During the discharge of a lead storage battery, the density of sulphuric acid fell from $1.294$ to $1.139 {g mL}^{- 1}$ . Sulphuric acid of density $1.294 {g mL}^{- 1}$ is $39 % H_{2} S O_{4}$ by mass and that of density $1.139 {g mL}^{- 1}$ is $20 % H_{2} S O_{4}$ 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

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Solution

We have
Mass of $H_{2} S O_{4}$ solution to start with, $ρ V = (1.294 {g mL}^{- 1}) (3.5 \times 10^{3} mL) = 4529 g$
Actual mass of $H_{2} S O_{4}$ in this solution $= (\frac{39}{100}) (4529 g) = 1766.3 g$
Mass of $H_{2} S O_{4}$ solution at the end $= (1.139 {g mL}^{- 1}) (3.5 \times 10^{3} mL) = 3986.5 g$
Actual mass of $H_{2} S O_{4}$ in this solution $= (\frac{20}{100}) (3986.5 g) = 797.3 g$
Mass of $H_{2} S O_{4}$ consumed $= (1766.3 - 797.3) g = 969.0 g$
Amount of $H_{2} S O_{4}$ consumed $= \frac{969.0 g}{98 {g mol}^{- 1}} = 9.888 mol$
Amount of $H^{+}$ consumed $= 2 \times 9.888 mol$

Since 4 mol of $H^{+}$ are consumed per 2 mol of electrons during discharge, we have
Amount of electrons discharged $= \frac{2 mol}{4 mol} (2 \times 9.888 mol) = 9.888 mol$
Quantity of electricity discharged $= (9.888 mol) (96500 {C mol}^{- 1}) = 954192 C$
Number of ampere-hour for which the battery has been used $= \frac{954192}{60 \times 60} = 265.05$

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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.