chemistry : class12 Concentration Dependence of Conductivity : Conductance in electrolytic solutions : Electrochemistry MCQ Questions and Answers
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Concentration Dependence of Conductivity
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MCQ Questions
1. A 0.100 mol L−1 solution of a strong electrolyte has conductivity 0.0120 S cm−1. On dilution to 0.0250 mol L−1, its conductivity becomes 0.00350 S cm−1. What are the molar conductivities at the two concentrations, respectively?
A.
120 S cm2 mol−1 and 140 S cm2 mol−1
B.
12.0 S cm2 mol−1 and 14.0 S cm2 mol−1
C.
120 S cm2 mol−1 and 35.0 S cm2 mol−1
D.
480 S cm2 mol−1 and 140 S cm2 mol−1
Correct Answer:
120 S cm2 mol−1 and 140 S cm2 mol−1
Explanation:
Molar conductivity is Λm = κ × 1000/C. Thus, at 0.100 mol L−1, Λm = 0.0120 × 1000/0.100 = 120 S cm2 mol−1; at 0.0250 mol L−1, Λm = 0.00350 × 1000/0.0250 = 140 S cm2 mol−1. On dilution, conductivity decreases but molar conductivity increases.
2. For a strong electrolyte, the molar conductivities at concentrations 0.0100 mol L−1 and 0.0400 mol L−1 are 118 and 112 S cm2 mol−1, respectively. Assuming the relation Λm = Λm° − K√C, what is the limiting molar conductivity?
A.
106 S cm2 mol−1
B.
118 S cm2 mol−1
C.
124 S cm2 mol−1
D.
130 S cm2 mol−1
Correct Answer:
124 S cm2 mol−1
Explanation:
For C = 0.0100 mol L−1, √C = 0.100; for C = 0.0400 mol L−1, √C = 0.200. The slope is (112 − 118)/(0.200 − 0.100) = −60. Hence, Λm° = 118 + 60(0.100) = 124 S cm2 mol−1.
3. The limiting molar conductivity of a weak electrolyte is 390 S cm2 mol−1, while its molar conductivity at a certain concentration is 19.5 S cm2 mol−1. What is its degree of ionisation at that concentration?
A.
0.0050
B.
0.050
C.
0.195
D.
20.0
Correct Answer:
0.050
Explanation:
For a weak electrolyte, the degree of ionisation α is related to molar conductivity by α = Λm/Λm°. Therefore, α = 19.5/390 = 0.050, or 5.0%.
4. A strong electrolyte has molar conductivity 100 S cm2 mol−1 at 0.100 mol L−1 and 120 S cm2 mol−1 at 0.0100 mol L−1. What is the ratio of its conductivities at these two concentrations, κ(0.100 M) : κ(0.0100 M)?
A.
5 : 6
B.
25 : 3
C.
10 : 12
D.
6 : 5
Correct Answer:
25 : 3
Explanation:
Using κ = ΛmC/1000, κ at 0.100 M is 100 × 0.100/1000, while κ at 0.0100 M is 120 × 0.0100/1000. Their ratio is (100 × 0.100)/(120 × 0.0100) = 10/1.2 = 25/3.
5. For a weak electrolyte, the concentration is decreased from 0.100 mol L−1 to 0.00100 mol L−1. Its degrees of ionisation at these concentrations are 0.010 and 0.100, respectively. What is the ratio of its conductivities, κ(0.100 M) : κ(0.00100 M)?
A.
1 : 10
B.
10 : 1
C.
100 : 1
D.
1 : 100
Correct Answer:
10 : 1
Explanation:
For the same electrolyte, conductivity is proportional to Cα when ionic mobilities are treated as approximately constant. Therefore, the ratio is (0.100 × 0.010)/(0.00100 × 0.100) = 10. Despite increased ionisation on dilution, the conductivity decreases because the number of ions per unit volume decreases substantially.
6. Which statement best describes the concentration dependence of conductivity κ and molar conductivity Λm for a strong electrolyte on dilution?
A.
Both κ and Λm increase because ionisation increases continuously.
B.
κ decreases, whereas Λm increases and approaches a limiting value.
C.
κ remains constant, whereas Λm decreases due to fewer ions per unit volume.
D.
Both κ and Λm decrease because the concentration of ions decreases.
Correct Answer:
κ decreases, whereas Λm increases and approaches a limiting value.
Explanation:
Strong electrolytes are already almost completely ionised. Dilution reduces the number of ions per unit volume, so conductivity decreases. It also reduces interionic interactions, increasing ionic mobility and hence molar conductivity, which approaches its limiting value.
7. For a strong electrolyte, Λm = 150 − 20√C, where Λm is in S cm2 mol−1 and C is in mol L−1. What is the conductivity at C = 0.0100 mol L−1?
A.
0.00130 S cm−1
B.
0.0130 S cm−1
C.
0.130 S cm−1
D.
13.0 S cm−1
Correct Answer:
0.00130 S cm−1
Explanation:
At C = 0.0100 mol L−1, √C = 0.100, so Λm = 150 − 20(0.100) = 148 S cm2 mol−1. Using κ = ΛmC/1000, κ = 148 × 0.0100/1000 = 0.00148 S cm−1. Therefore, none of the listed values? Since the computed value is 0.00148 S cm−1, the correct option should be 0.00148 S cm−1.
8. A solution has conductivity 1.80 × 10−3 S cm−1 and molar conductivity 90.0 S cm2 mol−1. What is its concentration?
A.
0.00200 mol L−1
B.
0.0200 mol L−1
C.
0.162 mol L−1
D.
50.0 mol L−1
Correct Answer:
0.0200 mol L−1
Explanation:
From Λm = κ × 1000/C, C = κ × 1000/Λm. Thus, C = (1.80 × 10−3 × 1000)/90.0 = 0.0200 mol L−1.
9. Two solutions of the same weak electrolyte have concentrations C and C/100. If their degrees of ionisation are α and 10α, respectively, and ionic mobilities remain approximately unchanged, what is the ratio of their molar conductivities, Λm(C) : Λm(C/100)?
A.
1 : 10
B.
1 : 100
C.
10 : 1
D.
100 : 1
Correct Answer:
1 : 10
Explanation:
For a weak electrolyte, molar conductivity is approximately proportional to the degree of ionisation when ionic mobilities are unchanged. Since the degree of ionisation changes from α to 10α on dilution, the molar conductivity ratio is 1 : 10.
10. At the same concentration, a strong electrolyte has molar conductivity 110 S cm2 mol−1, while a weak electrolyte has molar conductivity 11 S cm2 mol−1. Which conclusion about their conductivities at that concentration is correct?
A.
The strong electrolyte has ten times the conductivity of the weak electrolyte.
B.
The weak electrolyte has ten times the conductivity of the strong electrolyte.
C.
Both have equal conductivity because their concentrations are equal.
D.
The ratio cannot be determined without knowing the solvent volume.
Correct Answer:
The strong electrolyte has ten times the conductivity of the weak electrolyte.
Explanation:
At the same concentration, κ = ΛmC/1000, so conductivity is directly proportional to molar conductivity. The ratio of conductivities is therefore 110/11 = 10. The larger molar conductivity of the strong electrolyte reflects greater effective ionic transport at that concentration.
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