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)

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Solution

Assume 1 L of sulphuric acid is present.

Initial number of moles of sulphuric acid $= \frac{1294 \times 0.39}{98} = 5.15$ moles

Final number of moles of sulphuric acid $= \frac{1139 \times 0.20}{98} = 2.32$ moles

Number of moles of sulphuric acid consumed $= 5.15 - 2.32 = 2.83$ moles.

Number of moles of sulphuric acid consumed corresponds to number of moles of electrons.

Number of moles of electrons $= 2.83$

The number of ampere hours $= \frac{2.83 \times 96500}{3600} = 76$

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

1.294

1.139 {g mL}^{- 1}

. Sulphuric acid of density

1.294 {g mL}^{- 1}

39 % H_{2} S O_{4}

by mass and that of density

1.139 {g mL}^{- 1}

20 % H_{2} S O_{4}

by mass. The battery holds

3.5 L

of the acid and the volume remained practically constant during the discharge. 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)
The number of ampere-hour for which the battery must have been used is

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.