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Q.

A lead storage battery has initially 200 g of lead and 200 g of PbO₂ plus excess H₂SO₄. Theoretically, how long could this cell deliver a current of 10.0A, without recharging, if it were possible to operate it so that the reaction goes to completion? (Pb = 208)

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a

16083.33 s

b

8041.67 s

c

44.68 s

d

18557.7s

answer is A.

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Detailed Solution

Cell reaction during discharge
Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O
$n_{Pb} taken = \frac{200}{208} and n_{{PbO}_{2}} taken = \frac{200}{240}$
Hence, PbO₂ is L.R
Now, $n_{eq} ({PbO}_{2}) = \frac{Q}{F} \Rightarrow \frac{200}{240} \times 2 = \frac{10 \times t}{96500}$
t = 16083.33 sec

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