A lead storage battery has initially $200 g$ of lead and $200 g$ of $P b O_{2}$ , plus excess $H_{2} S O_{4}$ . How long could this cell deliver a current of $10 a m p$ , without recharging, if it was possible to operate it so that the reaction goes to completion?

2.48 h o u r

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3.48 h o u r

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4.48 h o u r

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6.48 h o u r

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Solution

The correct option is C $4.48 h o u r$
$m a s s o f P b = 200 g$
$m a s s o f P b O_{2} = 200 g$
$m a s s o f P b O_{2} = \frac{200}{239.2} = 0.8361 m o l e$
$m a s s o f P b i n P b O_{2} = 173.244 g$
$t o t a l m a s s o f P b = 200 + 173.244$
$= 373.244$
$w = Z i t$
$373.24 = \frac{207.2}{1 \times 96500} \times 10 \times t$
$t = 17383.23 s e c$
$t = 4.8286 h o u r s$

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