Regular practice with AP Inter 2nd Year Chemistry Study Material Chapter 1 Solutions Questions and Answers helps students stay prepared for examinations.
AP Inter 2nd Year Chemistry 1st Lesson Solutions Questions and Answers
I. Multiple Choice Questions
Question 1.
Which of the following concentration term is independent of temperature? [ ]
1. Molarity
2. Molality
3. Mass-Volume percentage
4. Volume -Volume percentage
Answer:
2. Molality
Molality depends on mass (temperature independent)
Question 2.
The boiling point of an azeotropic mixture of water and ethanol is less than that of water. This mixture shows [ ]
1. negative deviation from Raoult’s law
2. positive deviation from Raoult’s law
3. no deviation from Raoult’s law
4. deviation which cannot be predicted
Answer:
2. positive deviation from Raoult’s law
Lower boiling point → mixture vaporizes more easily. This means intermolecular forces are weaker than ideal. So vapour pressure is higher than expected.
Question 3.
The van’t Hoff factor for 0.1 m Ba(NO3)2 solution is 2.74. Its degree of dissociation (α) is [ ]
1. 0.74
2. 0.92
3.0.87
4. 0.78
Answer:
3.0.87
α = \(\frac{i-1}{n-1}\) = \(\frac{2.74-1}{3-1}\) = \(\frac{1.74}{2}\) = 0.87
[Ba(NO3)2→Ba+2+2NO3 n=3]
Question 4.
The solubility of gases in liquids increases with [ ]
1. increase in pressure and increase in temperature
2. decrease in pressure and decrease in temperature
3. decrease in pressure and increase in temperature
4. increase in pressure and decrease in temperature
Answer:
4. increase in pressure and decrease in temperature
Gas solubility follows: Increase in Pressure → more gas dissolves (Henry’s law)
Increase in Temperature → gas escapes→ solubility decreases
Question 5.
Which of the following is an example of an ideal solution?
1. CS2 + CH3COCH3
2. C6H5OH + C6H5NH2
3. C6H6 + C6H5CH3
4. C2H5OH + CH3COCH3
Answer:
3. C6H6 + C6H5CH3
C6H6 + C6H5CH3 is an ideal solution.

Question 6.
The mole fraction of benzene in solution containing 30% by mass in CCl4 is [ ]
1. 0.5611
2. 0.9102
3. 0.4586
4. 0.0214
Answer:
3. 0.4586
30% by mass of benzene means 30 g of benzene is present in 100g of solution.
Mass of benzene = 30 g; Mass of CCl4= 100-30-70g;
Molar mass of benzene = 78, Molar mass of CCl4 = 154
No. of moles of benzene (n1) = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{30}{78}\) = 0.385
No. of moles of CCl4 (n2) = \(\frac{70}{154}\) = 0.455
Mole fraction of Benzene = \(\frac{\mathrm{n}_1}{\mathrm{n}_1+\mathrm{n}_2}\) = \(\frac{0.385}{0.385+0.455}\) = \(\frac{0.385}{0.84}\) = 0.458
GMM of CCl4
(1 × 12) + (4 × 35.5) = 154
GMM of C6H6
(6 × 12) + (6 × 1) = 78
Question 7.
Which of the following solutions has the highest boiling point?
1.0.1 M KNO3
2. 0.1 M Na3PO4
3. 0.1 M BaCl2
4. 0.1 M K2SO4
Answer:
2. 0.1 M Na3PO4
Formula: Elevation of boiling point ∆Tb = ikb × m;
∆Tb is directly proportional to Van’t Hoff factor (i). If i is more ∆Tb is more.
From the given options we have

