Question

A galvanic cell is set up from a zinc bar weighing $100 \,g$ and $1.0$ litre of $1.0 \,M\, Cu $SO_4$ solution. How long would the cell run if it is assumed to deliver a steady current of $1.0$ ampere ? (Atomic mass of $Zn = 65$)

• A. 1.1 hr
• B. 46 hr
• C. 53.6 hr
• D. 24.00 hr

Answer 1

Answer: (C)

$100 \,g$ of $Zn = \frac{100}{65}$ mol. Thus, according to reaction,
$Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu, Cu^{2+}$ ions are limiting reagents.
Now, charge flowing for reduction of $1$ mole of $Cu^{2+}$ ions
$ = 2 \times 96500 \,C$
If $1$ ampere of current is to be delivered for $t$ hours,
the quantity of electricity is $3600\,t\,C$.
Now $3600\,t = 2 \times 96500$
$ t = \frac{2\times 96500}{3600} = 53.61\,hr$