Solutions-Solutions

CBSE Class–12 Chemistry

NCERT Solutions
Chapter – 02
Solutions

In-text question

1. Calculate the mass percentage of benzene () and carbon tetrachloride () if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.

Ans. Mass percentage of

= 15.28%

Mass percentage of =

=84.72%

Alternatively, Mass percentage of = (100 - 15.28) %

= 84.72%

2. Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.

Ans. Let the total mass of the solution be 100 g and the mass of benzene be 30 g.

∴Mass of carbon tetrachloride = (100 - 30) g

= 70 g

Molar mass of benzene () = (612 + 6)

= 78

∴Number of moles of

= 0.3846 mol

Molar mass of carbon tetrachloride ( ) = 112 + 4355

= 154

∴Number of moles of

= 0.4545 mol

Thus, the mole fraction of is given as:

= 0.458

3. Calculate the molarity of each of the following solutions: (a) 30 g of Co(NO3)2 .6H2O in 4.3 L of solution (b) 30 mL of 0.5 M diluted to 500 mL.

Ans. Molarity is given by:

(a) Molar mass of Co(NO3)2 = 59 + 2 (14 + 3 16) + 618

= 291

Therefore, Moles of Co(NO3)2 = 30/291 mol

= 0.103 mol

Therefore, molarity

= 0.023 M

(b) Number of moles present in 1000 mL of 0.5 M

∴Number of moles present in 30 mL of 0.5 M

= 0.015 mol

Therefore, molarity

= 0.03 M

4. Calculate the mass of urea () required in making 2.5 kg of 0.25 molal aqueous solution.

Ans. Molar mass of urea = 60

0.25 molar aqueous solution of urea means:

1000 g of water contains 0.25 mol = of urea

= 15 g of urea

That is,

(1000 + 15) g of solution contains 15 g of urea

Therefore, 2.5 kg (2500 g) of solution contains =

= 36.95 g

= 37 g of urea (approximately)

Hence, mass of urea required = 37 g

5. Calculate (a)molality (b)molarity and (c)mole fraction of KI if the density of 20% (mass/mass) aqueous KI is.

Ans. (a) Molar mass of KI = 39 + 127 = 166

20% (mass/mass) aqueous solution of KI means 20 g of KI is present in 100 g of solution.

That is,

20 g of KI is present in (100 - 20) g of water = 80 g of water

Therefore, molality of the solution =

= 1.506 m

= 1.51 m (approximately)

(b) It is given that the density of the solution =

Therefore, Volume of 100 g solution =

= 83.19 mL

Therefore, molarity of the solution =

= 1.45 M

Moles of water =

Therefore, mole fraction of KI =

= 0.0263

6. , a toxic gas with rotten egg like smell, is used for the qualitative analysis. If the solubility of in water at STP is 0.195 m, calculate Henry's law constant.

Ans. It is given that the solubility of in water at STP is 0.195 m, i.e., 0.195 mol of is dissolved in 1000 g of water.

Moles of water =

= 55.56 mol

∴Mole fraction of , x =

= 0.0035

At STP, pressure (p) = 0.987 bar

According to Henry's law:

p= KHx

= 282 bar

7. Henry's law constant for in water is 1.67 x 108 Pa at 298 K. Calculate the quantity of in 500 mL of soda water when packed under 2.5 atm pressure at 298 K.

Ans. It is given that:

KH = 1.67 x 108 Pa

= 2.5 atm = 2.5 x 1.01325 x 105

= 2.533 x 105 Pa

According to Henry's law:

PCO2 = KHx

= 0.00152

We can write,

[Since, is negligible as compared to]

In 500 mL of soda water, the volume of water = 500 mL

[Neglecting the amount of soda present]

We can write:

500 mL of water = 500 g of water

= mol of water

= 27.78 mol of water

Now,

Hence, quantity of in 500 mL of soda water =

= 1.848 g

8. The vapour pressure of pure liquids A and B are 450 and 700 mm Hg respectively, at 350 K. Find out the composition of the liquid mixture if total vapour pressure is 600 mm Hg. Also find the composition of the vapour phase.