Question 8.
For a dilute solution containing non-volatile solute Raoult’s law states that [ ]
1. the relative lowering of vapour pressure is equal to the mole fraction of the solute
2. the relative lowering of vapour pressure is equal to the mole fraction of the solvent
3. the lowering of vapour pressure is equal to the mole fraction of the solute
4. the lowering of vapour pressure is equal to the mole fraction of the solvent
Answer:
1. the relative lowering of vapour pressure is equal to the mole fraction of the solute
For dilute solutions with non-volatile solute: \(\frac{\mathrm{P}^{\mathrm{o}}-\mathrm{P}}{\mathrm{P}^{\mathrm{o}}}\) = χsolute.
RLVP = mole fraction of solute
Question 9.
45 g of ethylene glycol molar mass (62 g mol-1) is mixed with 600 g of water. The freezing point depression is (Kf = 1.86 K kg mol-1)
1. 5.66 K
2. 8.33 K
3. 2.25 K
4. 4.81 K
Answer:
3. 2.25 K
Given mass of ethylene glycol = 45 g.
Given molar mass of ethylene glycol = 62 g
Mass of water = 600g, Molar mass of water = 18
Freezing point constant K = 1.86 K kgmol-1
We know that ∆Tƒ = Kƒ × m, m = molality
∆Tƒ = 1.8 × \(\frac{\text { Mass of solute }}{\text { GMM of solute }}\) × \(\frac{1000}{\text { Mass of solvent (in g) }}\) = 1.8 × \(\frac{45}{62}\) × \(\frac{100}{600}\) = 2.32 K
The freezing point depression ∆Tƒ = ?
Question 10.
Which law explains the solubility of gases in liquids ?
1. Boyle’s law
2. Charles’ law
3. Henry’s law
4. Raoult’s law
Answer:
3. Henry’s law
Henry’s law explains the solubility of gases in liquids.
Question 11.
At 283 K, the osmotic pressure of 2% (w/v) solution of a substance X is 7.87 × 104 N.m-2. The molar mass of X (in g mol-1) is
1. 280
2. 660
3. 598
4. 300
Answer:
3. 598
Given T = 283K, Osmotic pressure П = 7.87 × 104 Nm-2
2% (w/v) means 2 g of solute present in 100 mL of solution,
ws = 2g, V = 100 mL = 10-4m3, Molar mass of solute (Ms)=?
Formula: Osmotic pressure П = CRT
П = \(\frac{\mathrm{w}_{\mathrm{s}} \mathrm{RT}}{\mathrm{M}_{\mathrm{s}} \mathrm{~V}}\)
⇒ Ms = \(\frac{\mathrm{w}_{\mathrm{s}} \mathrm{RT}}{\Pi \mathrm{~V}}\) = \(\frac{2 \times 8.314 \times 283}{7.87 \times 10^4 \times 10^{-4}}\) = 597.9 = 598 g
Question 12.
The vapour pressure of an aqueous solution obtained by adding 18 g of glucose to 180 g of water at 373 K is (Vapour pressure of pure water at 373 K is 760 mm Hg) [ ]
1. 752.4 mm Hg
2. 741.4 mm Hg
3. 759 mm Hg
4. 745.3 mm Hg
Answer:
1. 752.4 mm Hg
Given Po = 760 mm, we have to find Ps
Mass of glucose (ws) = 18 g, Molar mass of glucose (Ms) = 180 g.mol-1
Mass of water (wo) = 180 g, Molar mass of water (M) = 18 g.mol-1
According to Raoult’s law \(\frac{\mathrm{P}^0-\mathrm{P}^{\mathrm{s}}}{\mathrm{P}^0}\) = \(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}}\) × \(\frac{\mathrm{M}_0}{\mathrm{w}_0}\)
⇒ \(\frac{760-\mathrm{P}^{\mathrm{S}}}{760}\) = \(\frac{18}{180}\) × \(\frac{18}{180}\) ⇒ 1 – \(\frac{\mathrm{P}^{\mathrm{s}}}{760}\) = \(\frac{1}{100}\) ⇒ 1 – \(\frac{1}{100}\) = \(\frac{\mathrm{P}^{\mathrm{s}}}{760}\)
⇒ 1 – 0.01 = \(\frac{\mathrm{P}^{\mathrm{s}}}{760}\) ⇒ Ps = 0.99 × 760 = 752.4
Question 13.
The value of Henry’s law constant, KH is [ ]
1. greater for gases with higher solubility
2. constant for all gases
3. not related to the solubility of gases
4. greater for gases with lower solubility
Answer:
4. greater for gases with lower solubility
Henry’s law: Higher KH → gas is less soluble (needs more pressure).
So solubility ∝ < 1/KH. Greater for gases with lower solubility
Question 14.
The mass of solute (in g) required to be added to 100 g of water so as to observe an elevation of boiling point of 0.052 °C is
(Given: Kb (H2O) = 0.52 K kg mol-1 molar mass of solute = 100 g mol-1)
1.0.30
2. 0.05
3. 2.00
4. 1.00
Answer:
4. 1.00
Given Molar mass of solute Ms = 100,
Mass of solvent H2O = 100
ΔTb = 0.052 °C, Kb = 0.52 K kg mol-1, Mass of solute ws=?
Elevation in boiling point ΔTb = kb × m, molarity
⇒ 0.052 = 0.52 × \(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}}\) × \(\frac{1000}{\text { Mass of solvent }(\mathrm{g})}\) ⇒ 0.052 = 0.52 × \(\frac{w_s}{100}\) × \(\frac{1000}{100}\)
0.052 × 10 = 0.52 × ws ⇒ ws = 1
Question 15.
P°A and P°B are the vapour pressures of two pure liquids A and B respectively of an ideal solution. If XA is the mole fraction of liquid A, the total pressure of the solution will be
1. P°B + XA (P°A – P°B)
2. P°A + XA (P°B – P°A)
3. P°A + XA (P°A – P°B)
4. P°B + XA (P°B – P°B)
Answer:
1. P°B + XA (P°A – P°B)

II. Fill in the Blanks
Question 1.
The units of boiling point elevation constant Kb are ____
Answer:
K kg mol-1
Question 2.
Solubility of a gas in liquid ____ with increase in pressure.
Answer:
increases
Question 3.
For an ideal solution, ΔmixH is equal to ____.
Answer:
Zero

