Question

Work done in an open vessel at 300K, when 56g of iron reacts with dilute HCl is:
[A] 600cal
[B] 300cal
[C] 150cal
[D] 100cal

Answer 1

Hint: To solve this use the equation of work done i.e. \[W=PdV\]. Use the ideal gas equation and replace pressure and volume terms in the work done equation. To find the number of moles you can divide mass by molecular weight.

Complete step by step answer:
In the question it is given to us that iron reacts with dilute HCl. We know that it will give us ferrous chloride and hydrogen gas will be evolved.
Therefore, we can write the reaction as-
     \[Fe+2HCl\to FeC{{l}_{2}}+{{H}_{2}}(g)\]

Now, we know that work done is given by pressure multiplied by volume. We can write it as-
     \[W=PdV\]

Now, from the ideal gas equation we know that
     \[PV=nRT\]

Therefore, replacing PV in the work equation by nRT we can write that-
     \[W=nRT\]

Here W is work done, n is the number of moles of the gas, R is the universal gas constant and T is the temperature.
Now, let us calculate the number of moles of iron.
We can get a number of moles by dividing the weight used by the molecular weight of iron.
We know that the molecular weight of iron is 56.
Mass of iron used for the reaction with HCl is 56g.
Therefore, number of moles = n = $\dfrac{56g}{56g/mol}=1\text{ }mol$
Temperature is given to us as 300K.
The value of universal gas constant in cal/K.mol is 1.987cal/K.mol i.e. almost equal to 2cal/K.mol

Therefore, putting these values in the work done equation we can write that-
     \[W=1\text{ mol}\times 2\text{ cal mo}{{\text{l}}^{-1}}{{K}^{-1}}\times 300K=600\text{ cal}\]
From the above calculation it is clear that the work done in an open vessel at 300K, when 56g of iron reacts with dilute HCl is 600cal.
So, the correct answer is “Option A”.

Note: The work done can either be positive or negative. It depends if the work is done upon the system or by the system.
If the work is done on the system then the work done is negative. Energy is added to the system in this case.
If the work done is by the system on the surrounding then the work done is positive. Energy is removed from the system in this case.