}_{(g)}+H_{2}_{(g)}

Answer:

Suppose the pressure exerted by the hydrogen and ethene gas be p at equilibrium. 

the given reaction is-

                                    C_{2}H_{6}_{(g)}\rightleftharpoons C_{2}H_{4}_{(g)}+H_{2}_{(g)}
initial pressure                  4 atm              0                     0
At equilibrium                  4 - p                 p                    p

Now, 
K_p = p_{C_2H_4}\times p_{H_2}/p_{C_2H_6}
         0.04 = \frac{p^2}{4-p}

By solving the quadratic equation we can get the value of  p = 0.38

Hence,at equilibrium,

p_{C_2H_6} =  4  - p  = 4 -.038

= 3.62 atm

Question 7.18(ii)     Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

                CH_{3}COOH _{(l)}+C_{2}H_{5}OH_{(l)}\rightleftharpoons CH_{3}COOC_{2}H_{5}_{(l)}+H_{2}O_{(l)}

(ii)  At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.

Answer:

Let the volume of the mixture will be V.
                                               CH_{3}COOH _{(l)}+C_{2}H_{5}OH_{(l)}\rightleftharpoons CH_{3}COOC_{2}H_{5}_{(l)}+H_{2}O_{(l)}
initial conc.                                     1/V                             0.18/V                          0                                   0

At equilibrium                          \frac{1-.171}{V}  (= 0.829/V)  \frac{1-.171}{V}               0.171                         0.171

So the equilibrium constant for the reaction can be calculated as;

K_c = \frac{(0.171)^2}{(0.829)(0.009)}

        =3.92 (approx)

Question 7.18(iii)     Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

               CH_{3}COOH_{(l)}+C_{2}H_{5}OH_{(l)}\rightleftharpoons CH_{3}COOC_{2}H_{5}_{(l)}+H_{2}O_{(l)}

(iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after sometime. Has equilibrium been reached?

Answer:

Let the volume of the mixture will be V.
                                               CH_{3}COOH _{(l)}+C_{2}H_{5}OH_{(l)}\rightleftharpoons CH_{3}COOC_{2}H_{5}_{(l)}+H_{2}O_{(l)}
initial conc.                                     1/V                             0.5/V                          0                                   0

At equilibrium                          \frac{1-.214}{V}  (= 0.786/V)  \frac{1-.214}{V}               0.214                         0.214

Therefore the reaction quotient of the reaction-

Q_c = \frac{(0.214)^2}{(0.786)(0.286)}

        =0.2037 (approx)

Since Q_c<K_c equilibrium has not been reached.

Question 7.19     A sample of pure PCl5 was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl was found to be 0.5 × 10-1 mol L-1. If value of Kc is 8.3 × 10-3, what are the concentrations of PCl3 and Cl2 at equilibrium?

                PCl_{5}_{(g)}\rightleftharpoons PCl_{3}_{(g)}+Cl_{2}_{(g)}

Answer:

We have,

concentration of PCl_5 = 0.05 mol/L
and K_c = 8.3\times 10^{-3}

Suppose the concentrations of both PCl_3 and Cl_2 at equilibrium be x mol/L. The given reaction is:

                           PCl_5 (g) \rightleftharpoons PCl_3 (g) + Cl_2(g)

at equilibrium       0.05                    x                     x

it is given that the value of the equilibrium constant, K_c = 8.3\times 10^{-3}

Now we can write the expression for equilibrium as:

K_c = \frac{x^2}{0.05}=8.3\times 10^{-3}
\Rightarrow x = \sqrt{4.15\times 10^{-4}}
            =0.0204 (approx)

Hence the concentration of PCl_3 and Cl_2  is 0.0204 mol / L

Question 7.20    One of the reaction that takes place in producing steel from iron ore is the reduction of iron(II) oxide by carbon monoxide to give iron metal and CO2.FeO_{(s)}+CO_{(g)}\rightleftharpoons Fe_{(s)}+CO_{2}_{(g)}; Kp = 0.265 atm at 1050K What are the equilibrium partial pressures of CO and CO2 at 1050 K if the initial partial pressures are: p_{CO}= 1.4 atm and pCO_2  = 0.80 atm?

Answer:

We have,

K_p=0.265
the initial pressure of CO and CO_2 are 1.4 atm and 0.80atm resp.

The given reaction is-

                                FeO_{(s)}+CO_{(g)}\rightleftharpoons Fe_{(s)}+CO_{2}_{(g)}
initially,                                   1.4 atm                    0.80 atm

Q_p = \frac{pCO_2}{pCO}=\frac{0.80}{1.4} = 0.571
Since Q_p>K_c the reaction will proceed in the backward direction to attain equilibrium. The partial pressure of CO_2 will increase = decrease in the partial pressure of CO_2   = p                      

\therefore K_p = \frac{pCO_2}{pCO} = \frac{0.80-p}{1.4+p}=0.265
                                   =0.371+.265p=0.80-p

                                    By solving the above equation we get the value of p = 0.339 atm

Question 7.21     Equilibrium constant, Kc for the reaction

                N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}

At 500 K is 0.061 At a particular time, the analysis shows that composition of the reaction mixture is 3.0 mol L-1 N2, 2.0 mol L-1 H2 and 0.5 mol L-1 NH3. Is the reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?

Answer:

The given reaction is:

                                            N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}           

at a particular time:           3.0molL-1  2.0 molL-1     0.5molL-1

Now, we know that,

Qc = [NH_3]2^ / [N_2][H_2]^3
          \\ = (0.5)^2 / (3.0)(2.0)^3\\ = 0.0104

It is given that Kc = 0.061

Since, Qc \neq  Kc, the reaction mixture is not at equilibrium.

Again, Q_c < K_c, the reaction will proceed in the forward direction to attain the equilibrium.

Question 7.22     Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:

2BrCl_{(g)}\rightleftharpoons Br_{2}_{(g)}+Cl_{2}_{(g)}

For which Kc = 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10-3 mol L-1, what is its molar concentration in the mixture at equilibrium?

Answer:

Suppose the x amount of bromine and chlorine formed at equilibrium. The given reaction is:

                    2BrCl_{(g)}\rightleftharpoons Br_{2}_{(g)}+Cl_{2}_{(g)} 

Initial Conc.     3.3\times10^{-3}          0            0

at equilibrium   3.3\times10^{-3}- 2x    x          x

Now, we can write,

K_c =\frac{[BR_2][Cl_2]}{[BrCl_2]^2}
32=\frac{x^2}{(3.3\times 10^{-3}-2x)^2}
5.66=\frac{x}{(3.3\times 10^{-3}-2x)}
x+11.32x=18.678 \times 10^{-3}

By solving the above equation we get, 

       x = 1.51 \times 10^{-3}

Hence, at equilibrium [BrCl_2] = 3.3\times 10^{-3} - (2\times 1.51\times 10^{-3})
                                                      = 0.3\times 10^{-3} M

Question 7.23     At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO2 in equilibrium with soild carbon has 90.55% CO by mass

 C_{(s)}+CO_{2}_{(g)}\rightleftharpoons 2CO_{(g)}

 Calculate Kc for this reaction at the above temperature.