Ans. It is given that:

= 450 mm of Hg

= 700 mm of Hg

P total= 600 mm of Hg

From Raoult's law, we have:

Therefore, total pressure,

600= (450-700)xA + 700

-100 = -250 xA

xA = 100/250 = 0.4

Therefore,

= 1 - 0.4

= 0.6

Now,

= 180 mm of Hg

= 420 mm of Hg

Now, in the vapour phase:

Mole fraction of liquid A =

= 0.30

And, mole fraction of liquid B = 1 - 0.30 = 0.70

9. Vapour pressure of pure water at 298 K is 23.8 mm Hg. 50 g of urea () is dissolved in 850 g of water. Calculate the vapour pressure of water for this solution and its relative lowering.

Ans. It is given that vapour pressure of water, of Hg

Weight of water taken,

Weight of urea taken,

Molecular weight of water,

Molecular weight of urea,

Now, we have to calculate vapour pressure of water in the solution. We take vapour pressure as p1.

Now, from Raoult's law, we have:

Hence, the vapour pressure of water in the given solution is 23.4 mm of Hg and its relative lowering is 0.0173.

10. Boiling point of water at 750 mm Hg is . How much sucrose is to be added to 500 g of water such that it boils at . Molal elevation constant for water is.

Ans. Here, elevation of boiling point = (100 + 273) – (99.63 + 273)

= 0.37 K

Mass of water,

Molar mass of sucrose ( ),

Molal elevation constant, Kb =

We know that:

= 121.67 g (approximately)

Hence, 121.67 g of sucrose is to be added.

11. Calculate the mass of ascorbic acid (Vitamin C,) to be dissolved in 75 g of acetic acid to lower its melting point by..

Ans. Mass of acetic acid,

Molar mass of ascorbic acid

Lowering of melting point,

We know that:

= 5.08 g (approx)

Hence, 5.08 g of ascorbic acid is needed to be dissolved.

12. Calculate the osmotic pressure in pascals exerted by a solution prepared by dissolving 1.0 g of polymer of molar mass 185,000 in 450 mL of water at.

Ans. It is given that:

Volume of water, V= 450 mL = 0.45 L

Temperature, T = (37 + 273) K = 310 K

Number of moles of the polymer,

We know that:

Osmotic pressure,

= 30.98 Pa

= 31 Pa (approximately)

Chapter End Questions

1. Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.

Ans. Homogeneous mixtures of two or more than two components is known as solution. The component present in large amount is known as Solvent and the one present in less amount is known as solute.

There are three types of solutions.

(i) Gaseous solution:

The solution in which the solvent is a gas is called a gaseous solution. In these solutions, the solute may be liquid, solid, or gas. For example, a mixture of oxygen and nitrogen gas is a gaseous solution.

(ii) Liquid solution:

The solution in which the solvent is a liquid is known as a liquid solution. The solute in these solutions may be gas, liquid, or solid.

For example, a solution of ethanol in water is a liquid solution.

(iii) Solid solution:

The solution in which the solvent is a solid is known as a solid solution. The solute may be gas, liquid or solid. For example, a solution of copper in gold is a solid solution.

2. Give an example of solid solution in which the solute is a gas.

Ans. In case a solid solution is formed between two substances , an interstitial solid solution (smaller size particle will occupy interstitial position in solid crystal) will be formed. For example, a solution of hydrogen in palladium is a solid solution in which the solute is a gas.

3. Define the following terms:

(i) Mole fraction

(ii) Molality

(iii) Molarity

(iv) Mass percentage.

Ans. (i) Mole fraction:

The mole fraction of a component in a mixture is defined as the ratio of the number of moles of the component to the total number of moles of all the components in the mixture.

i.e.,

Mole fraction of a component =

Mole fraction is denoted by ‘x’.

If in a binary solution, the number of moles of the solute and the solvent are nA and nB respectively, then the mole fraction of the solute in the solution is given by,

Similarly, the mole fraction of the solvent in the solution is given as:

(ii) Molality

Molality (m) is defined as the number of moles of the solute per kilogram of the solvent. It is expressed as:

Molality (m) =

(iii) Molarity

Molarity (M) is defined as the number of moles of the solute dissolved in one Litre of the solution.

It is expressed as:

Molarity (M) =

(iv) Mass percentage:

The mass percentage of a component of a solution is defined as the mass of the solute in grams present in 100 g of the solution. It is expressed as:

Mass % of a component =

4. Concentrated nitric acid used in laboratory work is 68% nitric acid by mass in aqueous solution. What should be the molarity of such a sample of the acid if the density of the solution is?

