Question

The work done when $6.5g$ of zinc reacts with dilute $HCl$ in an open beaker at $298K$ is:
A. $ - 3.26J$
B. $ - 2.44J$
C. $4.56J$
D. None of the above

Answer 1

Hint: The pressure and change in the volume in an open vessel will be because of the formation of the hydrogen gas formed during the reaction. So, first calculate the number of moles of hydrogen gas formed in the reaction and then calculate the work done with the help of the ideal gas equation as change in volume in the reaction is negligible.

Complete answer:
Zinc reacts with dilute hydrochloric acid as per following reaction:
$Zn(s) + 2HCl(l) \to ZnC{l_2}(s) + {H_2}(g)$
Number of moles of zinc reacting with dilute hydrochloric acid ${n_{Zn}} = \dfrac{{{\text{given mass}}}}{{{\text{atomic mass}}}}$
As per question, given mass of zinc$ = 6.5g$ and atomic mass of zinc $ = 65g$. Substituting values:
$ \Rightarrow {n_{Zn}} = \dfrac{{6.5}}{{65}}$
$ \Rightarrow {n_{Zn}} = 0.1\;{\text{moles}}$
Now, according to the reaction:
1 mole of zinc reacts to form $ \Rightarrow $ 1 mole of hydrogen gas
Therefore, 0.1 moles of zinc will react to form $ \Rightarrow $ 0.1 moles of hydrogen gas
Now, we know that work done is given by the product of pressure of the system and the change in the volume during the reaction i.e., $W = - pdV$ and as after the reaction, solid zinc chloride is formed along with the removal of hydrogen gas. So, the pressure of the system is due to the hydrogen gas and the volume change in the reaction is also negligible. Thus, work done can be represented as:
$W = - {\left( {pV} \right)_{{H_2}}}$
According to ideal gas equation, $pV = nRT$
Therefore, $W = - {n_{{H_2}}}RT$
Substituting given values:
$ \Rightarrow W = - 0.1 \times 0.0821 \times 298$
$ \Rightarrow W = - 2.44J$
Hence, the work done for the given reaction is $ - 2.44J$.
So, option (B) is the correct answer.

Note:
Remember that the work done can either be positive or negative depending on the fact that work is done on the system or by the system. If the work is done on the system, then work done is negative whereas if the work is done by the system on the surrounding then work done is positive.