Answer:

Suppose the total mass of the gaseous mixture is 100 g.
Total pressure is 1 atm

Mass of CO = 90.55 g
And, mass of CO_2 = (100 - 90.55) = 9.45 g

Now, number of moles of  CO= 90.55/28 = 3.234 mol  (mol. wt of CO = 28)
Number of moles of CO_2 = 9.45/44 = 0.215 mol  (mol. wt of CO_2 = 44)

Partial pressure of CO ,

pCO=\frac{n_{CO}}{n_{CO}+n_{CO_2}}p_T

             =\frac{3.234}{3.234+0.215} \times 1
              = 0.938 atm

Similarly partial pressure of CO_2,

pCO_2=\frac{n_{CO_2}}{n_{CO}+n_{CO_2}}p_T
              = 0.062 atm

Thus, K_p = \frac{(0.938)^2}{(0.062)} \approx 14.19

By using the relationK_p = K_c(RT)^{\Delta n}
                                   K_c = \frac{14.19}{(0.083\times 1127)^1}
                                            = 0.159 (approx)      

Question 7.24     Calculate a) \Delta G^{0} for the formation of NO2 from NO and O2 at 298K

                NO{(g)}+\frac{1}{2}O_{2}(g) \rightleftharpoons NO_{2}(g)

                where

                \Delta _{f}G^{+}\left [ NO_{2} \right ]=52.0kJ/mol 

                \Delta _{f}G^{+}\left [ NO \right ]=87.0kJ/mol

                \Delta _{f}G^{+}\left [ O_{2} \right ]=0kJ/mol

Answer:

Given data,

     \Delta _{f}G^{+}\left [ NO_{2} \right ]=52.0kJ/mol 
    \Delta _{f}G^{+}\left [ NO \right ]=87.0kJ/mol

    \Delta _{f}G^{+}\left [ O_{2} \right ]=0kJ/mol

given chemical reaction-
NO{(g)}+\frac{1}{2}O_{2}(g) \rightleftharpoons NO_{2}(g)

for the reaction, 
\Delta G^0 = \Delta G^0(products) - \Delta G^0 (reactants)
           = (52-87-0)
           = -35 kJ/mol

Question 7.25     Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

 (a)        PCl_{5}_{(g)}\rightleftharpoons PCl_{3}_{(g)}+Cl_{2}_{(g)}

(b)     CaO(s)+CO_{2}(s)\rightleftharpoons CaCO_{3}(s)

(c)     3Fe(s)+4H_{2}O(g)\rightleftharpoons Fe_{3}O_{4}(s)+H_{2}(g)

Answer:

According to Le Chatellier's principle, if the pressure is decreased, then the equilibrium will shift in the direction in which more number of moles of gases is present.

So, 

  • (a)The number of moles of reaction products will increase.

  • (b)The number of moles of reaction products will decrease

  • (c)The number of moles of reaction products remains the same.

Question 7.26     Which of the following reactions will get affected by increasing the pressure? Also, mention whether the change will cause the reaction to go into forward or backward direction.

  (i)       COCl_{2}(g)\rightleftharpoons CO(g)+Cl_{2}(g)

  (ii)    CH_{4}(g)+2S_{2}(g)\rightleftharpoons CS_{2}(g)+2H_{2}S(g)

 (iii)      CO_{2}(g)+C(s)\rightleftharpoons 2CO(g)   

 (iv)     2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)

 (v)     CaCO_{3}(s)\rightleftharpoons CaO(s)+CO_{2(g) 

(vi)     4NH_{3}(g)+5O_{2}(g)\rightleftharpoons 4NO(g)+6H_{2}O(g)

Answer:

According to Le Chatellier's principle, if the pressure is increased, then the equilibrium will shift in the direction in which less number of moles of gases is present. So, as per this rule following given reactions are affected by the increasing pressure-

The reaction (i), (iii), and (vi)- all proceeds in the backward direction

Reaction(iv) will shift in the forward direction because the number of moles of gaseous reactants is more than that of products.

Question 7.27     The equilibrium constant for the following reaction is 1.6 ×105 at 1024K

               H_{2}(g)+Br_{2}(g)\rightleftharpoons 2HBr(g)

Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024K.

Answer:

Given that,
K_p for the reaction = 1.6\times 10^{5}

K'_p = 1/K_p = \frac{1}{1.6\times 10^{5}} = 6.25 \times 10^{-6}

Let the pressure of both H_2 and Br_2  at equilibrium be p.

                        2HBr\rightleftharpoons H_2(g)+Br_2(g)
initial conc.           10                   0              0
at eq                     10-2p             p                p

Now,
  K_p' = \frac{p^{Br_2}.p^{H_2}}{p^2_{HBr}}
6.25\times 10^{-6}=\frac{p^2}{(10-2p)^2}
5\times 10^{-3}=\frac{p}{(5-p)}
By solving the above equation we get, 

p = 0.00248 bar

Hence the pressure of  H_2 and Br_2  is 0.00248 bar and pressure of HBr is 0.00496 bar

Question 7.28(a)     Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

                CH_{4}(g)+H_{2}O(g)\rightleftharpoons CO(g)+3H_{2}(g)

Write an expression for Kp for the above reaction.

Answer:

CH_{4}(g)+H_{2}O(g)\rightleftharpoons CO(g)+3H_{2}(g)
the expression of ionisation constant ( Kp) for the reaction can be defined as the ratio of the product of concentration to the product of reactants.
K_p = \frac{p_{CO}.p^3_{H_2}}{p_{CH_4}.p_{H_2O}}

Question 7.28(b)     Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

                CH_{4}(g)+H_{2}O(g)\rightleftharpoons CO(g)+3H_{2}(g)

   How will the values of Kp and composition of equilibrium mixture be affected by

(i)      increasing the pressure

(ii)      increasing the temperature

(iii)      using a catalyst?

 

Answer:

(i) According to Le Chatellier's principle, if pressure is increased, then the reaction will shift towards the less number of moles of gases. So, here the direction of equilibrium is backward and the value of K_p decreases.

(ii) According to  Le Chatellier's principle, as the reaction is endothermic, the equilibrium will shift in the forward direction. The value of K_p is increases.

(iii) The equilibrium of the reaction is not affected by the presence of the catalyst. It only increases the rate of reaction.

Question 7.29(a)_        Describe the effect of :

(a)        addition of H2

                         2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)

Answer:

2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)
(a)According to Le Chatelliers principle, on the addition of dihydrogen, the number of mole of H_2 increases on the reactant side. Thus to attain the equilibrium again the reaction will move in the forward direction.