Ans. Concentrated nitric acid used in laboratory work is 68% nitric acid by mass in an aqueous solution. This means that 68 g of nitric acid is dissolved in 100 g of the solution.

Molar mass of nitric acid

Then, number of moles of

= 1.079 mol

Given,

Density of solution =

Therefore, Volume of 100 g solution =

= 66.49 mL

Molarity of solution =

= 16.23 M

5. A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is , then what will be the molarity of the solution?

Ans. 10% w/w solution of glucose in water means that 10 g of glucose in present in 100 g of the solution i.e., 10 g of glucose is present in (100 - 10) g = 90 g of water.

Molar mass of glucose

Then, number of moles of glucose =

= 0.056 mol

Molality of solution = = 0.62 m

Number of moles of water =

= 5 mol

Mole fraction of glucose

= 0.011

And, mole fraction of water

= 1 - 0.011

= 0.989

If the density of the solution is , then the volume of the 100 g solution can be given as:

= 83.33 mL

Molarity of the solution =

= 0.67 M

6. How many mL of 0.1 M HCl are required to react completely with 1 g mixture of and containing equimolar amounts of both?

Ans. Let the amount of in the mixture be x g.

Then, the amount of in the mixture is (1 - x) g.

Molar mass of

Number of moles =

Molar mass of

Number of moles of =

According to the question,

⇒ 84x = 106 - 106x

⇒ 190x = 106

⇒ x = 0.5579

Therefore, number of moles of =

= 0.0053 mol

And, number of moles of =

= 0.0053 mol

HCl reacts with and according to the following equation.

1 mol of reacts with 2 mol of HCl.

Therefore, 0.0053 mol of reacts with = 0.0106 mol of HCl.

Similarly, 1 mol of reacts with 1 mol of HCl.

Therefore, 0.0053 mol of reacts with 0.0053 mol of HCl.

Total moles of HCl required = (0.0106 + 0.0053) mol

= 0.0159 mol

In 0.1 M of HCl,

0.1 mol of HCl is preset in 1000 mL of the solution.

Therefore, 0.0159 mol of HCl is present in

= 159 mL of the solution

Hence, 159 mL of 0.1 M of HCl is required to react completely with 1 g mixture of and , containing equimolar amounts of both.

7. A solution is obtained by mixing 300 g of 25% solution and 400 g of 40% solution by mass. Calculate the mass percentage of the resulting solution.

Ans. Total amount of solute present in the mixture is given by,

= 75 + 160

= 235 g

Total amount of solution = 300 + 400 = 700 g

Therefore, mass percentage (w/w) of the solute in the resulting solution,

= 33.57%

And, mass percentage (w/w) of the solvent in the resulting solution,

= (100 - 33.57) %

= 66.43%

8. An antifreeze solution is prepared from 222.6 g of ethylene glycol () and 200 g of water. Calculate the molality of the solution. If the density of the solution is, then what shall be the molarity of the solution?

Ans. Molar mass of ethylene glycol

Number of moles of ethylene glycol

= 3.59 mol

Therefore, molality of the solution =

= 17.95 m

Total mass of the solution = (222.6 + 200) g

= 422.6 g

Given,

Density of the solution = 1.072 g mL - 1

Therefore, Volume of the solution =

= 394.22 mL

Molarity of the solution =

= 9.11 M

9. A sample of drinking water was found to be severely contaminated with chloroform () supposed to be a carcinogen. The level of contamination was 15 ppm (by mass):

(i) express this in percent by mass

(ii) determine the molality of chloroform in the water sample.

Ans. (i) 15 ppm (by mass) means 15 parts per million (106) of the solution.

Therefore, percent by mass =

(ii) Molar mass of chloroform

Now, according to the question,

15 g of chloroform is present in 106 g of the solution.

i.e., 15 g of chloroform is present in (106 - 15) per 106 g of water.

Therefore, Molality of the solution =

10. What role does the molecular interaction play in a solution of alcohol and water?

Ans. In pure alcohol and water, the molecules are held tightly by a strong hydrogen bonding. The interaction between the molecules of alcohol and water is weaker than alcohol-alcohol and water-water interactions. As a result, when alcohol and water are mixed, the intermolecular interactions become weaker and the molecules can easily escape. This increases the vapour pressure of the solution, which in turn lowers the boiling point of the resulting solution.