Question 4.
Desalination plants work on the basis of the phenomenon called ____.
Answer:
reverse osmosis
Question 5.
Human blood is isotonic with _____. solution (or) Saline.
Answer:
0.9% (w/v) NaCl
III. One Word Answer Questions
Question 1.
What is the term used for a solution that does not follow Raoult’s law?
Answer:
Non-ideal solution does not follow the Raoult’s law.
Question 2.
In which type of a solution, dynamic equilibrium exists between the dissolved solute and undissolved solute?
Answer:
In saturated solution dynamic equilibrium exists.
Question 3.
What is the name given to binary liquid mixtures which have same composition in liquid and vapour phase and boil at a constant temperature?
Answer:
Azeotropic mixtures have same composition in liquid and vapour phase.
Question 4.
In the expression ΔTf = Kfm, what is the name given to the constant Kf? Answer:
Kf is called Cryoscopic constant (or) Molal depression constant.
Question 5.
What is the name given to the solutions, when they have same osmotic pressure at a given temperature?
Answer:
Isotonic solutions have same osmotic pressure at a given temperature.
IV. Very Short Answer Questions
Question 1.
Define molarity.
Answer:
Molarity (M): It is the number of moles of the solute dissolved per litre of the solution.
Formula: Molarity(M) \(=\frac{\text { No.of moles of solute }}{\text { Volume of solution in Litre }}\)
Question 2.
Define molality.
Answer:
Molality(m): It is the number of moles of the solute dissolved in one kilogram (Kg) of the solvent
Formula: Molality(m) \(=\frac{\text { No.of moles of solute }}{\text { Mass of solvent in Kg }}\)
No. of moles of solute Mass of solvent in Kg
Question 3.
Define mole fraction.
Answer:
Mole Fraction(χ): It is the ratio of the number of moles of one component to the total number of moles of all the components present in the solution.
Formula: Mole fraction χ \(=\frac{\text { No. of moles of one component }}{\text { Total no. of moles of all the components }}\)
No. of moles of one component Total no. of moles of all the components
Question 4.
State Henry’s law.
Answer:
Henry’s law: The partial pressure (p) of a gas in vapour phase is directly proportional to the mole fraction (χ) of the gas in the solution.
Formula: Partial pressure of a gas Pgas = KHχgas.
Question 5.
What is Ebullioscopic constant?
Answer:
Ebullioscopic constant(Kb): It is the elevation in boiling point of a solution when one mole of non-volatile solute is added to 1kg of solvent. Formula: ΔTb = Kbm
Question 6.
What is Cryoscopic constant?
Answer:
Cryoscopic constant (Kf): It is the depression in the freezing point of a solution when one mole of non-volatile solute is dissolved in 1kg of solvent. Formula: ΔTf = Kf×m
Question 7.
Define osmotic pressure.
Answer:
Osmotic pressure(\(\Pi\)): It is the minimum pressure required to stop the flow of solvent particles through a semipermeable membrane from a pure solvent into a solute. (or)
The pressure required just to stop the Osmosis is called Osmotic pressure.
Formula: \(\Pi\) = CRT
Question 8.
What are isotonic solutions?
Answer:
Isotonic solutions: Solutions which have the same osmotic pressure at a given temperature are called isotonic solutions.
Ex: Blood is isotonic with 0.9% (w/v) NaCl.
Question 9.
Calculate the amount of benzoic acid (C6H5COOH) required for preparing 250 mL of 0.15 M solution of benzoic acid in methanol.
Answer:
Molarity(M)=0.15M, Volume (V)=250mL,
GMM (C6H5COOH) = 122, Weight of C6H5COOH (w) =?

Question 10.
What is van’t Hoff’s factor?
How is it related to ‘a’ in the case of a binary electrolyte (1:1)?
Answer:
Van’t Hoff’s factor(i): It is the ratio of the experimental value of the colligative property to the calculated value of the colligative property.
Incase of a binary electrolyte (1:1), the relation between a and i is as follows:
i = \(\frac{1+(n-1) \alpha}{1}\), Degree of dissociation, α = \(\frac{i-1}{n-1}\)
The Van’t Hoff factor i accounts for dissociation or association of solute.
V. Short Answer Questions
Question 1.
How many types of solutions are formed? Give an example for each type of solution.
Answer:
| Types of Solutions | Solute | Solvent | Common Examples |
| Gaseous Solutions | Gas Liquid Solid | Gas Gas Gas | Mixture of oxygen and nitrogen gases Chloroform mixed with nitrogen gas Camphor in nitrogen gas |
| Liquid Solutions | Gas Liquid Solid | Liquid Liquid Liquid | Oxygen dissolved in water Ethanol dissolved in water Glucose dissolved in water |
| Solid Solutions | Gas Liquid Solid | Solid Solid Solid | Solution of hydrogen in palladium Amalgam of mercury with sodium Copper dissolved in gold |
Question 2.
Define mass percentage, volume percentage and mass to volume percentage solutions.
Answer:
- Mass percentage (w/w): Mass of the component (in g) present in 100g of solution. Mass % of a component \(=\frac{\text { Mass of the component in the solution }}{\text { Total mass of the solution }}\) × 100
- Volume percentage (V/V): Volume of the component (in mL) present in 100 mL of solution.
Volume % (V/V) of a component \(=\frac{\text { Volume of the component }}{\text { Total volume of the solution }}\) × 100 - Mass by volume % (w/v): The mass of solute in (g) present in 100 mL of solution.
Mass by volume % (w/v) of solute \(=\frac{\text { Mass of the solute in the solution }}{\text { Total volume of the solution }}\) × 100
Question 3.
A solution of glucose in water is labeled as 10% w/w. What would be the molality of the solution ?
Answer:
10% w/w glucose solution means 10g of glucose is dissolved in 100g of solution.
Weight of Glucose solute (ws) = 10 g, GMM of glucose = 180,
Moles of glucose n \(=\frac{\text { weight }}{\text { GMM }}\) = \(\frac{10}{180}\), Weight of solvent (W) = 100 – 10 = 90g
Molality of the solution m = n × \(\frac{1000}{W(g)}\) = \(\frac{10}{180} \times \frac{1000}{90}\) = 0.617 m
∴ Molality of the given solution = 0.617m
GMM of C6H12O6
(6 × 12) + (12 × 1) + (6 × 16) + (16 × 2) + (1 × 1) = 122
Question 4.
A solution of sucrose in water is labeled as 20% w/w. What would be the mole fraction of each component in the solution?
Answer:
20% w/w sucrose solution means 20g of sucrose is present in 100g of solution.
Weight of sucrose solute = 20g, GMM of sucrose (C12H22O11)= 342 g mol-1.
Moles of sucrose, nA = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{20}{342}\) = 0.0585
Weight of solution = 100g, Mass of solvent = 100 – 20 = 80g, GMM of water (H2O) = 18 g mol-1.
GMM of C12H22O11
(12×12)+(22×1)+(11×16)
= 342
Moles of water, nB = \(=\frac{\text { weight }}{\mathrm{GMM}}\) = \(\frac{80}{18}\) = 4.4445
Mole fraction of sucrose (χA) \(=\frac{\mathrm{n}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{A}}+\mathrm{n}_{\mathrm{B}}}\) = \(\frac{0.0585}{0.0585+4.4445}\) = \(\frac{0.0585}{4.503}\) = 0.013
Mole fraction of sucrose (χB) = 1 – χA = 1 – 0.013 = 0.987 [∵ χA + χB = 1]
Mole fraction of water (χB) = 1 − χA = 1 – 0.013 = 0.987
Question 5.
What is meant by positive deviations from Raoult’s law and how is the sign of Amix H related to positive deviation from Raoult’s law ?
Answer:
- When the vapour pressure of a solution is higher than the predicted value by Raoult’s law, it is called positive deviation.
- In such cases, intermolecular interactions between solute and solvent particles (A and B) are weaker than those between solute-solute (A-A) and solvent-solvent (B-B).
- Hence, the molecules of (A or B) will escape more easily from the surface of solution than in their pure state. Therefore, the vapour pressure of the solution will be higher.
- Characteristics of a solution showing positive deviation
- Ptotal > PA + PB
- ΔHmix > 0 (+Ve)
- ΔVmix > 0 (+Ve)
- Ex:
- Ethyl alcohol and water
- Acetone and benzene.

