Van't Hoff Factor Solution - Daily Practice Problems 4

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Some important Facts and Definitions
1. Abnormal Molecular Mass. When the molecular mass of a substance determined by studying any of the colligative
properties comes out to be different than the theoretically expected value.
2. vant’t Hoff factor is defined as the ratio of the experimental value of the colligative property to the calculated value
of the colligative property,
Experimental value of the colligative property Observed value of the colligative property
i =
Calculated value of the colligative property Normal value of the same property
when the solution behaves ideally
=
()() C
O
Normal calculated molecular mass M
i= =
Abnormal Observed molecular mass M
3. Calculation of Degree of Dissociation or Association
(a) Degree of dissociation is defined as the fraction of the total substance that undergoes dissociation, i.e.,
Degree of dissociation (a) =
Numberof molesafterdissociation
Totalnumberof molestaken
() - a
- c o
o
M M
=
M n 1
(b) Degree of association is defined as the fraction of the total substance which exists in the form of associated
molecules, i.e.,
Degree of association (a) =
Number of moles associated
Total number of moles taken
() o c
o
M M n
=
M n 1
- a
- x
4. van’t Hoff factor, i > 1, if there is dissociation of the solute in the solution and i < 1 if there is association of the solute
in the solution.
5. For 100% dissociation of a solute, van’t Hoff factor, i = number of ions produced from one molecule of the solute.
Some Subjective Questions & their explanations
1. Equimolal solutions of NaCl and BaCl
2
 are prepared in water. Freezing point of NaCl is
found to be —2
0
C. What freezing point do you expect for BaCl
2
 solution ?
— i for NaCl = 2, i for BaCl
2
 = 3.
Hence,
()() f
NaCl
f
T
2
T 3
?
=
?
2
BaCl
 or() f
3
T
2
? =
2
0
BaCl
x2=3
 so that T
f
 for BaCl
2
 = —3
0
C
SOLUTIONS
(van’t Hoff Factor) DAILY  PRACTICE  PROBLEMS - 4
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 DPP : 04 / Solutions
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st
 floor,Sector -15, Panchkula
9217610408,8699438881,8699438882
Page No.1
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G od has never given dreams
Some important Facts and Definitions
1. Abnormal Molecular Mass. When the molecular mass of a substance determined by studying any of the colligative
properties comes out to be different than the theoretically expected value.
2. vant’t Hoff factor is defined as the ratio of the experimental value of the colligative property to the calculated value
of the colligative property,
Experimental value of the colligative property Observed value of the colligative property
i =
Calculated value of the colligative property Normal value of the same property
when the solution behaves ideally
=
()() C
O
Normal calculated molecular mass M
i= =
Abnormal Observed molecular mass M
3. Calculation of Degree of Dissociation or Association
(a) Degree of dissociation is defined as the fraction of the total substance that undergoes dissociation, i.e.,
Degree of dissociation (a) =
Numberof molesafterdissociation
Totalnumberof molestaken
() - a
- c o
o
M M
=
M n 1
(b) Degree of association is defined as the fraction of the total substance which exists in the form of associated
molecules, i.e.,
Degree of association (a) =
Number of moles associated
Total number of moles taken
() o c
o
M M n
=
M n 1
- a
- x
4. van’t Hoff factor, i > 1, if there is dissociation of the solute in the solution and i < 1 if there is association of the solute
in the solution.
5. For 100% dissociation of a solute, van’t Hoff factor, i = number of ions produced from one molecule of the solute.
Some Subjective Questions & their explanations
1. Equimolal solutions of NaCl and BaCl
2
 are prepared in water. Freezing point of NaCl is
found to be —2
0
C. What freezing point do you expect for BaCl
2
 solution ?
— i for NaCl = 2, i for BaCl
2
 = 3.
Hence,
()() f
NaCl
f
T
2
T 3
?
=
?