11. Why do gases always tend to be less soluble in liquids as the temperature is raised?

Ans. Solubility of gases in liquids decreases with an increase in temperature. This is because dissolution of gases in liquids is an exothermic process.

Therefore, when the temperature is increased, heat is supplied and the equilibrium shifts backwards ( exothermic reactions are favoured at low temp only according to Le-Chaterlie Principle )thereby decreasing the solubility of gases.

12. State Henry's law and mention some important applications?

Ans. Henry's law states that partial pressure of a gas in the vapour phase is proportional to the mole fraction of the gas in the solution. If p is the partial pressure of the gas in the vapour phase and x is the mole fraction of the gas, then Henry's law can be expressed as:

Where, is Henry's law constant

Some important applications of Henry's law are mentioned below.

(i) Bottles are sealed under high pressure to increase the solubility of in soft drinks and soda water.

(ii) Henry's law states that the solubility of gases increases with an increase in pressure. Therefore, when a scuba diver dives deep into the sea, the increased sea pressure causes the nitrogen present in air to dissolve in his blood in great amounts. As a result, when he comes back to the surface, the solubility of nitrogen again decreases and the dissolved gas is released, leading to the formation of nitrogen bubbles in the blood. This results in the blockage of capillaries and leads to a medical condition known as 'bends' or 'decompression sickness'.

Hence, the oxygen tanks used by scuba divers are filled with air and diluted with helium to avoid bends.

(iii) The concentration of oxygen is low in the blood and tissues of people living at high altitudes such as climbers. This is because at high altitudes, partial pressure of oxygen is less than that at ground level. Low-blood oxygen causes climbers to become weak and disables them from thinking clearly. These are symptoms of anoxia.

13. The partial pressure of ethane over a solution containing of ethane is 1 bar. If the solution contains of ethane, then what shall be the partial pressure of the gas?

Ans. Molar mass of ethane

Number of moles present in of ethane =

= 2.187 x 10-4

Let the number of moles of the solvent be 55.55 assuming solvent is water.

According to Henry's law,

1 bar = KH ( 2.187 x 10-4 / 55.55) [ assuming dilution condition i.e. moles of solvent >> moles of solute )

KH = 1 bar / ( 0.039 x 10-4 )

if mass of ethane =0.05g then moles of ethane = 0.05/30 mol = 0.00166 mol

so p =KH x

p = 1/ (0.039 x 10-4 ) x ( 0.00166/55.55)

= 7.66 bar

14. What is meant by positive and negative deviations from Raoult's law and how is the sign of related to positive and negative deviations from Raoult's law?

Ans. According to Raoult's law, the partial vapour pressure of each volatile component in any solution is directly proportional to its mole fraction. The solutions which obey Raoult's law over the entire range of concentration are known as ideal solutions. The solutions that do not obey Raoult's law (non-ideal solutions) have vapour pressures either higher or lower than that predicted by Raoult's law. If the vapour pressure is higher, then the solution is said to exhibit positive deviation, and if it is lower, then the solution is said to exhibit negative deviation from Raoult's law.

Vapour pressure of a two-component solution showing positive deviation from Raoult's law

Vapour pressure of a two-component solution showing negative deviation from Raoult's law

In the case of an ideal solution, the enthalpy of the mixing of the pure components for forming the solution is zero.

Δsol H= 0 because solute-solute interaction and solvent-solvent interaction = solute - solvent interaction

In the case of solutions showing positive deviations, absorption of heat takes place.

Therefore, = positive beacuse solue - solute interaction and solvent - solvent interaction > solute - solvent interaction.

In the case of solutions showing negative deviations, evolution of heat takes place.

Therefore, = Negative because solute - solute interacation and solvent solvent interaction < solute - solvent interaction.

15. An aqueous solution of 2% non-volatile solute exerts a pressure of 1.004 bar at the normal boiling point of the solvent. What is the molar mass of the solute?

Ans. Here,

Vapour pressure of the solution at normal boiling point (p1) = 1.004 bar

Vapour pressure of pure water at normal boiling point

Mass of solute, = 2 g

Mass of solvent (water), = 98 g

Molar mass of solvent (water), =

According to Raoult's law,

Hence, the molar mass of the solute is .

16. Heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components are 105.2 kPa and 46.8 kPa respectively. What will be the vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane?

Ans. Vapour pressure of heptane

Vapour pressure of octane = 46.8 kPa

We know that,

Molar mass of heptane

Therefore, Number of moles of heptane =

= 0.26 mol

Molar mass of octane

Therefore, Number of moles of octane =

= 0.31 mol

Mole fraction of heptane,

= 0.456

And, mole fraction of octane, = 1 - 0.456

= 0.544

Now, partial pressure of heptane,

= 47.97 kPa

Partial pressure of octane,

= 25.46 kPa

Hence, vapour pressure of solution,

= 47.97 + 25.46

= 73.43 kPa

17. The vapour pressure of water is 12.3 kPa at 300 K. Calculate vapour pressure of 1 molal solution of a non-volatile solute in it.

Ans. 1 molal solution means 1 mol of the solute is present in 1000 g of the solvent (water).

Molar mass of water =

Therefore, Number of moles present in 1000 g of water =

= 55.56 mol

Therefore, mole fraction of the solute in the solution is

It is given that,

Vapour pressure of water, = 12.3 kPa

Applying the relation,

⇒ 12.3 - = 0.2177

⇒ = 12.0823

= 12.08 kPa (approximately)

Hence, the vapour pressure of the solution is 12.08 kPa.

18. Calculate the mass of a non-volatile solute (molar mass 40 g) which should be dissolved in 114 g octane to reduce its vapour pressure to 80%.

Ans. Let the vapour pressure of pure octane be

Then, the vapour pressure of the octane after dissolving the non-volatile solute is

Molar mass of solute,

Mass of octane, = 114 g

Molar mass of octane,

Applying the relation,

Hence, the required mass of the solute is 8 g.

19. A solution containing 30 g of non-volatile solute exactly in 90 g of water has a vapour pressure of 2.8 kPa at 298 K. Further, 18 g of water is then added to the solution and the new vapour pressure becomes 2.9 kPa at 298 K. Calculate:

i. molar mass of the solute

ii. vapour pressure of water at 298 K.

Ans. (i) Let, the molar mass of the solute be

Now, the no. of moles of solvent (water),

And, the no. of moles of solute,

= 2.8 kPa

Applying the relation:

After the addition of 18 g of water:

Again, applying the relation:

Dividing equation (i) by (ii), we have:

87M + 435 = 84 M +504

3M = 69

M = 23u

Therefore, the molar mass of the solute is.

(ii) Putting the value of M in equation (i), we have:

Hence, the vapour pressure of water at 298 K is 3.53 kPa.

20. A 5% solution (by mass) of cane sugar in water has freezing point of 271 K. Calculate the freezing point of 5% glucose in water if freezing point of pure water is 273.15 K.

Ans. Here, = (273.15 - 271) K

= 2.15 K

Molar mass of sugar

5% solution (by mass) of cane sugar in water means 5 g of cane sugar is present in (100 - 5) g = 95 g of water.

Now, number of moles of cane sugar =

= 0.0146 mol

Therefore, molality of the solution,

Applying the relation,

Molar of glucose

5% glucose in water means 5 g of glucose is present in (100 - 5) g = 95 g of water.

Therefore, Number of moles of glucose =

= 0.0278 mol

Therefore, molality of the solution,

Applying the relation,

= 4.09 K (approximately)

Hence, the freezing point of 5% glucose solution is (273.15 - 4.09) K= 269.06 K.

21. Two elements A and B form compounds having formula and . When dissolved in 20 g of benzene, 1 g of AB2 lowers the freezing point by 2.3 K whereas 1.0 g of lowers it by 1.3 K. The molar depression constant for benzene is . Calculate atomic masses of A and B.

Ans. We know that,

Then,

Now, we have the molar masses of and as andrespectively.

Let the atomic masses of A and B be x and y respectively.

Now, we can write:

Subtracting equation (i) from (ii), we have

2y = 85.28

⇒ y = 42.64

Putting the value of y in equation (1), we have

⇒ x = 25.59

Hence, the atomic masses of A and B are 25.59 u and 42.64 u respectively.

22. At 300 K, 36 g of glucose present in a litre of its solution has a osmotic pressure of 4.98 bar. If the osmotic pressure of the solution is 1.52 bar at the same temperature, what would be its concentration?