(b) According to Le Chatellier's principle, on the addition of methyl alcohol, the number of moles of methyl alcohol increases on the product sides. So, to attain the equilibrium, the reaction will proceed in a backward direction.

(c) If we remove the CO from the reactant side, the concentration on the reactant side will decrease and to attain an equilibrium, the reaction will shift backward direction

(d) On removal of CH_{3}OH the equilibrium will shift in the forward direction.

Question 7.29(b)     Describe the effect of : 

 addition of CH3OH

        2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)

Answer:

2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)
According to Le Chatellier's principle, on the addition of methyl alcohol, the number of moles of methyl alcohol increases on the product sides. So, to attain the equilibrium, the reaction will proceed in a backward direction.

Question 7.29(c)       Describe the effect of :

removal of CO  

          2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)

Answer:

2H_{2}(g)+CO(g)\rightleftharpoons CH_{3}OH(g)
If we remove the CO from the reactant side, the concentration on the reactant side will decrease and to attain an equilibrium, the reaction will shift backward direction

Question 7.30     At 473 K, equilibrium constant Kc for decomposition of phosphorus pentachloride, PCl5 is 8.3 ×10-3. If decomposition is depicted as,

PCl_{5}(g)\rightleftharpoons PCl_{3}(g)+Cl_{2}(g), \Delta _{r}H^{+}=124.0kJ mol^{-1}

(a)       write an expression for Kc for the reaction.
(b)     what is the value of Kc for the reverse reaction at the same temperature ?
(c)      what would be the effect on Kc if

                (i) more PCl5 is added
                (ii)   pressure is increased
                (iii)  the temperature is increased ?  

Answer:

We have,
PCl_{5}(g)\rightleftharpoons PCl_{3}(g)+Cl_{2}(g), \Delta _{r}H^{+}=124.0kJ mol^{-1}
Equilibrium constant for the above reaction = 8.3\times 10^{-3}

(a) Expression of K_c for this reaction-
K_c=\frac{[PCl_3][Cl_2]}{PCl_5}

(b) The value of reverse equilibrium constant can be calculated as;

                  K'_c = \frac{1}{K_c} 
                           =\frac{1}{8.3\times 10^{-3}}=1.20\times 10^2

(c).i   K_c would remain the same because the temperature is constant in this case.

(c). ii  If we increase the pressure,  there is no change in K_c because the temperature is constant in this case also.

(c). iii  In an endothermic reaction, the value of   K_c increases with increase in temperature.

Question 7.31     Dihydrogen gas used in Haber’s process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of CO and H2. In second stage, CO formed in first stage is reacted with more steam in water gas shift reaction,

              CO(g)+H_{2}O(g)\rightleftharpoons CO_{2}+H_{2}(g)

If a reaction vessel at 400 °C is charged with an equimolar mixture of CO and steam such that p_{CO}=p_{H_{2}O} = 4.0 bar, what will be the partial pressure of H2 at equilibrium? Kp= 10.1 at 400°C  

Answer:

We have,
The partial pressure of CO and H_2O is 4 bar and the K_p = 10.1
Let p be the partial pressure of  CO_2 and H_2 at equilibrium. The given reaction is-

                                    CO(g)+H_{2}O(g)\rightleftharpoons CO_{2}+H_{2}(g)
Initial concentration        4 bar               4 bar             0              0
At equilibrium                4 - p                 4 - p             p          p

Therefore, we can write,
10.1= \frac{p_{CO_2}.p_{H_2}}{p_{CO}.p_{H_2O}}
\\10.1= \frac{p^2}{(4-p)^2}\\ 3.178 = \frac{p}{(4-p)}\\ p=(4-p)\times 3.178
By solving the above equation we get,  p = 3.04

Hence, the partial pressure of dihydrogen at equilibrium is 3.04 bar

Question 7.32     Predict which of the following reaction will have an appreciable concentration of reactants and products:

(a)     Cl_{2}(g)\rightleftharpoons 2Cl(g);K_{c}=5 \times 10^{-39} 
(b)     Cl_{2}(g) +2 NO(g)\rightleftharpoons 2NOCl(g);K_{c}=3.7 \times 10^{8} 
(c)     Cl_{2}(g) +2 NO_{2}(g)\rightleftharpoons 2NO_{2}Cl(g);K_{c}=1.8
 

Answer:

If the value of K_c is in the range of 10^{-3} to 10^{3}, then the reaction has appreciable concentrations of both reactants and products.

Therefore, the third reaction (c)(K_c=1.8) will have an appreciable concentration of reactants and products.

Question 7.33     The value of Kc for the reaction 3O_{2}(g)\rightleftharpoons 2O_{3}(g) is 2.0 ×10-50 at 25°C. If the equilibrium concentration of O2 in air at 25°C is 1.6 ×10-2, what is the concentration of O3?

Answer:

We have,

equilibrium constant of the reaction = 2\times 10^{-50}
the concentration of dioxygen [O_2] = 1.6 \times 10^{-2}

the given reaction is-

3O_{2}(g)\rightleftharpoons 2O_{3}(g)
Then we have,
(equilibrium constant)
K_c = [O_3 (g)]^2 / [O_2 (g)]^3

\\2\times 10^{-50} = [O_3]^2/(1.6\times 10^{-2})^3\\ {[O_3]^2} = 2\times 10^{-50}\times(1.6\times 10^{-2})^3

             =8.192\times 10^{-56}

              {[O_3]}=\sqrt{8.192\times 10^{-56}} = 2.86 \times 10^{-28}

Thus the concentration of dioxygen is 2.86 \times 10^{-28}

Question 7.34(a)     The reaction,

CO(g)+3H_{2}(g)\rightleftharpoons CH_{4}(g)+H_{2}O(g)

is at equilibrium at 1300 K in a 1L flask. It also contain 0.30 mol of CO, 0.10 mol of H_2 and 0.02 mol of H_2O and an unknown amount of CH4 in the flask. Determine the concentration of CH4 in the mixture. The equilibrium constant, Kc for the reaction at the given temperature is 3.90.

Answer:

Given that,
Total volume = 1L
0.3 mol of CO, 0.10 mol of dihydrogen(H_2)and the 0.02 mol of water(H_2O)
the equilibrium constant = 3.90

Let x be the concentration of methane at equilibrium. The given reaction is-

                                        CO(g)+3H_{2}(g)\rightleftharpoons CH_{4}(g)+H_{2}O(g)
At equilibrium,                    0.3 mol/L         0.1 mol/L        x           0.02 mol/L

Therefore,

K_c = \frac{0.02\times x}{(0.3)(0.1)}=3.90
        \Rightarrow x = \frac{(3.9)(0.3)(0.1)^3}{(0.02)}
                   =5.85\times 10^{-2}

Thus the concentration of methane at equilibrium is =5.85\times 10^{-2}

Question 7.34(b)     What is meant by the conjugate acid-base pair? Find the conjugate acid/base for the following species:

  HNO_{2},CN^{-},HClO_{4},F^{-},OH^{-},CO_{3}^{-2} and S^{2-}

Answer:

A conjugate acid-base pair means that the species are differed by only one proton. for example; HCl is an acid because it donates a proton to water. So HCl-Cl^-, and H_3O^+-H_2Othese pairs are called conjugate acid-base pair.