2
BaCl
 or() f
3
T
2
? =
2
0
BaCl
x2=3
 so that T
f
 for BaCl
2
 = —3
0
C
SOLUTIONS
(van’t Hoff Factor) DAILY  PRACTICE  PROBLEMS - 4
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2. Why is freezing point depression of 0.1 M sodium chloride solution nearly twice that of
0.1 M glucose solution ?
— NaCl, being an electrolytes, dissociates almost completely to give Na
+
 and Cl
—
 ions whereas glucose, being
non-electrolyte, does not dissociate. Hence the number of particles in 0.1 M NaCl solution is nearly double than
in 0.1 M glucose solution. Freezing point depression, being a colligative property, is therefore, nearly twice for NaCl
solution than for glucose solution of same molarity.
3. Explain why equimolar solutions of sodium chloride and sodium sulphate are not isotonic?
— NaCl dissociates to give 2 ions (Na
+
 and Cl
—
). Na
2
SO
4
 dissociates to give 3 ions (2 Na
+
 and ). Thus, equimolar
solutions of NaCl and Na
2
SO
4
 have different concentrations of ions in the solution. As osmotic pressure depends
upon concentration of particles in the solution, they have different osmotic pressures.
Objective Questions
1. The molal elevation constant of water is 0.51. The boiling point of 0.1 molal aqueous NaCl solution is nearly
(a) 100.05
0
C(b) 100.1
0
C(c) 100.2
0
C(d) 101.0
0
C
2. The ratio of elevation in boiling point of aqueous solution of sodium chloride to that of an aqueous
solution of glucose of same molalities is approximately
(a) 1(b) 2(c) 0.5(d) 2.5
3. Benzoic acid dissolved in benzene will show a molecular mass of
(a) 122(b) 61(c) 244(d) 366
4. If the observed and normal osmotic pressures of a KCl solution are 5.85 and 3.20 atm, the degree of dissociation
of KCl is
(a) 1(b) 0.082(c) 0.82(d) 0.28
5. Acetic acid exists in benzene solution in dimeric form. In an  actual experiment the Van’t Hoff’s factor  was found to
be 0.52. The degree of association of acetic acid is
(a) 0.48(b) 0.88(c) 0.96(d) 0.52
6. The van’t Hoff factor of a 0.005 M aqueous solution of KCl is 1.95. The degree of ionisation of KCl is
(a) 0.95(b) 0.97(c) 0.94(d) 0.96
7. Among the aqueous solutions given below which are isotonic at same temperature.
A (0.1 M urea); B (0.1 M NaCl); C (0.1 M Glucose); D (0.0541 M KCl, 85% diss); E (0.05 M BaCl
2
);
(a) A, E(b) A, B, D(c) A, C, D(d) A, C only
8. If the observed and normal osmotic pressures of 1% NaCl solution are 5.7 and 3.0 atm, the degree of dissociation
of NaCl is
(a) 0.9(b) 1.0(c) 0.57(d) 0.3
9. Which solution would exhibit abnormal osmotic pressure ?
(a) Aqueous solution of urea(b) Aqueous solution of common salt
(c) Aqueous solution of glucose(d) Aqueous solution of sucrose
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G od has never given dreams
Some important Facts and Definitions
1. Abnormal Molecular Mass. When the molecular mass of a substance determined by studying any of the colligative
properties comes out to be different than the theoretically expected value.
2. vant’t Hoff factor is defined as the ratio of the experimental value of the colligative property to the calculated value
of the colligative property,
Experimental value of the colligative property Observed value of the colligative property
i =
Calculated value of the colligative property Normal value of the same property
when the solution behaves ideally
=
()() C
O
Normal calculated molecular mass M
i= =
Abnormal Observed molecular mass M
3. Calculation of Degree of Dissociation or Association
(a) Degree of dissociation is defined as the fraction of the total substance that undergoes dissociation, i.e.,
Degree of dissociation (a) =
Numberof molesafterdissociation
Totalnumberof molestaken
() - a
- c o
o
M M
=
M n 1
(b) Degree of association is defined as the fraction of the total substance which exists in the form of associated
molecules, i.e.,
Degree of association (a) =
Number of moles associated
Total number of moles taken
() o c
o
M M n
=
M n 1
- a
- x
4. van’t Hoff factor, i > 1, if there is dissociation of the solute in the solution and i < 1 if there is association of the solute
in the solution.
