Question

The work done in an open vessel at $300{\text{K}}$ , when $112{\text{g}}$ iron reacts with dilute ${\text{HCl}}$ to form ${\text{FeC}}{{\text{l}}_{\text{2}}}$ is:
A.1.1Kcal
B.0.6Kcal
C.0.3Kcal
D.0.2Kcal

Answer 1

To answer this question you must recall the formula for work done by a gas. We are given the temperature at which the reaction proceeds and thus we consider it to be an isothermal process. We shall find out the amount of gas released in this process and then use the ideal gas equation to find the work done.
Formula Used:
${\text{W}} = - {\text{P}}\Delta {\text{V}}$
${\text{PV}} = {\text{nRT}}$
Where, ${\text{P}}$ is the pressure exerted by the gas
$\Delta {\text{V}}$ is the change in the volume of the gas
n is the number of moles
R is a constant
And T is the temperature.

Complete step by step answer:
The reaction taking place is:
${\text{Fe}} + {\text{2HCl}} \to {\text{FeC}}{{\text{l}}_2} + {{\text{H}}_2}$
We can see that one mole of iron reacts with two moles of hydrochloric acid to produce one mole of ferrous chloride and one mole of hydrogen gas.
The molar mass of iron is known to be $56{\text{g}}$.
Thus we can say, $56{\text{g}}$ of iron gives one mole of hydrogen gas.
So, $112{\text{g}}$ of iron will give 2 moles of gas.
The work done during the process will be done by gaseous molecules. The only gas involved in the above reaction is hydrogen gas which is formed as a product.
Thus, we can say that the initial volume of the system is zero and the final volume is equal to the volume occupied by the hydrogen gas.
We can write, ${{P\Delta V}} = {\text{PV}}$
Also we know the ideal gas equation, which is ${\text{PV}} = {\text{nRT}}$.
$\Rightarrow {\text{PV}} = 2 \times 8.314 \times 300 = 4988.4{\text{J}}$
$\therefore {\text{W}} = - {\text{PV}} = - 4988.4{\text{J}}$.
Since $1{\text{kcal}} = 4184{\text{J}}$
Thus, the work done by the system is $1.19{\text{kcal}}$

Hence option A is correct.

Note:
Generally, we shall consider all gases to be ideal gases unless specified otherwise in the question. It is assumed that there are no intermolecular forces between the gas particles and the volume of the particles is negligible as compared to that occupied by the gas.