Species

Conjugate acid-base

HNO_2

NO_2^{-}(Base)

CN^-

HCN(Acid)

HClO_4

ClO_4^-(base)

F^-

HF(acid)

OH^-

H_{2}O(acid)

CO_3^{2-}

HCO_3^{-}(acid)

S^{2-}

HS^{-}(acid)

 

Question 7.35     Which of the followings are Lewis acids?  H_{2}O, BF_{3},H^{+} and NH_{4}^{+}

Answer:

Lewis acid-
Those species which can accept the pair of electrons are called Lewis acids. For example  Boron trifluoride (BF_3), ammonium ion(NH_4^+) and the hydrogen ion(H^+). Among them water molecule is a Lewis base, it can donate pair of electrons.

Question 7.36     What will be the conjugate bases for the Brönsted acids:  HF,H_{2}SO_{4}and HCO^{-3}?

Answer:

When Brönsted acids lose their proton then they become a conjugate base of that corresponding acids.
Followings are the conjugate base of Brönsted acid-        

  • HF-F^-

  • H_2SO_4-HSO_{4}^-

  • HCO_{3}^--CO_3^{2-}

Question 7.38     Write the conjugate acids for the following Brönsted bases: NH_{2}^{-}, NH_{3}and HCOO ^{-}.

Answer:

When Brönsted base accepts a proton then they become a conjugate acid of that corresponding base.
Followings are the conjugate acid of Brönsted base-

NH_2^--NH_3
NH_3-NH_4^+

HCOO^--HCOOH

Question 7.39     The species: H_{2}O, HCO^{3-}, HSO_{4}^{-} and NH_{3} can act both as Brönsted acids and bases. For each case give the corresponding conjugate acid and base.

Answer:

When acid or base accept or lose a proton, they form conjugate acid or base of that corresponding species.

Lists of the conjugate acid and conjugate base of the given species-

Species

Conjugate acid

Conjugate base

H_2O

H_3O^+

OH^-

HCO_{3}^-

H_2CO_{3}

CO_{3}^{2-}

HSO_{4}^-

H_2SO_{4}

SO_{4}^{2-}

NH_3

NH_4^+

NH_2^-

 

Question 7.40     Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:
 (a) OH^-
 (b)    F^{-}
 (c)    H^{+} .
 (d)    BCl_{3}  

Answer:

Species which donate pair of an electron are called Lewis base and which accepts pair of electrons are called acid.

(a)  OH^-is a Lewis base since it can donate its lone pair of electrons.

(b) F^{-} is a Lewis base since it can donate a pair of electrons.

(c)  H^{+}is a Lewis acid since it can accept a pair of electrons.

(d)  BCl_{3} is a Lewis acid since it can accept a pair of electrons.

Question 7.41      The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10-3 M. what is its pH?

Answer:

We have,
the concentration of Hydrogen ion sample is 3.8\times 10^{-3} M
So, pH = -\log [H]^+
                \\= -\log (3.8\times 10^{-3})\\ =3-\log 3.8\\ =2.42

Question 7.42     The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.

Answer:

We have,
The pH of a sample of vinegar is 3.76
pH=?

Therefore,
\\pH=-\log [H^+]\\ \log[H^+] = -pH
Taking antilog on both sides we get,
[H^+] = antilog (-3.76)
 [H^+]=1.74 \times 10^{-4}

Hence the concentration of hydrogen ion [H^+]=1.74 \times 10^{-4}

Question 7.43     The ionization constant of HF, HCOOH and HCN at 298K are 6.8 × 10-4, 1.8 × 10-4 and 4.8 × 10-9 respectively. Calculate the ionization constants of the corresponding conjugate base.

Answer:

We have,
IOnization constant of hydrogen fluoride, methanoic acid and hydrogen cyanide are 6.8\times 10^{-4},\ 1.8 \times 10^{-4} and 4.8\times 10^{-9} respectively.

It is known that,
K_b = \frac{K_w}{K_a}...........................(i)

K_b of the conjugate base F^- 
=\frac{10^{-14}}{6.8 \times 10^{-4}}

=1.5 \times 10^{-11}
 

Similarly, 
By using the equation (i)
K_b of the conjugate base HCOO^- 
=\frac{10^{-14}}{1.8\times 10^{-4}}

=5.6\times 10^{-11}

Again, with the help of eq (i)
K_b of the conjugate base CN^-
=\frac{10^{-14}}{4.8\times 10^{-9}}
=2.8\times 10^{-6}

Question 7.44     The ionization constant of phenol is 1.0 × 10-10. What is the concentration of phenolate ion in 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01M in sodium phenolate?

Answer:

We have,
 The ionization constant of phenol is 1.0 \times 10^{-10}, and
the concentration of phenol is 0.05 M
degree of ionisation = ?

Ionization of phenol;
C_6H_5OH+H_2O\rightleftharpoons C_6H_5O^-+H_{3}O^+
At equilibrium, 
the concentration of various species are-
[C_6H_5OH] = 0.05-x
[C_6H_5O^-] = [H_3O^+]=x
As we see, the value of ionisation is very less. Also x will be very small. Thus we can ignore x.

\\K_a = \frac{[C_6H_5O^-][H_3O^+]}{[C_6H_5OH]}\\ 10^{-10}=\frac{x^2}{0.05}\\ x =\sqrt{10^{-10}\times 0.05}\\

x= 2.2\times 10^{-6}

Hence the concentration of phenolate ion is [C_6H_5O^-]= 2.2\times 10^{-6}

Let \alpha be the degree of dissociation of phenol in the presence of 0.01 M of phenolate ion.

                                       C_6H_5OH\rightleftharpoons C_6H_5O^-+H^+
Concentration                  (1 - \alpha) 0.05            0.05\alpha            0.05\alpha

So,
 [C_6H_5OH]= 0.05(1-\alpha) =0.05
[C_6H_5O^-]= 0.05\alpha+0.01 \approx 0.01M

[H_3O^+] = 0.05\alpha

therefore,

\\K_a =\frac{(0.01)(0.05\alpha)}{0.05}\\ 10^{-10}=0.01\alpha\\ \alpha = 10^{-8}
The degree of dissociation is 10^{-8}

Question 7.45   The first ionization constant of H2S is 9.1 × 10-8. Calculate the concentration of HS- ion in its 0.1M solution. How will this concentration be affected if the solution is 0.1M in HCl also? If the second dissociation constant of H2S is 1.2 × 10-13, calculate the concentration of S2- under both conditions.