5. For 100% dissociation of a solute, van’t Hoff factor, i = number of ions produced from one molecule of the solute.
Some Subjective Questions & their explanations
1. Equimolal solutions of NaCl and BaCl
2
 are prepared in water. Freezing point of NaCl is
found to be —2
0
C. What freezing point do you expect for BaCl
2
 solution ?
— i for NaCl = 2, i for BaCl
2
 = 3.
Hence,
()() f
NaCl
f
T
2
T 3
?
=
?
2
BaCl
 or() f
3
T
2
? =
2
0
BaCl
x2=3
 so that T
f
 for BaCl
2
 = —3
0
C
SOLUTIONS
(van’t Hoff Factor) DAILY  PRACTICE  PROBLEMS - 4
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2. Why is freezing point depression of 0.1 M sodium chloride solution nearly twice that of
0.1 M glucose solution ?
— NaCl, being an electrolytes, dissociates almost completely to give Na
+
 and Cl
—
 ions whereas glucose, being
non-electrolyte, does not dissociate. Hence the number of particles in 0.1 M NaCl solution is nearly double than
in 0.1 M glucose solution. Freezing point depression, being a colligative property, is therefore, nearly twice for NaCl
solution than for glucose solution of same molarity.
3. Explain why equimolar solutions of sodium chloride and sodium sulphate are not isotonic?
— NaCl dissociates to give 2 ions (Na
+
 and Cl
—
). Na
2
SO
4
 dissociates to give 3 ions (2 Na
+
 and ). Thus, equimolar
solutions of NaCl and Na
2
SO
4
 have different concentrations of ions in the solution. As osmotic pressure depends
upon concentration of particles in the solution, they have different osmotic pressures.
Objective Questions
1. The molal elevation constant of water is 0.51. The boiling point of 0.1 molal aqueous NaCl solution is nearly
(a) 100.05
0
C(b) 100.1
0
C(c) 100.2
0
C(d) 101.0
0
C
2. The ratio of elevation in boiling point of aqueous solution of sodium chloride to that of an aqueous
solution of glucose of same molalities is approximately
(a) 1(b) 2(c) 0.5(d) 2.5
3. Benzoic acid dissolved in benzene will show a molecular mass of
(a) 122(b) 61(c) 244(d) 366
4. If the observed and normal osmotic pressures of a KCl solution are 5.85 and 3.20 atm, the degree of dissociation
of KCl is
(a) 1(b) 0.082(c) 0.82(d) 0.28
5. Acetic acid exists in benzene solution in dimeric form. In an  actual experiment the Van’t Hoff’s factor  was found to
be 0.52. The degree of association of acetic acid is
(a) 0.48(b) 0.88(c) 0.96(d) 0.52
6. The van’t Hoff factor of a 0.005 M aqueous solution of KCl is 1.95. The degree of ionisation of KCl is
(a) 0.95(b) 0.97(c) 0.94(d) 0.96
7. Among the aqueous solutions given below which are isotonic at same temperature.
A (0.1 M urea); B (0.1 M NaCl); C (0.1 M Glucose); D (0.0541 M KCl, 85% diss); E (0.05 M BaCl
2
);
(a) A, E(b) A, B, D(c) A, C, D(d) A, C only
8. If the observed and normal osmotic pressures of 1% NaCl solution are 5.7 and 3.0 atm, the degree of dissociation
of NaCl is
(a) 0.9(b) 1.0(c) 0.57(d) 0.3
9. Which solution would exhibit abnormal osmotic pressure ?
(a) Aqueous solution of urea(b) Aqueous solution of common salt
(c) Aqueous solution of glucose(d) Aqueous solution of sucrose
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10. What is osmolarity of a 0.20 M KCl solution ?
