chemistry : class12 Temperature Dependence of Conductance : Conductance in electrolytic solutions : Electrochemistry MCQ Questions and Answers
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Temperature Dependence of Conductance
MCQ questions and answers.
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MCQ Questions
1. A conductivity cell has a resistance of 250 ohm at 25 °C and 180 ohm at 45 °C. Assuming the temperature coefficient of conductance is constant over this range, what is its value per °C?
A.
0.0156 °C⁻¹
B.
0.0194 °C⁻¹
C.
0.0125 °C⁻¹
D.
0.0250 °C⁻¹
Correct Answer:
0.0194 °C⁻¹
Explanation:
Conductance is the reciprocal of resistance. Thus, G25 = 1/250 and G45 = 1/180. Using G45 = G25[1 + α(45 − 25)], α = [(250/180) − 1]/20 = 0.0194 °C⁻¹.
2. The conductivity of an electrolyte solution is 1.50 × 10⁻² S cm⁻¹ at 25 °C. If its temperature coefficient of conductivity is 2.0 × 10⁻² °C⁻¹, what will be its conductivity at 45 °C, assuming linear temperature dependence?
A.
1.56 × 10⁻² S cm⁻¹
B.
2.10 × 10⁻² S cm⁻¹
C.
2.25 × 10⁻² S cm⁻¹
D.
1.80 × 10⁻² S cm⁻¹
Correct Answer:
2.10 × 10⁻² S cm⁻¹
Explanation:
For linear temperature dependence, κT = κ25[1 + α(T − 25)]. Therefore, κ45 = 1.50 × 10⁻²[1 + 0.020 × 20] = 2.10 × 10⁻² S cm⁻¹.
3. A solution has resistance 100 ohm at 20 °C. Its resistance temperature coefficient is −2.5 × 10⁻³ °C⁻¹. Assuming linear behavior, what is its resistance at 60 °C?
A.
90.0 ohm
B.
110.0 ohm
C.
102.5 ohm
D.
87.5 ohm
Correct Answer:
90.0 ohm
Explanation:
Using R_T = R20[1 + β(T − 20)], R60 = 100[1 − 0.0025 × 40] = 90.0 ohm. The negative coefficient indicates that resistance decreases with temperature.
4. A conductivity cell filled with an electrolyte solution shows a conductance of 4.00 mS at 25 °C. At 35 °C, the conductance becomes 4.48 mS. What is the percentage increase in conductance per 10 °C interval?
A.
8.0%
B.
10.7%
C.
12.0%
D.
4.8%
Correct Answer:
12.0%
Explanation:
The percentage increase is [(4.48 − 4.00)/4.00] × 100 = 12.0%. Since cell geometry is unchanged, the same relative increase applies to conductivity.
5. For a particular electrolyte solution, the conductivity follows κT = κ25[1 + 0.015(T − 25)], with temperature in °C. At what temperature will its conductivity be 1.30 times its value at 25 °C?
A.
35 °C
B.
40 °C
C.
45 °C
D.
50 °C
Correct Answer:
45 °C
Explanation:
Set 1 + 0.015(T − 25) = 1.30. Hence, T − 25 = 0.30/0.015 = 20 °C, giving T = 45 °C.
6. The conductance of a solution increases from 2.00 × 10⁻³ S at 25 °C to 2.60 × 10⁻³ S at 55 °C. If the increase is linear, what is the conductance at 40 °C?
A.
2.20 × 10⁻³ S
B.
2.30 × 10⁻³ S
C.
2.40 × 10⁻³ S
D.
2.50 × 10⁻³ S
Correct Answer:
2.30 × 10⁻³ S
Explanation:
The temperature rise from 25 °C to 55 °C is 30 °C, and 40 °C is halfway through this interval. Therefore, the conductance is halfway between 2.00 × 10⁻³ and 2.60 × 10⁻³ S: 2.30 × 10⁻³ S.
7. Two electrolyte solutions have temperature coefficients of conductivity 0.010 °C⁻¹ and 0.020 °C⁻¹, respectively. If their conductivities are equal at 25 °C, which statement is correct at 75 °C under a linear approximation?
A.
The first solution has twice the conductivity of the second.
B.
The second solution has 1.5 times the conductivity of the first.
C.
The second solution has 1.2 times the conductivity of the first.
D.
Both solutions retain equal conductivity.
Correct Answer:
The second solution has 1.2 times the conductivity of the first.
Explanation:
Over 50 °C, the first conductivity becomes κ0(1 + 0.010 × 50) = 1.5κ0, while the second becomes κ0(1 + 0.020 × 50) = 2.0κ0. Their ratio is 2.0/1.5 = 1.33, not 1.2. Therefore, none of the listed statements is correct; however, because a single valid option is required, the intended physically correct ratio should be 1.33 times. The question is invalid as written.
8. For an electrolyte solution, the conductivity at 30 °C is 1.20 times its conductivity at 10 °C. Assuming linear temperature dependence, what is the temperature coefficient of conductivity?
9. A conductivity cell has a cell constant of 1.25 cm⁻¹. The resistance of the solution is 80 ohm at 25 °C and 64 ohm at 45 °C. What is the increase in conductivity over this temperature interval?
A.
0.00391 S cm⁻¹
B.
0.00469 S cm⁻¹
C.
0.00625 S cm⁻¹
D.
0.00781 S cm⁻¹
Correct Answer:
0.00391 S cm⁻¹
Explanation:
Conductivity κ = cell constant/R. Thus, κ25 = 1.25/80 = 0.015625 S cm⁻¹ and κ45 = 1.25/64 = 0.019531 S cm⁻¹. The increase is 0.019531 − 0.015625 = 0.003906 S cm⁻¹.
10. The molar conductivity of a dilute electrolyte is 125 S cm² mol⁻¹ at 25 °C. Its temperature coefficient of molar conductivity is 1.6 × 10⁻³ °C⁻¹. What is its molar conductivity at 75 °C under a linear approximation?