Answer:

We have,
1st ionisation constant of hydrogen sulphide is 9.1\times 10^{-8} and the 2nd dissociation constant is 1.2\times 10^{-13}

Case 1st-(absence of hydrochloric acid)

To calculate the concentration of HS^-
Let x be the concentration of HS^-and the ionisation of hydrogen sulphide is;
H_2S\rightleftharpoons H^++HS^-
 0.1 M

At equilibrium, the concentration of various species are,
Since the dissociation constant is is very small. So, x can be neglected.
the concentration of H_2S = 1-x M
the concentration of HS^- and H^+ is x M
So, 
K_a = \frac{x^2}{0.1}=9.1\times 10^{-8}
from here x can be calculated and we get,  x = 9.54\times 10^{-5}M

Case 2nd (In presence of 0.1 M, HCl)
Suppose H_2S is dissociated is x .Then at equilibrium, 
[H_2S] = 0.1-x\simeq 0.1,\ [H^+]=0.1+x\simeq 0.1 and the [HS^-] = x M
So, 
K_a = \frac{x(0.1)}{0.1}=9.1\times 10^{-8}
Thus the concentration of [HS^-] is 9.1\times 10^{-8}

Question 7.46     The ionization constant of acetic acid is 1.74 × 10-5. Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.

Answer:

It is given,
The ionisation constant of acetic acid is 1.74\times 10^{-5} and concentration is 0.05 M

The ionisation of acetic acid is;

CH_{3}COOH\rightleftharpoons CH_3COO^-+H^+
Therefore, 
K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}= \frac{[H^+]^2}{[CH_3COOH]} 
\therefore [H^+] = \sqrt{(1.74\times10^{-5})(5\times 10^{-2})} = 9.33\times 10^{-4}=[CH_3COO^-] 

So, the pH of the solution = -\log(9.33\times 10^{-4})
                                            =4-\log(9.33)
                                            =3.03

We know that,
\alpha = \sqrt{\frac{K_a}{C}}
\alpha = \sqrt{\frac{1.74\times10^{-5}}{0.05}} =1.86\times 10^{-2}

Question 7.47     It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its pKa.

Answer:

We have,
pH of organic acid is 4.15 and its concentration is 0.01M

Suppose the organic acid be HA. The dissociation of organic acid can be written as;

HA \rightleftharpoons H^+ + A^-

pH = 4.15
\\-\log[H^+] = 4.15\\ {[H^+]} = 7.08\times 10^{-5}(By taking antilog of -4.15)

Now,
K_a = [H^+] [A^-] / [HA]

[H^+] = [A^-] = 7.08\times10^{-5}

[HA]  = 0.01

Then,

\\K_a = (7.08\times10^{-5})^2 / 0.01\\ K_a = 5.01\times 10^{-7}

Thus 
pK_a=-\log ( 5.01\times 10^{-7}) = 6.30

Question 7.48     Assuming complete dissociation, calculate the pH of the following solutions:

(a)      0.003 M HCl

(b)      0.005 M NaOH

(c)      0.002 M HBr 

(d)       0.002 M KOH

Answer:

Assuming the complete dissociation. So, \alpha =1

(a) The ionisation of hydrochloric acid is 
HCl\rightleftharpoons H^++Cl^-
Since it is fully ionised then [H^+]=[Cl^-]=0.003M
Therefore, 
pH of the solution-\log (0.003)
                                = 3-\log (3)
                                = 2.52 

(b) The ionisation of 0.005 M NaOH
  NaOH\rightleftharpoons Na^++OH^-
[Na^+]=[OH^-]=0.005M
Therefore,
pOH of the solution = 
                                   \\=-\log(0.005)\\ =3-\log5\\ =2.301
pH of the solution is equal to (14 - 2.301 =11.70) 

(c)  The ionisation of 0.002 M HBr
  HBr\rightleftharpoons H^++Br^-
[Br^-]=[H^+]=0.002M
Therefore,
pH of the solution = 
                                   \\=-\log(0.002)\\ =3-\log2\\ =2.69
pH of the solution is equal to (2.69) 

 

(d)  The ionisation of 0.002 M\ KOH
  KOH\rightleftharpoons K^++OH^-
[OH^-]=[K^+]=0.002M
Therefore,
pOH of the solution = 
                                   \\=-\log(0.002)\\ =3-\log2\\ =2.69
pH of the solution is equal to (14 - 2.69 = 11.31) 

Question 7.49(a)     Calculate the pH of the following solutions:

2 g of TlOH dissolved in water to give 2 litre of solution.

Answer:

Here, 2 g of TlOH dissolves in water to give 2 litres of solution
So, the concentration of   TlOH = 
[TlOH(aq)] = \frac{2}{2}g/L = \frac{1}{221}M     (the molar mass of  TlOH is 221)

TlOH can be dissociated as TlOH(aq)\rightarrow Tl^{+}+OH^-

OH^-(aq)= TlOH(aq)=\frac{1}{221}M

Therefore, K_w = [H^+][OH^-]            (since Kw = 10^{-14})

So, the concentration of [H^+] = 221\times 10^{-14}

Thus P^H = -\log[H^+] = -\log(221\times 10^{-14})
                                               = 11.65(approx)

Question 7.49(b)     Calculate the pH of the following solutions: 

 0.3 g of Ca(OH)_2 dissolved in water to give 500 mL of solution. 

Answer:

The calcium hydroxide ion dissociates into-
Ca(OH)_{2}\rightarrow Ca^{2+}+2OH^-
Molecular weight of Ca(OH)_{2} = 74 
the concentration of [Ca(OH)_{2}] = \frac{0.3\times 1000}{74\times500} = 0.0081 M

 \therefore [OH^-]= [Ca(OH)_2] = 0.0081 M

We know that,
[H^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{0.0162}
                                  = 61.7 \times 10^{-14}

Thus P^H = - \log [H^+]= -\log (61.7 \times 10^{-14})
                                               = 14 - 1.79  = 12.21

Question 7.49(c)     Calculate the pH of the following solutions:

0.3 g of NaOH dissolved in water to give 200 mL of solution. 

Answer:

NaOH dissociates into NaOH\rightarrow Na^+ +OH^-
So, the concentration of [NaOH]  = \frac{0.3\times 1000}{200\times 40} M = 0.0375 M

\therefore [OH^-] = [NaOH] = 0.0375 M
 

We know that ,
[H^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{0.0375} = 2.66\times 10^{-13}

Now, P^H = - \log[H^+]
                  \\=- \log(2.66\times 10^{-13})\\ =12.57

Question 7.49(d)     Calculate the pH of the following solutions:

1mL of 13.6 M HCl is diluted with water to give 1 litre of solution.

Answer:

We know that,
M1V1(before dilution) = M2V2(after dilution)

initially V1 = 1mL and M= 13.6 M
and V2 = 1L and M= ?