(a) 0.10 osmol(b) 0.20 osmol(c) 0.30 osmol(d) 0.40 osmol
11. The van't Hoff factor for 0.1 M Ba(NO
3
) 2
 solution is 2.74. The degree of dissociation is
(a) 91.3%(b) 87%(c) 100%(d) 74%
12. The molal freezing point constant for water is 1.86 K kg mol
—1
. Therefore, the freezing point of 0.1 M NaCl solution
in water is expected to be
(a) —1.86
0
C(b) —0.186
0
C(c) —0.372
0
C(d) +0.372
0
C
13. Assuming the salts to be unionised in solution, which of the following has highest osmotic pressure ?
(a) 1% CsCl(b) 1% RbCl(c) 1% KCl(d) 1% NaCl
14. Which has maximum value of van’t hoff factor ?
(a) KO
2
(b) NH
2
CONH
2
(c) C
6
H
12
O
6
(d) Na
2
O
15. Decimolar solution of potassium ferricyanide, K
3
[Fe(CN) 6
] has osmotic pressure of 3.94 atm at 27°C. Hence per
cent ionisation of the solute is
(a)         10%(b) 20%(c) 30%(d) 40%
16. Assuming each salt to be 90% dissociated which of the following will have highest  osmotic pressure?
(a) Decimolar  Al
2
(SO
4
) 3
(b) Decimolar BaCl
2
(c) Decimolar Na
2
SO
4
(d) A solution obtained by mixing  equal volumes of (b) and (c) and filtering
17. Which solution will show maximum elevation in b.pt.?
(a) 0.1 M KCl(b) 0.1 M BaCl
2
(c) 0.1 M FeCl
3
(d) 0.1 M Fe
2
(SO
4
) 3
18. Which has minimum osmotic pressure ?
(a) 200 mL of 2 M NaCl solution(b) 200 mL of 1 M glucose solution
(c) 200 mL of 2M urea solution(d) All have same
19. The van’t Hoff’s factor (i) for a dilute solution of K
3
[Fe(CN) 6
] is
(a) 10(b) 4(c) 5(d) 0.25
20. The values of observed and calculated molecular weights of silver nitrate are 92.64 and 170 respectively The
degree of dissociation of silver nitrate is
(a) 60%(b) 83.5%(c) 46.7%(d) 30%
21. The freezing point of equimolal aqeous solution will be highest for:
(a) C
6
H
5
NH
3
Cl(b) Ca(NO
3
) 2
(c) La(NO
3
) 5
(d) C
6
H
12
O
6
22. Which one of the following statements is false ?
(a) Raoult’s law states that vapour pressure of a component over a solution is proportional to mole fraction
(b) The osmotic pressure (p) of a solution is given by the relation = M RT where M is the molarity of the solution
Page 4


 DPP : 04 / Solutions
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st
 floor,Sector -15, Panchkula
9217610408,8699438881,8699438882
Page No.1
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G od has never given dreams
Some important Facts and Definitions
1. Abnormal Molecular Mass. When the molecular mass of a substance determined by studying any of the colligative
properties comes out to be different than the theoretically expected value.
2. vant’t Hoff factor is defined as the ratio of the experimental value of the colligative property to the calculated value
of the colligative property,
Experimental value of the colligative property Observed value of the colligative property
i =
Calculated value of the colligative property Normal value of the same property
when the solution behaves ideally
=
()() C
O
Normal calculated molecular mass M
i= =
Abnormal Observed molecular mass M
3. Calculation of Degree of Dissociation or Association
(a) Degree of dissociation is defined as the fraction of the total substance that undergoes dissociation, i.e.,
Degree of dissociation (a) =
Numberof molesafterdissociation
Totalnumberof molestaken
() - a
- c o
o
M M
=
M n 1
(b) Degree of association is defined as the fraction of the total substance which exists in the form of associated
molecules, i.e.,
Degree of association (a) =
Number of moles associated
Total number of moles taken
() o c
o
M M n
=
M n 1
- a
- x
4. van’t Hoff factor, i > 1, if there is dissociation of the solute in the solution and i < 1 if there is association of the solute
in the solution.
5. For 100% dissociation of a solute, van’t Hoff factor, i = number of ions produced from one molecule of the solute.
Some Subjective Questions & their explanations
1. Equimolal solutions of NaCl and BaCl
2
 are prepared in water. Freezing point of NaCl is
found to be —2
0
C. What freezing point do you expect for BaCl
2
 solution ?
— i for NaCl = 2, i for BaCl
2
 = 3.
Hence,
()() f
NaCl
f
T
2
T 3
?
=
?
