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STD 12 - 2. Electrochemistry — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 2. Electrochemistry4 Marks
MCQ
Consider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and $298 K$. Its cell reaction is

$H _2( g )+\frac{1}{2} O _2( g ) \rightarrow H _2 O (\ell)$

The work derived from the cell on the consumption of $1.0 \times 10^{-3} mol$ of $H _2( g )$ is used to compress $1.00 mol$ of a monoatomic ideal gas in a thermally insulted container. What is the change in the temperature (in $K$ ) of the ideal gas ?

The standard reduction potentials for the two half-cells are given below.

$\left. O _2( g )+4 H ^{+} \text {(aq. }\right)+4 e ^{-} \rightarrow 2 H _2 O (\ell), E ^{\circ}=1.23 V,$

$\left.2 H ^{+} \text {(aq. }\right)+2 e ^{-} \rightarrow H _2( g ), E ^{\circ}=0.00 V.$

Use $F =96500 C mol ^{-1}, R =8.314 J mol ^{-1} K ^{-1}$

  • ✓
    $13.32$
  • B
    $13.35$
  • C
    $13.40$
  • D
    $13.45$
✓

Answer

Correct option: A.
$13.32$
a
$E _{\text {cell }}^0=1.23-0.00=1.23 V$

$\Delta G _{\text {cell }}^0=- nF E _{\text {cell }}^0=-2 \times 96500 \times 1.23 J$

$\therefore \quad$ Work derived from this fuel cell

$=\frac{70}{100} \times\left(-\Delta G _{\text {cell }}^0\right) \times 10^{-3}= xJ$

Since insulated vessel, hence $q=0$

From equation, for monoatomic gas,

$w =\Delta U \quad \Rightarrow \quad x = nC _{ V _{ m }} \Delta T \left\{ C _{ V _{ m }}=\frac{3 R }{2}\right\}$

or,$\quad \frac{70}{100} \times(2 \times 96500 \times 1.23) \times 10^{-3}=1 \times \frac{3}{2} \times 8.314 \times \Delta T$

$\therefore \quad \Delta T =13.32$

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