Question 6.
What is meant by negative deviation from Raoult’s law and how is the sign of ΔmixH related to negative deviation from Raoult’s law?
Answer:
- When the vapour pressure of a solution is lower than the predicted value by Raoult’s law, it is called negative deviation.
- In such cases, intermolecular interactions between solute and solvent particles (A and B) are stronger than those between solute-solute (A-A) and solvent-solvent (B-B).
- It leads to decrease in vapour pressure resulting in negative deviation.
- Characteristics of a solutions showing negative deviation
- Ptotal < PA + PB;
- ΔНmix < 0, (-Ve)
- ΔVmix < 0, (-Ve)
- Ex:
- Nitric acid and water
- Hydrochloric acid and water.

Question 7.
Calculate the mass of a non-volatile solute (molar mass 40g mol-1) which should be dissolved in 114g Octane to reduce its vapour pressure to 80%.
Answer:
Vapour pressure is reduced 80% means vapour pressure of the solution reduces to 80.
Vapour pressure of solvent Po=100, Vapour pressure of solution Ps=80
Mass of solvent (octane) (wo)=114g, Molar mass of Octane (C8H18) is Mo=114 g/mol
Molar mass of solute is Ms=40 g/mol, Mass of solute is ws =?
GMM of C8H18
=96+18=122
From Raoult’s law \(\frac{\mathrm{P}^{\mathrm{o}}-\mathrm{P}^{\mathrm{S}}}{\mathrm{P}^{\mathrm{o}}}\) = \(\frac{w_s}{M_s} \times \frac{M_o}{w_o}\)
⇒ \(\frac{100-80}{100}\) = \(\frac{w_s}{40} \times \frac{114}{114}\) ⇒ \(\frac{20}{100}\) ⇒ \(\frac{w_s}{40}\) ⇒ ws = \(\frac{20 \times 40}{100}\) = 8 g

Question 8.
If the osmotic pressure of glucose solution is 1.52 bar at 300K. What would be its concentration if R=0.083 L bar mol-1 K-1 ?
Answer:
Given osmotic pressure Π = 1.52, R = 0.083 L bar mol-1 K-1, T= 300K, Concentration C = ?
Formula: П=CRT ⇒ C = \(\frac{\Pi}{\mathrm{RT}}\) = \(\frac{1.52}{0.083 \times 300}\)
= 0.061 M
Question 9.
What is relative lowering of vapour pressure? How is it useful to determine the molar mass of a solute?
Answer:
When a non-volatile solute is dissolved in a volatile solvent, the vapour pressure decreases.
LVP (Δp):This difference between the vapour pressure of pure solvent (Po) and the vapour pressure of the solution (PS). Thus, Δp = po – ps
RLVP: It is the ratio of lowering of vapour pressure (ΔP) to the vapour pressure of pure solvent (Po) Also, RVP is equal to the molefraction of the solute (χ2)

Question 10.
How is molar mass related to the depression in freezing point of a solution?
Answer:
Depression in Freezing point ΔTƒ=Kƒ×m, where m= molality of the solution
⇒ ΔTf = Kf×\(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}}\)×\(\frac{1000}{w_0(g)}\) ⇒ Ms = \(\frac{\mathrm{K}_{\mathrm{f}} \times \mathrm{w}_{\mathrm{s}} \times 1000}{\Delta \mathrm{~T}_{\mathrm{f}} \times \mathrm{w}_{\mathrm{o}}}\)
Here, Ms = molar mass of solute, Kf = molal depression constant
Ws = Mass of solute in grams, ΔTf = depression in freezing point, wo = Mass of solvent in grams
VI. Long Answer Questions
Question 1.
Calculate the depression in the freezing point of water when 10g of CH3CH2 CHClCOOH is added to 250g of water. Ka = 1.4 × 10-3, Kf = 1.86 K kgmol-1.
Answer:
We know depression in the freezing point ΔTf = iKfm
So we have to find
(i) molality (m)
(ii) Degree of dissociation (α)
(iii) Van’t Hoff factor (i)
(i) To find molality(m):

(ii) To find Degree of dissociation (α) :

(iii) To find Van’t Hoff factor (i)
Calculation of Van’t Hoff factor: ”

Question 2.
19.5g of CH2FCOOH is dissolved in 500g of water. The depression in freezing point of water observed is 1.0°C. Calculate the van’t Hoff factor and dissociation constant of fluoroacetic acid.
Answer:
(i) Calculation of Van’t Hoff factor(i):

(ii) Calculation of dissociation constant, (K1):