2
BaCl
 or() f
3
T
2
? =
2
0
BaCl
x2=3
 so that T
f
 for BaCl
2
 = —3
0
C
SOLUTIONS
(van’t Hoff Factor) DAILY  PRACTICE  PROBLEMS - 4
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2. Why is freezing point depression of 0.1 M sodium chloride solution nearly twice that of
0.1 M glucose solution ?
— NaCl, being an electrolytes, dissociates almost completely to give Na
+
 and Cl
—
 ions whereas glucose, being
non-electrolyte, does not dissociate. Hence the number of particles in 0.1 M NaCl solution is nearly double than
in 0.1 M glucose solution. Freezing point depression, being a colligative property, is therefore, nearly twice for NaCl
solution than for glucose solution of same molarity.
3. Explain why equimolar solutions of sodium chloride and sodium sulphate are not isotonic?
— NaCl dissociates to give 2 ions (Na
+
 and Cl
—
). Na
2
SO
4
 dissociates to give 3 ions (2 Na
+
 and ). Thus, equimolar
solutions of NaCl and Na
2
SO
4
 have different concentrations of ions in the solution. As osmotic pressure depends
upon concentration of particles in the solution, they have different osmotic pressures.
Objective Questions
1. The molal elevation constant of water is 0.51. The boiling point of 0.1 molal aqueous NaCl solution is nearly
(a) 100.05
0
C(b) 100.1
0
C(c) 100.2
0
C(d) 101.0
0
C
2. The ratio of elevation in boiling point of aqueous solution of sodium chloride to that of an aqueous
solution of glucose of same molalities is approximately
(a) 1(b) 2(c) 0.5(d) 2.5
3. Benzoic acid dissolved in benzene will show a molecular mass of
(a) 122(b) 61(c) 244(d) 366
4. If the observed and normal osmotic pressures of a KCl solution are 5.85 and 3.20 atm, the degree of dissociation
of KCl is
(a) 1(b) 0.082(c) 0.82(d) 0.28
5. Acetic acid exists in benzene solution in dimeric form. In an  actual experiment the Van’t Hoff’s factor  was found to
be 0.52. The degree of association of acetic acid is
(a) 0.48(b) 0.88(c) 0.96(d) 0.52
6. The van’t Hoff factor of a 0.005 M aqueous solution of KCl is 1.95. The degree of ionisation of KCl is
(a) 0.95(b) 0.97(c) 0.94(d) 0.96
7. Among the aqueous solutions given below which are isotonic at same temperature.
A (0.1 M urea); B (0.1 M NaCl); C (0.1 M Glucose); D (0.0541 M KCl, 85% diss); E (0.05 M BaCl
2
);
(a) A, E(b) A, B, D(c) A, C, D(d) A, C only
8. If the observed and normal osmotic pressures of 1% NaCl solution are 5.7 and 3.0 atm, the degree of dissociation
of NaCl is
(a) 0.9(b) 1.0(c) 0.57(d) 0.3
9. Which solution would exhibit abnormal osmotic pressure ?
(a) Aqueous solution of urea(b) Aqueous solution of common salt
(c) Aqueous solution of glucose(d) Aqueous solution of sucrose
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10. What is osmolarity of a 0.20 M KCl solution ?