Ans. Here,

T = 300 K

= 1.52 bar

R = 0.083 bar L

Applying the relation,

= CRT

= 0.061 mol/L

The concentration of the solution would be 0.061 M.

23. Suggest the most important type of intermolecular attractive interaction in the following pairs.

(i) n-hexane and n-octane

(ii) and

(iii) and water

(iv) methanol and acetone

(v) acetonitrile and acetone .

Ans. (i) Van der Wall forces of attraction as both are non polar.

(ii) Van der Wall forces of attraction as they are non polar.

(iii) Ion-diople interaction as NaClO4 is ionic in nature.

(iv) Dipole-dipole interaction as they are polar.

(v) Dipole-dipole interaction as they are polar.

24. Based on solute-solvent interactions, arrange the following in order of increasing solubility in n-octane and explain. Cyclohexane, KCl, ,.

Ans. n-octane is a non-polar solvent. Therefore, the solubility of a non-polar solute is more than that of a polar solute in the n-octane as like dissolves in like.

The order of increasing polarity is:

Cyclohexane < < < KCl

Therefore, the order of increasing solubility is:

KCl < < < Cyclohexane

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

(i) phenol

(ii) toluene

(iii) formic acid

(iv) ethylene glycol

(v) chloroform

(vi) pentanol.

Ans. (i) Phenol has the polar group -OH and non-polar group. Thus, phenol is partially soluble in water.

(ii) Toluene has no polar groups. Thus, toluene is insoluble in water.

(iii) Formic acid (HCOOH) has the polar group -OH and can form H-bond with water. Thus, formic acid is highly soluble in water.

(iv) Ethylene glycol has polar -OH group and can form H-bond. Thus, it is highly soluble in water.

(v) Chloroform is insoluble in water.

(vi) Pentanol has polar -OH group, but it also contains a very bulky non-polar group. Thus, pentanol is partially soluble in water.

26. If the density of some lake water is and contains 92 g of ions per kg of water, calculate the molality of ions in the lake.

Ans. Number of moles present in 92 g of ions = (92g) /( 23g/mol) = 4 mol

Therefore, molality of Na+ ions in the lake = 4 m

27. If the solubility product of CuS is, calculate the maximum molarity of CuS in aqueous solution.

Ans. Solubility product of CuS,

Let s be the solubility of CuS in.

Now,

Then, we have,

= 2.45 × 10 - 8

Hence, the maximum molarity of CuS in an aqueous solution is.

28. Calculate the mass percentage of aspirin in acetonitrile when 6.5 g of is dissolved in 450 g of

Ans. 6.5 g of is dissolved in 450 g of .

Then, total mass of the solution = (6.5 + 450) g

= 456.5 g

Therefore, mass percentage of =

= 1.424%

29. Nalorphene , 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 m aqueous solution required for the above dose.

Ans. The molar mass of nalorphene is given as:

In aqueous solution of nalorphene,

1 kg (1000 g) of water contains mol of nalorphene i.e. = 0.4665g of nalorphene

Therefore, total mass of the solution = (1000 + 0.4665) g

= 1000.4665 g

This implies that the mass of the solution containing 0.4665 g of nalorphene is 1000.4665 g.

Therefore, mass of the solution containing 1.5 mg of nalorphene is:

= 3.22 g

Hence, the mass of aqueous solution required is 3.22 g.

30. Calculate the amount of benzoic acid required for preparing 250 mL of 0.15 M solution in methanol.

Ans. 0.15 M solution of benzoic acid in methanol means,

1000 mL of solution contains 0.15 mol of benzoic acid

Therefore, 250 mL of solution contains = mol of benzoic acid

= 0.0375 mol of benzoic acid

Molar mass of benzoic acid

= 122 g

Hence, required benzoic acid =

= 4.575 g

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.

Ans.

Among H, Cl, and F, H is least electronegative while F is most electronegative. Then, F can withdraw electrons towards itself more than Cl and H. Thus, trifluoroacetic acid can easily lose ions i.e., trifluoroacetic acid ionizes to the largest extent. Now, the more ions produced, the greater is the depression of the freezing point. Hence, the depression in the freezing point increases in the order:

Acetic acid < trichloroacetic acid < trifluoroacetic acid

32. Calculate the depression in the freezing point of water when 10 g of is added to 250 g of water. .

Ans. Molar mass of

Therefore, No. of moles present in 10 g of

= 0.0816 mol

It is given that 10 g of is added to 250 g of water.