Question 3.
Determine the osmotic pressure of a solution prepared by dissolving 25mg of K2SO4 in two litre of water at 25°C assuming that it is completely disassociated.
Answer:
Weight of K2SO4 dissolved (Ws) = 25 mg = 0.025 g, Volume of solution = 2L, T=25+273=298K
GMM of K2SO4 (Ms)= 174, Gas constant R= 0.083
K2SO4 dissociates completely: K2SO4 → 2K+ + SO2

Question 4.
Benzene and Toluene form ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at 300K are 50.71mm of Hg and 32.06mm of Hg respectively. Calculate the mole fraction of benzene in vapour phase of 80g of benzene is mixed with 100g of toluene.
Answer:

Textual Solved Questions
Question 1.
Calculate the mole fraction of ethylene glycol (C2H6O2) in a solution containing 20% of C2H6O2 by mass.
Answer:
Assume that we have 100 g of solution.
20% of C2H6O2 means 20 g of ethylene glycol and 80 g of water.
Weight of ethylene glycol = 20g, GMM of C2H6O2 = 12 × 2 + 1 × 6 + 16 ×
Moles of C2H6O2, n1 \(=\frac{\text { weight }}{\text { GMM }}\) = \(\frac{20}{62}\) = 0.322
Weight of water H2O = 80g, GMM of H2O = 18
Moles of water H2O, n2 \(=\frac{\text { weight }}{\mathrm{GMM}}\) = \(\frac{80}{18}\) = 4.444
Mole fraction of ethylene glycol (χ1) = \(\frac{\mathrm{n}_1}{\mathrm{n}_1+\mathrm{n}_2}\) = \(\frac{0.322}{0.322+4.444}\) = \(\frac{0.322}{4.766}\) = 0.068
Mole fraction of water (χ2) = 1 – χ1 = 1 – 0.068 = 0.932
Question 2.
Calculate the molarity of a solution containing 5 g of NaOH in 450 ml solution.
Answer:
Given weight of solute (NaOH) is w = 5 g; GMM of NaOH = 40
Moles of NaOH, n = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{5}{40}\)
Volume of the solution in mL = 450 mL, Molarity=?
Molarity M = n × \(\frac{1000}{V(\mathrm{~mL})}\) = \(\frac{5}{40} \times \frac{1000}{450}\) = 0.278 mol dm -3
Question 3.
Calculate molality of 2.5 g of ethanoic acid (CH3COOH) in 75g of benzene.
Solution:
Given weight of ethanoic acid = 2.5g
GMM of ethanoic acid C2H4O2 = (12 × 2) + (1 × 4) + (16 × 2)= 60
Moles of C2H4O2, n = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{2.5}{60}\)
weight of solvent (benzene)= 75 g Molality (m)=?
Molality(m) = n × \(\frac{1000}{\text { Mass of solvent (in g) }}\) = \(\frac{2.5}{60} \times \frac{1000}{75}\) = 0.556 mol.kg-1
Question 4.
If N2 gas is bubbled through water at 293 K, how many millimoles of N2 gas would dissolve in 1 litre of water? Assume that N2 exerts a partial pressure of 0.987 bar. Given that Henry’s law constant for N2 at 293 K is 76.48 kbar.
Answer:
Weight of water 1 liter = 1000 mL, GMM of H2O =
No.of moles of water (n2) = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{1000}{18}\) = 55.5
Given that p = 0.987 bar. Kн = 76.48 k bar = 76,480 bar
From Henry’s law p = KHχ1 ⇒ χ1 = \(\frac{\mathrm{p} \text { (nitrogen) }}{\mathrm{K}_{\mathrm{H}}}\) = \(\frac{0.987}{76480}\) = 1.29 × 10-5
We have n1 <<<<55.5 ⇒ n1 + n2 = 55.5
Mole fraction of nitrogen, χ1 = \(\frac{n_1}{n_1+n_2}\) ⇒ 1.29 × 10-5 = \(\frac{\mathrm{n}_1}{55.5}\)
⇒ n1 = 1.29 × 10-5 × 55.5 = 7.16 × 10-4 = 0.716 moles
Question 5.
Vapour pressure of chloroform (CHCl3) and dichloromethane (CH2Cl2) at 298 K are 200mm Hg and 415 mm Hg respectively.
(i) Calculate the vapour pressure of the solution prepared by mixing 25.5 g of CHCl3 and 40 g of CH2Cl2 at 298 K and,
(ii) mole fractions of each component in vapour phase.
Solution:
(i) Weight of dichloromethane = 40 g,
GMM of CH2Cl2 = 12 × 1 + 1 × 2 + 35.5 × 2 = 85
Moles of CH2Cl2, n1 = \(\frac{\text { weight }}{\text { GMM }}\) = \(\frac{40}{85}\) = 0.47 mol
Weight of chloroform = 25.5 g
GMM of CHCl3 = 12 × 1 + 1 × 1 + 35.5 × 3 = 119.5
Moles of CHCl3, n2 = \(\frac{25.5}{119.5}\) = 0.213 mol
Total number of moles is n1 + n2 = 0.47 + 0.213 = 0.683 mol
Mole fraction of CH2Cl2(χ1) = \(\frac{n_1}{n_1+n_2}\) = \(\frac{0.47}{0.683}\) = 0.688
Mole fraction of CHCl3 (χ2) = 1 – χ1 = 1.00 0.688 = 0.312
Given \(\mathrm{p}_1{ }^0\) = 200mm Hg \(\mathrm{p}_2{ }^0\) = 415 mm Hg
According to Raoult’s law, Ptotal = \(\mathrm{p}_1{ }^0\) + (\(\mathrm{p}_2{ }^0\) – \(\mathrm{p}_1{ }^0\))χ1
= 200 + (415 – 200) × 0.688 = 200 + 147.9 = 347.9 mm Hg
In vapour phase p1 = χ1 × Ptotal ⇒ χ1 = P1/Ptotal
∴ p1(CH2Cl2) = 0.688 × 415 = 285.5 mm Hg; p2(CHCl2) = 0.312 × 200 = 62.4 mm Hg
(ii) Mole fraction of CH2Cl2(χ1) = 285.5 /347.9 = 0.82 [∵ χ1 = p1/total]
Mole fraction of CHCl3 (χ2) = 62.4/347.9= 0.18 [∵ χ2 = p2/total]