(a) 0.10 osmol(b) 0.20 osmol(c) 0.30 osmol(d) 0.40 osmol
11. The van't Hoff factor for 0.1 M Ba(NO
3
) 2
 solution is 2.74. The degree of dissociation is
(a) 91.3%(b) 87%(c) 100%(d) 74%
12. The molal freezing point constant for water is 1.86 K kg mol
—1
. Therefore, the freezing point of 0.1 M NaCl solution
in water is expected to be
(a) —1.86
0
C(b) —0.186
0
C(c) —0.372
0
C(d) +0.372
0
C
13. Assuming the salts to be unionised in solution, which of the following has highest osmotic pressure ?
(a) 1% CsCl(b) 1% RbCl(c) 1% KCl(d) 1% NaCl
14. Which has maximum value of van’t hoff factor ?
(a) KO
2
(b) NH
2
CONH
2
(c) C
6
H
12
O
6
(d) Na
2
O
15. Decimolar solution of potassium ferricyanide, K
3
[Fe(CN) 6
] has osmotic pressure of 3.94 atm at 27°C. Hence per
cent ionisation of the solute is
(a)         10%(b) 20%(c) 30%(d) 40%
16. Assuming each salt to be 90% dissociated which of the following will have highest  osmotic pressure?
(a) Decimolar  Al
2
(SO
4
) 3
(b) Decimolar BaCl
2
(c) Decimolar Na
2
SO
4
(d) A solution obtained by mixing  equal volumes of (b) and (c) and filtering
17. Which solution will show maximum elevation in b.pt.?
(a) 0.1 M KCl(b) 0.1 M BaCl
2
(c) 0.1 M FeCl
3
(d) 0.1 M Fe
2
(SO
4
) 3
18. Which has minimum osmotic pressure ?
(a) 200 mL of 2 M NaCl solution(b) 200 mL of 1 M glucose solution
(c) 200 mL of 2M urea solution(d) All have same
19. The van’t Hoff’s factor (i) for a dilute solution of K
3
[Fe(CN) 6
] is
(a) 10(b) 4(c) 5(d) 0.25
20. The values of observed and calculated molecular weights of silver nitrate are 92.64 and 170 respectively The
degree of dissociation of silver nitrate is
(a) 60%(b) 83.5%(c) 46.7%(d) 30%
21. The freezing point of equimolal aqeous solution will be highest for:
(a) C
6
H
5
NH
3
Cl(b) Ca(NO
3
) 2
(c) La(NO
3
) 5
(d) C
6
H
12
O
6
22. Which one of the following statements is false ?
(a) Raoult’s law states that vapour pressure of a component over a solution is proportional to mole fraction
(b) The osmotic pressure (p) of a solution is given by the relation = M RT where M is the molarity of the solution
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  Answers
1. b 2. b 3. c 4. c 5. c 6. a 7. c
8. a 9. b 10. d 11. b 12. c 13. d 14. d
15. b 16. a 17. d 18. b 19. b 20. b 21. d
22. d 23. c 24. c 25. c 26. b 27. b 28. d
29. a 30. c
(c) The correct order of osmotic pressure for 0.01 M aqueous solution of each component is
BaCl
2
 > KCl > CH
3
COOH > Sucrose
(d) Two sucrose solutions of same molality prepared in different solvents will have the same freezing point
sepression
23. van’t Hoff’s factor of very dilute solution of Ca(NO
3
) 2
 is
(a) 1(b) 2(c) 3(d) 4
24. Aqueous solution of 0.004 M Na
2
SO
4
 and 0.01 M glucose are isotonic.The degree of dissociation of Na
2
SO
4
 is
(a) 25%(b) 60%(c) 75%(d) 85%
25. Solution A contains 7 g/L of MgCl
2
 and solution B contains 7g/L of NaCl. At room temperature, the osmotic
pressure of
(a) solution A is greater than B(b) both have same osmotic pressure
(c) solution B is greater than A(d) can’t determine
26. Consider the following aqueous solution (M = molarity) I. 0.1 M Na
2
SO
4
II. 0.1 M urea III. 0.1 M Na
3
PO
4
IV . 0.1 M NaCl
The increasing order of their boiling points will be
(a) I < II < III < IV(b) II < IV < I < III(c) II < IV < III < I(d) III < I < IV < II
27. The correct relationship between the boiling points of very dilute solution of AlCl
3
 (T
1
K) and CaCl
2
 (T
2
K) having the
same molar concentration is
(a) T
1
 = T
2
(b) T
1
 > T
2
(c) T
2
 > T
1
(d) T
2
= T
1
.
28. 1.0 molal aqueous solution of an electrolyte A
2
B
3
 is 60% ionised. The boiling point of the solution at 1 atm is
2
-1
b(H O)(K = 0.52K kgmol)(a) 274.76 K(b) 377 K(c) 376.4 K(d) 374.76 K
29. The van’t Hoff factor for BaCl
2
 at 0.01 M concentration is 1.98. The percentage dissociation of BaCl
2
 at this
concentration is
(a) 49(b) 69(c) 89(d) 98
30. pH of a 1.0 M monobasic acid HA is 2. The van’t Hoff factor for the aqueous solution should be considered as
(a) 2(b) 1.1(c) 1.01(d) 1.0