By putting all these values we get,

M_2 = \frac{13.6\times 10^{-3}}{1}=1.36\times 10^{-2}
\therefore [H^+]=1.36\times 10^{-2}

Thus P^H = -\log [H^+] = -\log(1.36\times 10^{-2})
                                               = 1.86 (approx)

Question 7.50     The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pKa of bromoacetic acid.

Answer:

We have,

Degree of ionization(a) = 0.132 
Concentration of bromoacetic acid (C) =  0.1 M

Thus the concentration of   H_{3}O^+ = C.a
                                                           = 0.0132 

Therefore 
p^H = -\log[H^+] = -\log(0.0132)
                                    = 1.879 

Now, we know that, 
K_a = C.a^2
So, pK_a = -\log(C.a^2)
                  \\=-\log (0.1\times (0.0132)^2)\\ =-\log (0.0017)\\ =2.76(approx)   

Question 7.51     The pH of 0.005M codeine \left ( C_{18}H_{21}NO_{3} \right ) solution is 9.95. Calculate its ionization constant and pKb.

Answer:

We have,
C = 0.005 M
P^H = 9.95 and P^{OH} = 14 - 9.95 = 4.05 

we know that P^{OH} = -\log[OH^-]
                       4.05 = -\log [OH^-]

By taking antilog on both sides we get.

concentration of [OH^-] = 8.91 \times 10^{-5}

C.a = 8.91 \times 10^{-5}
So, a = 1.782\times 10^{-2}

We know that,
K_b = C.a^2
        \\= 0.005 \times (1.782\times 10^{-2})^2\\ =0.0158\times 10^{-4}

Thus 
pK_b = -\log (K_b)
            \\= -\log (0.0158\times 10^{-4})\\ =5.80

Question  7.52     What is the pH of 0.001M aniline solution?  Calculate the degree of ionization of aniline in the solution. Also, calculate the ionization constant of the conjugate acid of aniline.(K= 4.27\times 10^{-10})

Answer:

We have,
C = 0.001 M
K_b = 4.27\times 10^{-10}
Degree of inozation of aniline (a) = ?
Ionization constant of the conjugate acid (K_a) = ?

We know that 
  K_b = C.a^2
  4.27\times 10^{-10}     =  (0.001)a^2
Thus  a={\sqrt{4270\times 10^{-10}}}
               = 65.34\times 10^{-4}

Then [Base] = C.a = (65.34\times 10^{-4})(0.001)
                               = 0.653\times 10^{-5}

Now, P^{OH} = -\log (0.65\times 10^{-5})=6.187
P^H = 14-P^{OH} 
           = 14 - 6.187
           = 7.813

It is known that,

K_a\times K_b = K_w
So, K_a = \frac{10^{-14}}{4.27\times10^{-10}}
               =2.34\times 10^{-5}   This is ionization constant.

Question 7.53(a)     Calculate the degree of ionization of 0.05M acetic acid if its pKa value is 4.74. How is the degree of dissociation affected when its solution also contains

0.01M 

Answer:

We have,
C = 0.05 M
pK_a = 4.74 = -\log(K_a)
By taking antilog on both sides we get,
(K_a) = 1.82\times 10^{-5} = C.(\alpha)^2
from here we get the value of \alpha= \sqrt{\frac{1.82\times 10^{-5}}{5\times10^{-2}}}
                                                      = 1.908\times 10^{-2}

After adding hydrochloric acid, the concentration of H^+ ions increases and due to that the equilibrium shifts towards the backward direction. It means dissociation will decrease.

(i) when 0.01 HCl is taken
                           CH_{3}COOH\rightleftharpoons CH_{3}COO^- +H^+
 Initial conc.                  0.05                     0                              0
after dissociation        0.05 - x               0.001+x                 x

As the dissociation is very small.
So we can write 0.001+x  \approx 0.001 and  0.05 - x  \approx 0.05

Now, K_a= \frac{[CH_{3}COO^-][H^+]}{[CH_{3}COOH]}
                  \\=\frac{(0.001)(x)}{(0.05)}\\ =\frac{x}{50}

So, the value of x = \frac{(1.82\times10^{-5})(0.05)}{0.01}

Now degree of dissociation  = (amount dissociated) /(amount taken)

                                             = \frac{1.82\times 10^{-3}(0.05)}{0.05}
                                             = 1.82\times 10^{-3}

Question 7.53(b)     Calculate the degree of ionization of 0.05M acetic acid if its pKa value is 4.74. How is the degree of dissociation affected when its solution also contains 

0.1M in HCl ?

Answer:

Let the x amount of acetic acid is dissociated in this case

                                CH_{3}COOH\rightleftharpoons CH_{3}COO^- +H^+

 Initial conc.                  0.05                     0                              0
after dissociation        0.05 - x               0.1+x                 x

As the dissociation is very small.
So we can write 0.1+x  \approx 0.1 and  0.05 - x  \approx 0.05

 K_a= \frac{[CH_{3}COO^-][H^+]}{[CH_{3}COOH]}
                  \\=\frac{(0.1)(x)}{(0.05)}\\ =2x

So, the value of x = \frac{(1.82\times10^{-4})(0.05)}{0.1}

Now the degree of dissociation  = (amount dissociated) /(amount is taken)

                                             = \frac{1.82\times 10^{-4}(0.05)}{0.05}
                                             = 1.82\times 10^{-4}

Question 7.54     The ionization constant of dimethylamine is 5.4 × 10-4. Calculate its degree of ionization in its 0.02M solution. What percentage of dimethylamine is ionized if the solution is also 0.1M in NaOH?

Answer:

We have,

(Degree of ionization) K_b = 5.4\times 10^{-4}
Concentration of dimethylamine = 0.02 M

\therefore \alpha = \sqrt{\frac{K_b}{C}}= \sqrt{\frac{5.4\times 10^{-4}}{0.02}}
     \alpha = 0.1643

If we add 0.1 M of sodium hydroxide. It is a strong base so, it goes complete ionization

                     NaOH\rightleftharpoons Na^++OH^-
                                                (0.1 M)      (0.1 M)

and also,

(CH_{3})_2NH+H_{2}O\rightleftharpoons (CH_{3})_2NH^+_2+OH^-
    0.02- x                                           x                       x   

[OH^-]=x+0.1\approx 0.1 (since the dissociation is very small)

Therefore, 

K_b = \frac{x(0.1)}{0.02}
x=5.4\times 10^{-4}(\frac{0.02}{0.1})
     =0.0054

Hence in the presece of 0.1 M of sodium hydroxide , 0.54% of dimethylamine get dissociated.

Question 7.55(a)     Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human muscle-fluid, 6.83 

Answer:

 We have P^H =6.83

It is known that P^H = -\log[H^+]

Therefore,
6.83= -\log[H^+]
By taking antilog on both sides we get,
[H^+]= 1.48\times 10^{-7}M 

Question 7.55(b)     Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below: 

Human stomach fluid, 1.2 

Answer:

We have P^H = 1.2

It is known that P^H = -\log[H^+]

Therefore,
1.2= -\log[H^+]
By taking antilog on both sides we get,
[H^+]= 0.063\ M 

Question 7.55(c)     Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human blood, 7.38 

Answer:

 we have P^H = 7.38

It is known that P^H = -\log[H^+]

Therefore,
7.38 = -\log[H^+]
By taking antilog on both sides we get,
[H^+]= 4.17\times 10^{-8}\ M 

Question 7.55(d)     Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human saliva, 6.4.