Therefore, Molality of the solution,

m= 0.3264

Let a be the degree of dissociation of

undergoes dissociation according to the following equation:

Initial conc. At equilibrium = CH3CH2CHClCOOH <--> CH3CH2CHClCOO- + H+

c(1-x) cx cx

Ka = c2x2/c(1-x)

Since x is very small with respect to 1so x can be ignored , 1 - α =1

now, Ka= cx2/1

x = (Ka / c)0.5

= 0.0655

Again, CH3CH2CHClCOOH <--> CH3CH2CHClCOO- + H+

initial 1 mol 0 0

at eqillibrium 1-x x x

i ( vant hoff factor ) = 1-x+x+x = 1+x

= 1 + 0.0655

= 1.0655

Hence, the depression in the freezing point of water is given as:

= 0.65 K

33. 19.5 g of is dissolved in 500 g of water. The depression in the freezing point of water observed is . Calculate the van't Hoff factor and dissociation constant of fluoroacetic acid.

Ans. It is given that:

We know that:

Therefore, observed molar mass of

The calculated molar mass of is:

Therefore, van't Hoff factor,

= 1.0753

Let αbe the degree of dissociation of

At equilibrium =

Total =

= 1.0753 – 1

= 0.0753

Now, the value of is given as:

Taking the volume of the solution as 500 mL, we have the concentration:

= 0.5 M

Therefore,

= 0.00307 (approximately)

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.

Ans. Vapour pressure of water, = 17.535 mm of Hg

Mass of glucose,

Mass of water,

We know that,

Molar mass of glucose

= 180 g

Molar mass of water,

Then, number of moles of glucose,

= 0.139 mol

And, number of moles of water,

= 25 mol

We know that,

Hence, the vapour pressure of water is 17.44 mm of Hg.

35. Henry's law constant for the molality of methane in benzene at 298 K is 4.27 x 10 5. Calculate the solubility of methane in benzene at 298 K under 760 mm Hg.

Ans. Here,

p = 760 mm Hg

KH = 4.27 x 105

According to Henry's law,

= (approximately)

Hence, the mole fraction of methane in benzene is .

36. 100 g of liquid A (molar mass 140 g) was dissolved in 1000 g of liquid B (molar mass 180 g ). 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 of the solution is 475 Torr.

Ans. Number of moles of liquid A,

= 0.714 mol

Number of moles of liquid B,

= 5.556 mol

Then, mole fraction of A,

= 0.114

And, mole fraction of B,

= 0.886

Vapour pressure of pure liquid B, = 500 torr

Therefore, vapour pressure of liquid B in the solution,

= 443 torr

Total vapour pressure of the solution, ptotal = 475 torr

Therefore, Vapour pressure of liquid A in the solution,

= 475 - 443

= 32 torr

= 280.7 torr

Hence, the vapour pressure of pure liquid A is 280.7 torr.

37. Vapor pressure of pure acetone and chloroform at 328 K are 741.8 mm Hg and 632.8 mm Hg respectively. Assuming that they form ideal solution over the entire range of composition, plot p total' p chloroform' and p acetone as a function of x acetone. The experimental data observed for different compositions of mixture is.

Ans. From the question, we have the following data

It can be observed from the graph that the plot for the p total of the solution curves downwards. Therefore, the solution shows negative deviation from the ideal behaviour.

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 of toluene.

Ans. Molar mass of benzene

Molar mass of toluene

Now, no. of moles present in 80 g of benzene =

= 1.026 mol

And, no. of moles present in 100 g of toluene =

=1.087 mol

Therefore, Mole fraction of benzene,

= 0.486

And, mole fraction of toluene,

= 0.514

It is given that vapour pressure of pure benzene,

And, vapour pressure of pure toluene,

Therefore, partial vapour pressure of benzene,

= 24.645 mm Hg

And, partial vapour pressure of toluene,

= 16.479 mm Hg

Hence, mole fraction of benzene in vapour phase is given by:

= 0.599

= 0.6

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 are 3.30 x 107and 6.51 x 107 respectively, calculate the composition of these gases in water.

Ans. Percentage of oxygen in air = 20 %