The electrolysis of acetate solution produces ethane according to reaction:
$2 {CH}_{3} {COO}^{-} \to C_{2} H_{6} (g) + 2 {CO}_{2} (g) + 2 e^{-}$ . The current efficiency of the process is 80%. What volume of gases would be produced at 27°C and 740 torr. if the current of 0.5 amp is passed through the solution for 96.45 min? $(V_{C_{2} H_{6}} + V_{{CO}_{2}}) = ?$

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0.91 L

1.365 L

6.0 L

0.60 L

answer is D.

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Detailed Solution

$2 {CH}_{3} COONa + 2 H_{2} O ⟶ C_{2} H_{6 (g)} + 2 {CO}_{2 (g)} + 2 NaOH + H_{2 (g)}$
$2 \times 96500 C \to 4 moles of gases$
$0.8 \times (0.5 \times 96.45 \times 60) C \to n gases = ?$
$n_{gases} = 0.8 \times \frac{0.5 \times 96.45 \times 60 \times 4}{2 \times 96500} = 0.04797$
$moles of gases = \frac{PV}{RT} = \frac{740 \times V}{760 \times 0.0821 \times 300}$
$V = 1.21 L; V_{(C_{2} H_{6} + {CO}_{2})} = 1.21 \times 0.75 = 0.91 L$