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2.41    Determine the osmotic pressure of a solution prepared by dissolving 25\; mg  of K_{2}SO_{4}  in  2\; litre  of water at 25^{\circ}C,  assuming that it is completely dissociated.

Dissociation of K2SO4 is as follows :-                                     It is clear that 3 ions are produced, so the value of i will be 3. Molecular weight of K2SO4 = 2(39) + 1(32) + 4(16) = 174u.                                                  Putting all the values :-                                                                                    

2.40    Determine the amount of  CaCl_{2} (i=2.47)  dissolved in 2.5\; litre of water such that its osmotic pressure is 0.75 \; atm at  27^{\circ}C.

We know that osmotic pressure :                                                      or                                                  We have been given the values of osmotic pressure, V, i and T. So the value of w can be found.                                                                                                                                                                  ...

2.39     The air is a mixture of a number of gases. The major components are oxygen and nitrogen with approximate proportion of 20\% is to 79\%  by volume  at 298 \; K. The water is in equilibrium with air at a pressure of 10 \; atm. At 298 \; K. if the Henry’s law constants for oxygen and nitrogen at 298 \; K are 3.30\times 107 \; mm and 6.51\times 107 \; mm respectively, calculate the composition of these gases in water

We have been given that the water is in equilibrium with air at a pressure of 10 atm or 7600 mm of Hg.  So the partial pressure of oxygen :                                                              and partial pressure of nitrogen :                                                              Now, by Henry's Law :                                       For oxygen :                           ...

2.38    Benzene and toluene form ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at 300 \; K are 50.71\; mm \; Hg and  32.06\; mm \; Hg  respectively. Calculate the mole fraction of benzene in vapour phase if 80 g of benzene is mixed with  100 \; g  toluene.

Firstly, we will find the no. of moles of the given compounds. No. of moles of benzene :                                                  and the no. of moles of toluene :                                                  . Now we will find mol fraction of both:-  Mole fraction of benzene :-                                                       and mole fraction of toluene :                     ...

2.37   Vapour pressures of pure acetone and chloroform at 328 \; K are 741.8 \; mm\; Hg and 638.8 \; mm\; Hg  respectively. Assuming that they form ideal solution over the entire range of composition, plot ptotal, pchloroform, and pacetone as a function of xacetone. The experimental data observed for different compositions of mixture is:

            

100 \times x_{acetone}                            0         11.8        23.4      36.0     50.8     58.2     64.5      72.1

p_{acetone}/mm\; Hg                       0         54.9      110.1     202.4    322.7   405.9   454.1   521.1

p_{chloroform}/mm\; Hg             632.8     548.1    469.4      359.7    257.7   193.6   161.2   120.7

p_{total}                                        632.8    603         579.5     562.1    580.4   599.5   615.5    64.18

 

Plot this data also on the same graph paper. Indicate whether it has positive deviation or negative deviation from the ideal solution.

 

it has negative deviation from the ideal solution.

2.36   100\; g of liquid A (molar\; mass \; 140\; g\; mol^{-1}) was dissolved in 1000\; g of liquid B (molar\; mass\; 180\; g\; mol^{-1}). The vapour pressure of pure liquid B was found to be 500 \; Torr.Calculate the vapour pressure of pure liquid A and its vapour pressure in the solution if the total vapour pressure the solution is  475 \; Torr.

For calculating partial vapour pressure we need to calculate mole fractions of components. So number of moles of liquid A :                                                          and  moles of liquid B :                                                         Mole fraction of A (xA)   :                                                        and mole fraction of B (xB)  :                     ...

2.35    Henry’s law constant for the molality of methane in benzene at 298\; K is 4.27\times10^{5} mm\ Hg. Calculate the solubility of methane in benzene at  298\; K under 760\; mm\; Hg.

We know that :             We are given value of P and k, so C can be found.                                       Hence solubility of methane in benzene is .

2.34    Vapour pressure of water at  293 \; K is  17.535\; mm\; Hg. Calculate the vapour pressure of water at 293 \; K  when  25 \; g  of glucose is dissolved in 450 \; g of water.

