During the discharge of a lead storage battery, the density of sulphuric acid fell from $1.294$ to $1.139 g m l^{- 1}$ . Sulphuric acid of density $1.294 g m l^{- 1}$ is 39% by weight and that of density $1.139 g m l^{- 1}$ is 20% by weight. The battery holds 3.5 L of the acid and the volume remained practically constant during the discharge. Find the number of ampere-hours for which the battery must has been used.

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)

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Solution

Discharging reaction :
$P b O_{2} + 4 H^{\oplus} + S O_{4}^{2 -} + 2 e^{-} ⇌ P b S O_{4} + 2 H_{2} O$
$M_{1} = \frac{10 \times d \times % by mass}{M Wt} = \frac{10 \times 1.294 \times 39}{98} = 5.149$
$M_{2} = \frac{10 \times 1.139 \times 20}{98} = 2.324$
Change in molarity $(M_{2} - M_{1}) = 5.149 - 2.324 = 2.825 M$
Decrease in amount of $H_{2} S O_{4}$ as battery yields current $=$ Change in molarity $\times M wt of H_{2} S O_{4} \times$ Volume of acid
$= 2.825 \times 98 \times 3.5 = 969 g$
Overall change :
$P b (s) + P b O_{2} (s) + 2 H_{2} S O_{4} (a q) ⇌ 2 P b S O_{4} (s) + 2 H_{2} O (l)$
$2 F \equiv 2 mol of H_{2} S O_{4}$ or $1 F \equiv 1 Mol of H_{2} S O_{4}$
969 g of $H_{2} S O_{4}$ is condemned by $= \frac{1}{98} \times 969 = 9.888 F$
Ampere hour $= \frac{9.888 \times 96500 ampere second}{3600 second/hour}$
$= 265$ ampere hour.

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Q. During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to 1.139

g m L^{- 1}

H_{2} S O_{4}

of density

1.294 g m L^{- 1}

is 39% and that of density

1.139 g m L^{- 1}

is 20% by weight.The battery holds 3.5 L of acid and the volume practically remains constant during discharge. The number of ampere hours for which the battery must have been used are........................
The discharging and charging 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)

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.