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Electrochemical Cells, Galvanic Cells

During the di...

Question

During the discharge of a lead storage battery, the density of sulphuric acid fell from $1.294$ to $1.139$ gm $L^{- 1}$ . Sulphuric acid of density $1.294$ gm $L^{- 1}$ is $39$ % by weight and that of density 1.139 gm $L^{- 1}$ is $20$ % by weight. The battery holds $3.5$ litres of acid and the column practically remained constant during the discharge.
Calculate the number of ampere-hours for which the battery must have been used. The charging and discharging reactions are :
$P b + S O {_{4}}^{2 -} \to P b S O_{4} + 2 e^{-}$ (charging)
$P b O_{2} + 4 H^{+} + S O {_{4}}^{2 -} + 2 e^{-} \to P b S O_{4} + 2 H_{2} O$ (discharging)

297

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189

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274

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200

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Solution

The correct option is A $297$
Mass of sulphuric acid consumed:
$\frac{1.294 g}{1 m L} \times 3500 m L = 4529 g$

$\frac{1.139 g}{1 m L} \times 3500 m L = 3986 g$

weight consumed=4529-3986=543 g
moles of sulphuric acid = $\frac{543}{98} = 5.54 m o l e s$
moles of electrons consumed = 11 moles
total charge = $96500 \times 11 = 1069377$ C
= $\frac{1069377}{3600} = 297$ A-hr

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Similar questions

g m L^{- 1}

H_{2} S O_{4}

1.294 g m L^{- 1}

1.139 g m L^{- 1}

P b + S O_{4}^{2 -} \to P b S O_{4} + 2 e^{-}

P b O_{2} + 4 H^{+} + S O_{4}^{2 -} + 2 e^{-} \to P b S O_{4} + 2 H_{2} O

m l^{- 1}

m l^{- 1}

m l^{- 1}

P b + S O_{4}^{2 -} \to P b S O_{4} + 2 e ⟹

P b O_{2} + 4 H^{+} + S O_{4}^{2 -} + 2 e \to P b S O_{4} + 2 H_{2} O ⟹

1.294

1.139 {g mL}^{- 1}

1.294 {g mL}^{- 1}

39 % H_{2} S O_{4}

1.139 {g mL}^{- 1}

20 % H_{2} S O_{4}

3.5 L

P b + S O_{4}^{2 -} \to P b S O_{4} + 2 e^{-}

P b O_{2} + 4 H^{+} + S O_{4}^{2 -} + 2 e^{-} \to P b S O_{4} + 2 H_{2} O

1.294

1.139 g m l^{- 1}

1.294 g m l^{- 1}

1.139 g m l^{- 1}

The charging and discharging reactions are as follows:

$P b + S O_{4}^{2 -} \to P b S O_{4} + 2 e^{-}$ (charging)

$P b O_{2} + 4 H^{\oplus} + S O_{4}^{2 -} + 2 e^{-} \to P b S O_{4} + 2 H_{2} O$ (discharging)

1.294

1.139 {g mL}^{- 1}

H_{2} S O_{4}

1.294 {g mL}^{- 1}

1.139 {g mL}^{- 1}

3.5 L

P b + S O_{4}^{2 -} \to P b S O_{4} + 2 e^{-} (anode)

P b O_{2} + 4 H^{+} + S O_{4}^{2 -} + 2 e^{-} \to P b S O_{4} + 2 H_{2} O (cathode)

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