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4.15 (1)    The experimental data for decomposition of

$2 N_2 O_5 \rightarrow 4 NO_2 + O_2$
in gas phase at 318K are given below:

Plot $[N_2O_5]$ against t.

On increasing time, the concentration of  gradually decreasing exponentially.

4.14   The half-life for radioactive decay of $^{14} C$ is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.

Given , half-life of radioactive decay = 5730 years So,                  per year we know that, for first-order reaction,                  = 1845 years (approximately) Thus, the age of the sample is 1845 years

4.13 (3)   Calculate the half-life of a first order reaction from their rate constants given  below:
$4 years ^{-1}$

The half-life for the first-order reaction is                                                                               = 0.693/4                                                                             =  0.173 year (approximately)

4.13 (2)   Calculate the half-life of a first order reaction from their rate constants given below:
$2\: \: min ^{-1}$

the half-life for the first-order reaction is expressed as ;           =  0.693/2           = 0.35 min (approx)

4.13 (1)   Calculate the half-life of a first order reaction from their rate constants given below:
$200 s^{-1}$

We know that, half-life () for first-order reaction =                                                             =

4.12   The reaction between A and B is first order with respect to A and zero order
with respect to B. Fill in the blanks in the following table:

The given reaction is first order wrt A and zero order in wrt B. So, the rate of reaction can be expressed as;   Rate = k[A] from exp 1, k = 0.2 per min. from experiment 2nd, [A] =  from experiment 3rd,             from the experiment 4th, from here [A] = 0.1 mol/L

4.11   The following results have been obtained during the kinetic studies of the reaction:
2A + B $\rightarrow$ C + D

Determine the rate law and the rate constant for the reaction.

Let assume the rate of reaction wrt A is  and wrt B is  . So, the rate of reaction is expressed as- Rate =  According to given data,  these are the equation 1, 2, 3 and 4 respectively Now,  divide the equation(iv) by (i) we get, from here we calculate that  Again, divide equation (iii) by (ii) from here we can calculate the value of y is 2 Thus, the rate law is now,   So,         ...

4.10   In a reaction between A and B, the initial rate of reaction (r0) was measure for different initial concentrations of A and B as given below:

What is the order of the reaction with respect to A and B?

we know that  rate law () =  As per data   these are the equation 1, 2 and 3 respectively Now, divide eq.1 by equation2, we get from here we calculate that y = 0 Again, divide eq. 2 by Eq. 3, we get Since y =0 also substitute the value of y  So,   =  =  taking log both side we get,     = 1.496     = approx 1.5 Hence the order of reaction w.r.t A is 1.5 and w.r.t B is 0(zero)

4.8 In pseudo first order hydrolysis of ester in water, the following results were obtained:

(i) Calculate the average rate of reaction between the time interval 30 to 60 seconds.

The average rate of reaction between the time 30 s to 60 s is expressed as-

4.9     A reaction is first order in A and second order in B.

(iii) How is the rate affected when the concentrations of both A and B are doubled?

If the concentration of [A] and[B] is increased by 2 times, then                 Therefore, the rate of reaction will increase 8 times.

.
4.9    A reaction is first order in A and second order in B.

(ii) How is the rate affected on increasing the concentration of B three times?

If the concentration of [B] is increased by 3 times, then                 Therefore, the rate of reaction will increase 9 times.

4.9     A reaction is first order in A and second order in B.

(i)Write the differential rate equation.

the reaction is first order in A and second order in B. it means the power of A is one and power of B is 2 The differential rate equation will be-

4.7     What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?

The rate constant is nearly double when there is a 10-degree rise in temperature in a chemical reaction. effect of temperature on rate constant be represented quantitatively by Arrhenius equation,  where k is rate constant                                                                                                            A is Arrhenius factor           R is gas  constant                 ...

4.6    A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is  reduced to half ?

Let assume the concentration of reactant be x So, rate of reaction, R =  Now, if the concentration of reactant is doubled then  . So the rate of reaction would  be   Hence we can say that the rate of reaction reduced to 1/4 times.

4.6     A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is doubled

Let assume the concentration of reactant be x So, rate of reaction,   Now, if the concentration of reactant is doubled then  . So the rate of reaction would  be   Hence we can say that the rate of reaction increased by 4 times.

4.5     Mention the factors that affect the rate of a chemical reaction.

The following factors that affect the rate of reaction- the concentration of  reactants  temperature, and presence of catalyst

4.4  The decomposition of dimethyl ether leads to the formation of $CH_{4}$, $H_{2}$ and $CO$  and the reaction rate is given by $Rate=k\left [ CH_{3}OCH_{3} \right ]^{3/2}$
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
$Rate=k\left [ P_{CH_{3}OCH_{3} \right ]^{3/2}$
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

Given that  So, the unit of rate is bar/min.() And thus the unit of k = unit of rate

4.3     The decomposition of  $NH_{3}$ on platinum surface is zero order reaction. What are the rates of production of $N_{2}$ and $H_{2}$ if $k=2.5\times 10^{-4}mol^{-1}L s^{-1}$?

The decomposition of  on the platinum surface reaction  therefore,    Rate =  For zero order reaction rate = k therefore,  So    and the rate of production of dihydrogen  = 3(2.5)                                                                             = 7.5

4.2     For the reaction:
$2A+B\rightarrow A_{2}B$
the rate =$k\left [ A \right ]\left [ B \right ]^{2}$ with $k=2.0\times 10^{-6}mol^{-2}L^{2}s^{-1}$. Calculate the initial rate of the reaction when$\left [ A \right ]=0.1 mol L^{-1}\: \: ,\left [ B \right ]=0.2 mol L^{-1}$. Calculate the rate of reaction after $\left [ A \right ]$ is reduced to $0.06molL ^{-1}$.

The initial rate of reaction =   substitute the given values of [A], [B] and k, rate  =          =8 When [A] is reduced from 0.1 mol/L to 0.06 mol/L  So, conc. of A reacted = 0.1-0.06 = 0.04 mol/L and conc. of B reacted = 1/2(0.04) = 0.02mol/L conc. of B left = (0.2-0.02) = 0.18 mol/L     Now,  the rate of the reaction is (R) =                                                                  ...

4.1  From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.

$C_{2}H_{5}Cl(g\rightarrow )C_{2}H_{4}(g)+HCL(g) \: Rate=k\left [ C_{2}H_{5}Cl \right ]$

so the order of the reaction is 1 and the dimension of k =
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