Firstly we will find number of moles of both water and glucose. Moles of glucose :                                                                           and moles of water :                                                                                 Now,                                               or                                        or                                       ...

2.33    19.5 \; g of CH_{2}FCOOH is dissolved in 500\; g  of water. The depression in the freezing point of water observed is 1.0^{\circ}C. Calculate the van’t  Hoff factor and dissociation constant of fluoroacetic acid.

Firstly we need to calculate molality in order to get vant's hoff factor. So moles of CH2FCOOH :                                                  We need to assume volume of solution to be nearly equal to 500 mL.         (as 500 g water is present) Now, we know that :             or                                            Now for dissociation constant :-                                     ...

2.32     Calculate the depression in the freezing point of water when 10 \; g of  CH_{3}CH_{2}CHCICOOH  is added to 250 \; g  of water.   

                  K_{a}=1.4\times 10^{-3}  , K_{f}=1.86\; K\; kg\; mol^{-1}                 

Firstly we will find the Vant's Hoff factor the dissociation of given compound.                  So we can write,                                              or                                                                                                                        or                                                                       Putting values of Ka and C in the last...

2.31    The depression in freezing point of water observed for the same amount of acetic acid, trichloroacetic acid and trifluoroacetic acid increases in the order given above. Explain briefly.

We know that depression in freezing point of water will depend upon the degree of ionisation. The degree of ionisation will be highest in the case of trifluoroacetic acid as it is most acidic among all three. The order of degree of ionisation on the basis if acidic nature will be:-     Trifluoroacetic acid > Trichloroacetic acid > Acetic acid. So the depression in freezing point will be reverse...

2.30    Calculate the amount of benzoic acid (C_{6}H_{5}COOH) required for preparing 250\; mL  of  0.15 \; M solution in methanol.

Molar mass of benzoic acid = 7(12) + 6(1) + 2(16) = 122u. We are given with the molarity of solution.                                                    or                                                           or                                       So mass of benzoic acid :                                                                                               Hence the required...

2.29    Nalorphene (C_{19}H_{21}NO_{3}), similar to morphine, is used to combat withdrawal symptoms in narcotic users. Dose of nalorphene generally given is 1.5 \; mg. Calculate the mass of 1.5 -10^{-3} m aqueous solution required for the above dose.

We are given with molality of the solution, so we need to find the moles of Nalorphene. Molar mass of nalorphene =  19(12) + 21(1)  + 1(14) + 3(16)  =  311u. So moles of nalorphene :                                               Molality :                                                            or                                                        or                                     ...

2.28   Calculate the mass percentage of aspirin  (C_{9}H_{8}O_{4})  in acetonitrile (CH_{3}CN) when 6.5 \; g of C_{9}H_{8}O_{4} is dissolved in 450\; g of CH_{3}CN.

Total mass of solution = Mass of aspirin + Mass of acetonitrile = 6.5 + 450 = 456.5 g. We know that :                             So,                                                  Thus the mass percentage of aspirin is

2.27   If the solubility product of CuS is 6\times10^{-16}, calculate the maximum molarity of CuS in aqueous solution.

We are given,       The dissociation equation of CuS is given by :-                                         So, the equation becomes :-    or                                             or                                                      Thus maximum molarity of solution is   .

2.26   If the density of some lake water is 1.25g\; mL^{-1} and contains 92\; g of Na^{+}\; ions per kg of water, calculate the molality of Na^{+}\; ions in the lake.

We know that, Molality :                                            So, for moles of solute we have :                                Thus,  molality :                                          Molality of Na+ ions is 4m.

2.25   Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water? 

                (vi) pentanol

Pentanol has both polar and non-polar groups so it is partially soluble in water.

2.25   Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water?

                (v) chloroform

Chloroform is a non-polar compound so it is insoluble in water.

2.25   Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water? 

  (iv) ethylene glycol

Ethylene glycol is an organic compound but is polar in nature. Also, it can form H-bonds with water molecules, thus it is highly soluble in water.

2.25   Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water?

               (iii) formic acid

Since the -OH group in formic acid (polar) can form H-bonds with water thus it is highly soluble in water.
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