Answer:

 we have P^H = 6.4

It is known that P^H = -\log[H^+]

Therefore,
6.4 = -\log[H^+]
By taking antilog on both sides we get,
[H^+]= 3.98\times 10^{-7}\ M 

Question 7.56     The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each

Answer:

We already know that p^H can be calculated as- -\log[H^+] 
to calculate the concentration of [H^+] = antilog (-p^H)

Thus, the hydrogen ion concentration of followings p^H values are-

(i)  p^Hof milk = 6.8
Since, p^H=-\log[H^+]
6.8 = -\log[H^+]
\log[H^+] = -6.8

[H^+] = anitlog(-6.8)

        = 1.5\times10^{-7}M

 

(ii) p^Hof black coffee = 5.0

Since, p^H=-\log[H^+]

5.0 =-\log[H^+]

\log[H^+]= -5.0

[H^+]= anitlog(-5.0)

= 10^{-5}M

 

(iii) p^H of tomato juice = 4.2

Since, p^H=-\log[H^+]

4.2 =-\log[H^+]

\log[H^+]= -4.2

[H^+]= anitlog(-4.2)

= 6.31\times10^{-5}M

 

(iv) p^H of lemon juice = 2.2

Since, p^H=-\log[H^+]

2.2 = -\log[H^+]

\log[H^+]= -2.2

[H^+]= anitlog(-2.2)

=6.31\times10^{-3}M

(v) p^H of egg white = 7.8

Since, p^H=-\log[H^+]

7.8 = -\log[H^+]

\log[H^+] = -7.8

[H^+]= anitlog(-7.8)

= 1.58\times10^{-8}M

Question 7.57     If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions.What is its pH?

Answer:

We have 0.562 g of potassium hydroxide (KOH). On dissolving in water gives 200 mL of solution.
Therefore, concentration of [KOH(aq)] = \frac{0.561\times 1000}{200}g/L

                                                                     = 2.805 g/L

                                                                      =2.805 \times \frac{1}{56.11} M=0.05M                                                                     
KOH(aq) \rightarrow K^+(aq) + OH^-(aq)
It is a strong base. So, that it goes complete dissociation.

[OH^-] = 0.05M = [K^+]

It is known that,

\\K_w = [H^+][OH^-]\\ {[H^+]}=\frac{K_w}{[OH^-]}
             =\frac{10^{-14}}{0.05} = 2\times 10^{-13}M

Therefore,
 p^H = -\log (2\times 10^{-13})=12.69

Question 7.58     The solubility of Sr(OH)_2 at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution.

Answer:

By given abova data, we know the solubility of Sr(OH)_2 at 298 K = 19.23 g/L

So, concentration of [Sr(OH)_2]    

= 19.23 / 121.63 M (Molecular weight of Sr(OH)_2 = 121.63 u)

= 0.1581 M

Sr(OH)_2(aq) \rightarrow Sr^{2+}(aq) + 2 (OH^-)(aq)

\therefore Sr^{2+} = 0.1581M
and the concentration of [OH^-]= 2 \times 0.1581M = 0.3162 M
Now

It is known that,
K_w = [OH^-] [H^+]

[H^+] = \frac{10^{-14}}{0.3162}
             = 3.16 \times 10^{-14}

Therefore p^H = -\log(3.16 \times 10^{-14}) =13.5

Question 7.59     The ionization constant of propanoic acid is 1.32\times 10^{-5} . Calculate the degree of ionization of the acid in its 0.05M solution and also its pH. What will be its degree of ionization if the solution is 0.01M in HCl also?

Answer:

Let the degree of ionization of propanoic acid be \alpha. Then Let suppose we can write propanoic acid to be HA, 

 It is known that,

We have 
ionization constant of propanoic acid (K_a)= 1.32\times 10^{-5} and the concentration is 0.005 M

\alpha = \sqrt{\frac{K_a}{C}}   
By putting the values in above formula we get,

\alpha = \sqrt{\frac{1.32\times 10^{-5}}{0.05}} = 1.62\times 10^{-2}
[Acid] = [H_{3}O]^+ = C.\alpha = 8.15\times 10^{-4}

Therefore, p^H = -\log [H_{3}O^+]
                         \\= -\log [8.15\times 10^{-4}]
                          =3.08


If we add 0.01M hydrochloric acid then,

                                  AH+H_{2}O\rightleftharpoons H_{3}O^+ +A^-
initial con                     C                               0                 0
at equi.                     C - x \approx C                    0.01 + x            x

Now, by using the formula of K_a = \frac{(x)(0.01)}{C-x}       
                                                        =\frac{(x)(0.01)}{C}

The value of x is calculated as  ;
 \Rightarrow 1.32\times 10^{-5}\times \frac{0.01}{0.01} = 1.32 \times 10^{-5}  (Degree of ionisation)

Question 7.60     The pH of 0.1M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.

Answer:

We have,
Concentration of cyanic acid = 0.1 M
p^H=-\log [H^+] = 2.34

Therefore, the concentration of [H^+] = antilog (-2.34)
                                                            = 4.5 \times 10^{-3}

It is known that,
[H^+] =C.\alpha  = 4.5 \times 10^{-3}
 \alpha = \frac{4.5\times 10^{-3}}{0.1} = 4.5\times 10^{-2}

Then Ionization constant (K_a) =C.\alpha^2 = 
                                                   =(0.1)(4.5\times10^{-2})^2
                                                     =2.02\times 10^{-4}

Question 7.61     The ionization constant of nitrous acid is 4.5 × 10-4. Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.

Answer:

We have,
Ionization constant of nitrous acid = 4.5\times 10^{-5}
Concentration of sodium nitrite (NaNO_2) = 0.04 M
Degree of hydrolysis can be calculated as;
K_h = \frac{K_w}{K_a}=\frac{10^{-14}}{4.5\times 10^{-4}} = 0.22\times 10^{-10}
Sodium nitrite is a salt of sodium hydroxide (strong base) and the weak acid (HNO_2)
NO_2^-+H_{2}O\rightleftharpoons HNO_{2}+OH^-
Suppose x moles of salt undergoes hydrolysis, then the concentration of-
[NO_2^-]=0.04-x \approx 0.04
[HNO_2^-]=x, and 
[OH^-] = x

Therefore 
k_h = \frac{x^2}{0.04}=0.22\times 10^{-10}
from here we can calculate the value of x ;
\Rightarrow x = \sqrt{0.0088\times 10^{-10}} = 0.093 \times 10^{-5} = [OH^-]

\Rightarrow [H_3O^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{0.093\times 10^{-5}}
                                              =10.75 \times 10^{-9} M

Now p^H = -\log (10.75 \times 10^{-9} M) = 7.96

Therefore the degree of hydrolysis  

Question 7.62     A 0.02M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.

