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Electrochemistry question

2024 · 27 Jan · Shift 2 · Q25
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Electrochemistry question

2024 · 27 Jan · Shift 2 · Q25

JEE MainChemistryElectrochemistryNumerical+4 / −1
The hydrogen electrode is dipped in a solution of pH=3\mathrm{pH}=3pH=3 at 25∘C25^{\circ} \mathrm{C}25∘C. The potential of the electrode will be ‾×10−2 V\underline{\hspace{2cm}}\times 10^{-2} \mathrm{~V}​×10−2 V. (2.303RTF=0.059 V)\left(\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}\right)(F2.303RT​=0.059 V)
Numerical answer
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Correct answer: 18

  1. Write the half-cell reaction for hydrogen electrode

For a hydrogen electrode, 2H++2e−⇌H2(g)2H^+ + 2e^- \rightleftharpoons H_2(g)2H++2e−⇌H2​(g)

  1. Use the Nernst equation

For the reduction reaction, E=E∘−0.0592log⁡PH2[H+]2E = E^\circ - \frac{0.059}{2} \log \frac{P_{H_2}}{[H^+]^2}E=E∘−20.059​log[H+]2PH2​​​

For the standard hydrogen electrode, E∘=0E^\circ = 0E∘=0

Assuming hydrogen gas is at standard pressure, PH2=1P_{H_2}=1PH2​​=1 atm. So, E=−0.0592log⁡1[H+]2E = -\frac{0.059}{2} \log \frac{1}{[H^+]^2}E=−20.059​log[H+]21​

This simplifies to E=−0.0592(−2log⁡[H+])E = -\frac{0.059}{2}(-2\log[H^+])E=−20.059​(−2log[H+]) E=0.059log⁡[H+]E = 0.059\log[H^+]E=0.059log[H+]

Since pH=−log⁡[H+]\mathrm{pH} = -\log[H^+]pH=−log[H+] we get log⁡[H+]=−pH\log[H^+] = -\mathrm{pH}log[H+]=−pH

Therefore, E=−0.059×pHE = -0.059\times \mathrm{pH}E=−0.059×pH

  1. Substitute pH = 3

E=−0.059×3=−0.177 VE = -0.059\times 3 = -0.177\,\text{V}E=−0.059×3=−0.177V

  1. Express in the required form

−0.177 V=−17.7×10−2 V-0.177\,\text{V} = -17.7\times 10^{-2}\,\text{V}−0.177V=−17.7×10−2V

As an integer-type answer, this is taken as 18×10−2 V18\times 10^{-2}\,\text{V}18×10−2V with negative sign for the electrode potential.

So the potential is approximately −18×10−2 V-18\times 10^{-2}\,\text{V}−18×10−2V

Hence the blank should be filled with 18.

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