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Current Electricity question

2003 · Shift 0 · Q129
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Current Electricity question

2003 · Shift 0 · Q129

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
The nagative ZnZnZn pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by 0.13g0.13g0.13g in 303030 minutes. If the electrochemical equivalent of ZnZnZn and CuCuCu are 32.532.532.5 and 31.531.531.5 respectively, the increase in the mass of the positive CuCuCu pole in this time is
  1. A
    0.180g0.180g0.180g
  2. B
    0.141g0.141g0.141g
  3. C
    0.126g0.126g0.126g
  4. D
    0.242g0.242g0.242g
View written solutionFree

Correct answer: C

  1. Use Faraday’s law of electrolysis
    For the same quantity of electricity passing through the cell, the mass deposited or dissolved is proportional to the electrochemical equivalent:

m=ZQm = ZQm=ZQ

So, for zinc and copper in the Daniell cell,

mCumZn=ZCuZZn\frac{m_{Cu}}{m_{Zn}} = \frac{Z_{Cu}}{Z_{Zn}}mZn​mCu​​=ZZn​ZCu​​

  1. Given data
  • Loss in mass of zinc pole: mZn=0.13 gm_{Zn} = 0.13\,gmZn​=0.13g
  • Electrochemical equivalent of zinc: ZZn=32.5Z_{Zn} = 32.5ZZn​=32.5
  • Electrochemical equivalent of copper: ZCu=31.5Z_{Cu} = 31.5ZCu​=31.5

We need mass gained by copper pole:

mCu=mZn⋅ZCuZZnm_{Cu} = m_{Zn}\cdot \frac{Z_{Cu}}{Z_{Zn}}mCu​=mZn​⋅ZZn​ZCu​​

  1. Substitute values

mCu=0.13×31.532.5m_{Cu} = 0.13 \times \frac{31.5}{32.5}mCu​=0.13×32.531.5​

mCu=0.13×0.96923m_{Cu} = 0.13 \times 0.96923mCu​=0.13×0.96923

mCu≈0.126 gm_{Cu} \approx 0.126\,gmCu​≈0.126g

  1. Match with options The correct option is:

C: 0.126 g\boxed{\text{C: }0.126\,g}C: 0.126g​

  1. Comparison with stored answer
    Stored correct answer: C
    Derived answer: C
    They agree.
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