Answer:

Given,
  p^H  =  3.44

We know that

p^H=-\log [H^+]
By taking antilog on both sides we get,
[H^+] = antilog (- 3.44)

\therefore [H^+] = 3.63\times 10^{-4}

pyridinium hydrochloride completely ionised.

Then K_h =  (conc. of products)/ (conc, of reactants)
                 =\frac{ ( 3.63\times10^{-2} )^2 }{0.02}        (? Concentration is 0.02M)

\Rightarrow K_h = 6.58 \times 10^-6

Now,
K_h = K_w / K_a

\Rightarrow Ka = K_w / K_h


   = 10^{-14} / 6.58 \times 10^{-6} = 1.51 \times 10^{-9}(approx)

Question 7.63     Predict if the solutions of the following salts are neutral, acidic or basic: NaCl, KBr,NaCN,NH_{4}NO_{3},NaNO_{2}and KF

Answer:

Salts of strong acid and strong base are neutral in nature for example- 

  • NaCl (NaOH + HCl)

  • KBr(KOH+ HBr)

Salts of a strong base and weak acid are basic in nature for example-

  • NaCN(HCN+NaOH)

  • NaNO_{2}(HNO_{2}+NaOH)

  • KF (KOH+HF)

Salts of strong acid and a weak base are acidic in nature for example-

  • NH_4NO_{3} (NH_4OH+HNO_{2})

Question 7.64     The ionization constant of chloroacetic acid is 1.35 × 10-3. What will be the pH of 0.1M acid and its 0.1M sodium salt solution?

Answer:

We have,
Ionisation constant of chloroacetic acid(K_a) is 1.35\times 10^{-3}
The concentration of acid = 0.1 M
Ionisation if acid, = 
ClCH_2COOH\rightleftharpoons ClCH_2COO^-+H^+

We know that,
\Rightarrow K_a =\frac{[ClCH_2COO^-][H^+]}{[ClCH_2COOH]}....................(i)
As it completely ionised
[ClCH_2COO^-]=[H^+]

Putting the values in eq (i)
1.35\times 10^{-3} = \frac{[H^+]^2}{0.02}
[H^+] = \sqrt{1.35\times 10^{-3}\times 0.02}=1.16\times 10^{-2}
Therefore, pH of the solution = -\log (1.16\times 10^{-2})
                                                  = 2-\log(1.16)
                                                  = 1.94

Now,  

0.1 M  ClCH_2COONa (sod. chloroacetate) is basic due to hydrolysis-

ClCH_2COO^-+ \: H_2O\rightleftharpoons CH_2ClCOOH+OH^-

For a salt of strong base+strong acid

\\pH=7+\frac{pK_a+logC}{2}=7+\frac{2.87+log0.1}{2}\\pH=7.94

Question 7.65     Ionic product of water at 310 K is 2.7 × 10-14. What is the pH of neutral water at this temperature?

Answer:

We have the ionic product of water at 310 K is 2.7 \times 10^{-14}
It is known that,
ionic product K_w = [H^+][OH^-]

SInce [H^+]=[OH^-], therefore K_w = [H^+]^2

\Rightarrow K_w at 310 K is 2.7 \times 10^{-14}
\therefore K_w = 2.7\times 10^{-14} = [H^+]^2
 here we can calculate the value of [H^+] concentration.

[H^+] = \sqrt{2.7 \times 10^{-14}} = 1.64 \times 10^{-7}

Thus, p^H = -\log[H^+]
                   = -\log(1.64\times 10^{-7})
                  = 6.78

Hence the p^H of neutral water is 6.78

Question 7.66(a)     Calculate the pH of the resultant mixtures:

10 mL of 0.2M Ca(OH)2 + 25 mL of 0.1M HCl 

Answer:

Given that,
Vol. of 0.2 M Ca(OH)_2 = 10 mL
Vol. of 0.1 M HCl = 25 mL

 therefore, by using the formula,

M(OH^-)= \frac{M_1V_1(base)-M_2V_2(acid)}{V_1+V_2}
By substituting the value in these equations, we get;

\\\Rightarrow \frac{(0.2 \times 2)- (0.1\times 2)}{10+25}\\ =\frac{1.5}{25}=0.06

Now, p^{OH} = -\log[OH^-]
                     \\= -\log(0.06)\\ =1.221

since p^H+p^{OH} = 14
          p^H=14-p^{OH}
                   = 14-1.221
                   =   12.78

Question 7.66(b)     Calculate the pH of the resultant mixtures:

10 mL of 0.01M H2SO4 + 10 mL of 0.01M Ca(OH)2

Answer:

In this case, both the solutions have the same number of moles of H^+and OH^-, therefore they both can get completely neutralised. Hence the  pH = 7.0

Question 7.66(c)     Calculate the pH of the resultant mixtures:

     c) 10 mL of 0.1M H2SO4 + 10 mL of 0.1M KOH

Answer:

Given that,

Volume of 0.1 M KOH = 10 mL, and 

Volume of 0.1 M H_2SO_{4} = 10 mL

So, by using the formula of,

M(H^+)=\frac{M_1V_1(acid)-M_2V_2(base)}{V_1+V_2}
By putting the values we get,

\\\Rightarrow \frac{2(0.1\times 10)-0.1\times 10}{10+10}\\ =\frac{1}{20}\\ =5\times 10^{-2}

Hence, pH = -\log[H^+] = -\log(5\times 10^{-2})= 1.30

Question 7.67     Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants given in Table. Determine also the molarities of individual ions.

Answer:

Solubility product is the product of ionic concentrations in a saturated solution.
K_{sp}=[A^+][B^-]
(i) silver chromate (Ag_2CrO_{4})
Ionization of silver chromate

Ag_2CrO_{4}\rightleftharpoons 2Ag^++CrO_{4}^{2-}
Let "s" be the solubility of Ag_2CrO_{4}
[Ag^+] = 2s 
[CrO_{4}^{2-}] = s
According to the table K_{sp} of Ag_2CrO_{4} = 1.1\times 10^{-12}

\\\Rightarrow 1.1\times 10^{-12} = (2s)^2.s\\ =1.1\times 10^{-12} =2s^3

s = \sqrt[3]{\frac{1.1\times 10^{-12}}{4}}
     =0.65 \times 10^{-4}

(ii) Barium chromate (BaCrO_{4})
Ionization of silver chromate

BaCrO_{4}\rightleftharpoons Ba^{2+}+CrO_{4}^{2-}
Let "s" be the solubility of BaCrO_{4}
[Ba^{2+}] = s 
[CrO_{4}^{2-}] = s
According to the table