Question 6.
The vapour pressure of pure benzene at a certain temperature is 0.850 bar. A non- volatile, non-electrolyte solid weighing 0.5 g when added to 39.0 g of benzene (molar mass 78 g mol-1). Vapour pressure of the solution, then, is 0.845 bar. What is the molar mass of the solid substance?
Answer:
Given that po = 0.850bar, M0 = 78 g mol-1, w0 = 39g
Ps = 0.845 bar, ws = 0.5g, Ms = ?
From Raoult’s law \(\frac{\mathrm{P}^{\mathrm{O}}-\mathrm{P}^{\mathrm{S}}}{\mathrm{P}^{\mathrm{O}}}\) = \(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}}\) × \(\frac{\mathrm{M}_0}{\mathrm{w}_0}\) ⇒ Ms = \(\frac{\mathrm{P}^{\mathrm{O}}}{\mathrm{P}^{\mathrm{O}}-\mathrm{P}^{\mathrm{S}}}\) × \(\frac{w_s \times \mathbf{M}_o}{\mathbf{w}_o}\)
= \(\frac{0.850}{0.850-0.845}\) × \(\frac{0.5 \times 78}{39}\) = 170 g mol-1
∴ Ms = 170 g mol-1
Question 7.
18 g of glucose, C6H12O6, is dissolved in 1 kg of water in a saucepan. At what temperature will water boil at 1.013 bar? Kb for water is 0.52 K kg mol-1.
Answer:
Given Kb = 0.52 K kg mol-1.
Weight of glucose w = 18 g, GMM of glucose Mo = 180, Mass of solvent W0 = 1000g,
Moles of glucose n \(=\frac{\text { weight }}{\mathrm{GMM}}\) = \(\frac{18}{180}\)
ΔTb = Kb × m = Kb × n × \(\frac{1000}{\mathrm{~W}_0(\mathrm{~g})}\) = 0.52 × \(\frac{18}{180}\) × \(\frac{1000}{1000}\) = 0.052
Water boils at 373.15 K at 1.013 bar pressure,
∴ the boiling point of solution is 373.15 + 0.052 = 373.202 K.
Question 8.
The boiling point of benzene is 353.23 K. When 1.80 g of a non-volatile solute was dissolved in 90 g of benzene, the boiling point is raised to 354.11 K. Calculate the molar mass of the solute. Kb for benzene is 2.53 K kg mol-1.
Answer:
Given boiling point of the solution (Tb) = 354.11k, boiling point of pure solvent (To) = 353.23K
Weight of solute (w) = 1.80 g, Weight of solvent (w)=90 g, GMM of solute Ms=?
The rise in the boiling point ΔTb = Tb – T0 = 354.11 K – 353.23 K = 0.88 K
Elevation in boiling point ΔTb = Kbm, m = molality
ΔTb = Kb × \(\frac{\mathrm{W}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}}\) × \(\frac{1000}{w_{\mathrm{o}}(\mathrm{~g})}\) ⇒ 0.88 = 2.53 × \(\frac{1.8}{\mathrm{M}_{\mathrm{s}}}\) × \(\frac{1000}{90}\)
⇒ Ms = \(\frac{2.53 \times 1.8 \times 1000}{0.88 \times 90}\) = 58g mol-1
Question 9.
45g of ethylene glycol (C2H6O2) is mixed with 600g of water. Calculate (a) the freezing point depression and
(b) the freezing point of the solution.
Answer:
Given weight of ethylene glycol = 45g, weight of solvent (H2O) = 600g
GMM of ethylene glycol (C2H6O2) = 62, Kf = 1.86 K kgmol-1 (for H2O)
(a) Depression in Freezing point ΔTf = Kfm
ΔTf = Kf\(\left(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}} \times \frac{1000}{\mathrm{~W}_0(\mathrm{~g})}\right)\) = 1.86 × \(\frac{45}{62}\) × \(\frac{1000}{600}\) = 2.2K
(b) We know ΔTf = T0 – Tf·
∴ Freezing point of aqueous solution Tf – T0 – ΔTf = 273.15 K -2.2 K= 270.95 K
Question 10.
1.00 g of a non-electrolyte solute dissolved in 50 g of benzene lowered the freezing point of benzene by 0.40 K. The freezing point depression constant of benzene is 5.12 K kg mol-1. Find the molar mass of the solute.
Answer:
Given Kf = 5.12 K kg mol-1, ΔTf = 0.40 K, Weight of solute (ws) = 1.00 g
Weight of solvent (w) = 50 g, GMM of solute (Ms)=?
Depression in Freezing point ΔTf = Kfm, m=molality
ΔTf = Kf\(\left(\frac{\mathrm{w}_{\mathrm{s}}}{\mathrm{M}_{\mathrm{s}}} \times \frac{1000}{\mathrm{~W}_0(\mathrm{~g})}\right)\) ⇒ Ms = \(\frac{\mathrm{K}_{\mathrm{f}} \times \mathrm{w}_{\mathrm{s}} \times 1000}{\Delta \mathrm{~T}_{\mathrm{f}} \times \mathrm{w}_0}\) = \(\frac{5.12 \times 1.00 \times 1000}{0.40 \times 50}\) = 256 g mol-1
Thus, GMM of the solute = 256 g mol-1
Question 11.
200 cm3 of an aqueous solution of a protein contains 1.26 g of the protein. The osmotic pressure of such a solution at 300 K is found to be 2.57 × 10-3 bar. Calculate the molar mass of the protein.
Answer:
Given data: П = 2.57 × 10-3 bar, Weight of protein W= 1.26g.
V = 200 cm3 = 0.200 litre, T = 300 K, R= 0.083 L bar mol-1 K-1,
C = molality, Molar mass of protein M=?
П = CRT = \(\left(\frac{\text { mass }}{\text { molar mass }} \times \frac{1000}{V(\mathrm{~mL})}\right)\)RT ⇒ 2.57 × 10-3 = \(\frac{1.26}{\text { molar mass }}\) × \(\frac{1000}{200}\) × 0.083 × 300
Molar mass = \(\frac{1.26 \times 5 \times 0.083 \times 30}{2.57 \times 10^{-3}}\) = 61.022 g.mol-1
Question 12.
2 g of benzoic acid (C6H5COOH) dissolved in 25 g of benzene shows a depression in freezing point equal to 1.62 K. Molal depression constant for benzene is 4.9K kg mol. What is the percentage association of acid if it forms dimer in solution?
Answer:
Given data: Weight of solute ws = 2 g; GMM of solute(C6H5COOH) = 122,
moles of solute n \(=\frac{\text { weight }}{\mathrm{GMM}}\) = \(\frac{2}{122}\) = 0.01639 mol
Weight of solvent W = 25 g = 0.025kg
molality, m = \(\frac{\mathrm{n}}{\mathrm{~W}(\mathrm{Kg})}\) = \(\frac{0.01639}{0.025}\) = 0.6556 mol kg-1
Given Kf = 4.9 K kg mol-1; ΔTf = 1.62 K
Depression in freezing point ΔTf = iKfm ⇒ i = \(\frac{\Delta \mathrm{T}_{\mathrm{f}}}{\mathrm{~K}_{\mathrm{f}} \cdot \mathrm{~m}}\) = \(\frac{1.62}{4.9 \times 0.6556}\) = \(\frac{1.62}{3.212}\) = 0.504
Now consider the following equilibrium for the benzoic acid:

If x is a degree of association, 1-α moles of benzoic acid are left undissociated and the corresponding α/2 are associated moles of benzoic acid at equilibrium.
∴ 1 – \(\frac{\alpha}{2}\) = i ⇒ 1 – \(\frac{\alpha}{2}\) = 0.504 ⇒ \(\frac{\alpha}{2}\) = 0.4958 ⇒ α = 0.9916
Percentage of association of acid if it forms dimer = α × 100 = 0.9916 × 100 = 99.16%
∴ degree of association of benzoic acid in benzene is 99.2%.
Question 13.
0.6 mL of acetic acid (CH3COOH), having density 1.06 g mL-1, is dissolved in 1 litre of water. The depression in freezing point observed for this strength of acid was 0.0205°C. Calculate the van’t Hoff factor and the dissociation constant of acid.
Answer:
Given data: density d = 1.06 g mL-1, V = 0.6 mL
Mass = V × d = 0.6 × 1.06 = 0.6408, Kf = 1.86 K kg mol-1
GMM of CH3COOH
(2 × 12) + (4 × 1) + (2 × 16)
= 24 + 4 + 32 = 60
No.of moles, n \(=\frac{\text { mass }}{\text { molar mass }}\) = \(\frac{0.6408}{60}\)
Molality(m) = n × \(\frac{1000}{\mathrm{~W}(\mathrm{~g})}\) = \(\frac{0.6408}{60}\) × \(\frac{1000}{1000}\) = 0.0106 mol kg-1
Depression in freezing point ΔTf = Kf × m = 1.86 K × 0.0106 = 0.0197 K
Van’t Hoff Factor, i \(=\frac{\text { Observed freezing point }}{\text { Calculated freezing point }}\) = \(\frac{0.0205 \mathrm{~K}}{0.0197 \mathrm{~K}}\) = 1.041

