Question

2 mol of zinc is dissolved in $HCl$at ${25}^{\circ }C$. The work done in an open vessel is:

• A. $-2.447kJ$
• B. $-4.955kJ$
• C. $\frac{R}{2}$
• D. $3R$

Answer 1

The correct option is B

$-4.955kJ$

The following reaction takes place:

$2Zn+4HCl\to 2ZnC{l}_2+2H_2$

It is very impiortant to understand that this is an irreversible process since this reaction happens pretty quickly and hydrogen gas escapes the system.

When $H_2$ gas is liberated, it pushes back its surrounding and thus does some work against it.
Since it is an irreversible process, we can use the following equation:

$W=P_{ext}\Delta V=-P_{ext}(V_f-V_x)$

$V_i=0$ thus $\Delta V=V_f$

$V_f=\frac{nRT}{P_{ext}}$

$W=-Pext\times \frac{nRT}{P_{ext}}=-nRT$

Given that $n=2,R=8.314J/Kmol$

$T=25+273=298K$

$W=-2\times 8.314\times 298=4955.144J=4.955kJ$

Tip: You can use approximations for $R=25/3$ and $T=300$ for quicker calculations!