Thus, total moles of particles at equilibrium: n (1 – α + α + α) = n(1 + α)
∴ i = \(\frac{\mathrm{n}(1+\alpha)}{\mathrm{n}}\) = 1 + α
⇒ i = 1 + α ⇒ α = i – 1 = 1.041 – 1 = 0.041(Degree of dissociation)
For [CH3COOH]= n(1 – α) = 0.0106(1 – 0.041)
For [CH3COO ̄]̄]= nα = 0.0106 × 0.041,[H+] = nα = 0.0106 × 0.041
Ka = \(\frac{\left[\mathrm{CH}_3 \mathrm{COO}^{-}\right]\left[\mathrm{H}^{+}\right]}{\left[\mathrm{CH}_3 \mathrm{COOH}\right]}\) = \(\frac{0.0106 \times 0.041 \times 0.0106 \times 0.041}{0.0106(1-0.041)}\)
= 1.86 × 10-5
Objective Questions
Question 1.
On dissolving sugar in water at room temperature solution feels cool to touch. Under which of the following cases dissolution of sugar will be most rapid?
1) Sugar crystals in cold water.
2) Sugar crystals in hot water.
3) Powdered sugar in cold water.
4) Powdered sugar in hot water.
Answer:
4) Powdered sugar in hot water.
Question 2.
A beaker contains a solution of substance ‘A’. Precipitation of substance ‘A’ takes place when small amount of ‘A’ is added to the solution. The solution is _____
1) saturated
2) supersaturated
3) unsaturated
4) concentrated
Answer:
2) supersaturated
Question 3.
Maximum amount of,a solid solute that can be dissolved ¡n a specified amount of a given liquid solvent does not depend upon ___
1) Temperature
2) Nature of solute
3) Pressure
4) Nature of solvent
Answer:
3) Pressure
Question 4.
Concentrated aqueous sulphuric acid is 98% H2SO4 by mass and has a density of 1.80 g mL-1. Volume of add acid required to make one litre of MH2SO4 solution is
1) 11.10 mL
2) 16.65 mL
3) 22.20 mL
4)5.55 mL
Answer:
4)5.55 mL
Question 5.
At equilibrium, the rate of dissolution of a solid solute in a volatile liquid solvent ____
Is _______
1) less than the rate of crystallisation
2) greater than the rate of crystallisation
3) equal to therate of crystallisation
4) zero
Answer:
3) equal to therate of crystallisation
Question 6.
4L of 0.02 M aqueous solution of NaCH was diluted by adding one litre of water. The molality of the resultant solution is
1) 0.004
2) 0.008
3) 0.012
4) 0.016
Answer:
4) 0.016
Question 7.
Which of the following is dependent on temperature?
1) Molarity
2) Mole fraction
3) Weight percentage
4) Molality
Answer:
1) Molarity
Question 8.
Which of the following units is useful in relating concentration of solution with its vapour pressure?
1) molefraction
2) partspermillion
3) mass percentage
4) molality
Answer:
1) molefraction
Question 9.
Colligative properties depend on ____
1) the nature of the solute particles dissolved in solution.
2) the number of solute particles in solution.
3) the physical properties of the solute particles dissolved in solution.
4) the nature of solvent particles.
Answer:
2) the number of solute particles in solution.

Question 10.
At a given temperature, osmotic pressure of a concentrated solution of a substance
1) is higher than that at a dilute solution.
2) is lower than that of a dilute solution.
3) is same as that of a dilute solution.
4) cannot be compared with osmotic pressure of dilute solution.
Answer:
1) is higher than that at a dilute solution.
Question 11.
Value of Henry’s constant K ____
1) increases with increase in temperature.
2) decreases wìth increase in temperature.
3) remains constant.
4) first increases then decreases
Answer:
1) increases with increase in temperature.
Question 12.
The value of Henry’s constant KH is
1) greater for gases with higher solubility.
2) greater for gases with lower solubility.
3) constant for all gases.
4) not related to the solubility of gases.
Answer:
2) greater for gases with lower solubility.
Question 13.
A solution containing components A and B follows Raoult’s law, when
1) A-B attraction force is greater than A-A and B-B
2) A-B attraction force is less than A-A and B-B
3) A-B attraction force remains same as A-A and B-B
4) Volume of solution is different from sum of volumes of solute and solvent.
Answer:
3) A-B attraction force remains same as A-A and B-B
Question 14.
For an ideal solution, the correct option is
1) Δmix G=0 at constant T and P
2) ΔmixS=0 at constant T and P
3) ΔmixV#0 at constant T and P
4) ΔmixH=0 at constant T and P
Answer:
4) ΔmixH=0 at constant T and P
Question 15.
An ideal solution is formed when its components
1) have no volume change on mixing
2) have no enthalpy change on mixing
3) have both the above characteristics
4) have high solubility
Answer:
3) have both the above characteristics
Question 16.
A solution of acetone in ethanol
1) shows a negative deviation from Raoult’s law
2) shows a positive deviation from Raoult’s law
3) behaves like a near ideal solution
4) obeys Raoult’s law
Answer:
2) shows a positive deviation from Raoult’s law
Question 17.
Which of the following aqueous solutions should have the highest boiling point?
1) 1.0 M NaOH
2) 1.0 M Na2SO4
3) 1.0 M NH4NO3
4) 1.0 M KNO3
Answer:
2) 1.0 M Na2SO4
Question 18.
Pure water can he obtained from sea water by
1) centrifugation
2) plasmolysis
3) reverse osmosis
4) sedimentation
Answer:
3) reverse osmosis
Question 19.
The unit of ebulioscopic constant is
1) K kg mol-1 or K (molality)-1
2) mol kg K-1 or K-1(molality)
3) kg mol-1 K-1 or K-1(molality)-1
4) K mol kg-1 or K (molality)
Answer:
1) K kg mol-1 or K (molality)-1
Question 20.
In comparison to a 0.01 M solution of glucose, the depression in freezing point of a 0.01 M MgCl2 solution is
1) the same
2) about twice
3) about three times
4) about six times
Answer:
3) about three times
Question 21.
Blood cells retain their normal shape in solutions which are
1) hypotonic to blood
2) isotonic to blood
3) hypertonic to blood
4) equinormal to blood
Answer:
2) isotonic to blood
Question 22.
An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because ____
1) it gains water due to osmosis.
2) it loses water due to reverse osmosis.
3) it gains water due to reverse osmosis.
4) it loses water due to osmosis.
Answer:
4) it loses water due to osmosis.
Question 23.
Of the following 0.10 m aqueous solutions, which one will exhibit the largest freezing point depression?
1) KCl
2) C6H12O6
3) Al2(SO4)3
4) K2SO4
Answer:
3) Al2(SO4)3
Question 24.
In water saturated air, the mole fraction of water vapour is 0.02. If the total pressure of the saturated air is 1.2 atm, the partial pressure of dry air is
1) 1.18 atm
2) 1.76 atm
3) 1.176 atm
4) 0.98 atm
Answer:
3) 1.176 atm
Question 25.
The values of Van’t Hoff factors for KCl, NaCl and K2SO4, respectively, are ____ water by
1) 2, 2 and 2
2) 2, 2 and 3
3) 1, 1 and 2
4) 1, 1 and 1
Answer:
2) 2, 2 and 3