Question

At 50 g of Iron reacts with HCl to form . The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is \[\_\_\_\_\_\_\] J. (Round off to the nearest integer).
[Given: R =8.314\[Jmo{l^{ - 1}}{K^{ - 1}}\] . Assume, hydrogen is an ideal gas]
[Atomic mass of Fe is 55.84u]

Answer 1

Hint: Work done by an ideal gas against a constant pressure is given by the expression
\[W = - pdV\]
Where p = constant pressure and
           dV= volume.
W= work
A negative sign here implies that work is done by the system on the surroundings.
The system while expanding against a constant pressure loses some energy which is represented by the negative sign.

Formula Used:
No. of moles =\[\dfrac{{Givenmass}}{{Molarmass}}\]
\[pV = nRT\]; where
p = pressure
V = volume
n = total no.of moles
R = universal gas constant and
T = temperature

Complete Step by Step Solution:
Here, we are given a reaction
\[Fe + 2HCl \to FeC{l_2} + {H_2}\]

Given:
p = pressure = 1 bar
R = universal gas constant = 8.314 \[Jmo{l^{ - 1}}{K^{ - 1}}\]
T = temperature = 25°C.
To find: work done, w =\[ - pdV\]; where p = constant pressure and
            dV = change in volume.

We are given the amount of Fe present which is \[50g.\]
The Iron's molar mass is 55.85 g.
Hence, the number of moles of this element present
\[ \Rightarrow \dfrac{{50g}}{{55.85gmo{l^{ - 1}}}}\]
\[ \Rightarrow 0.895moles\]

The temperature is \[25^\circ C\].
Thus, the temperature in K
\[ \Rightarrow (273 + 25)K\]
\[ \Rightarrow 298K\]

Given that, \[R = 8.314Jmo{l^{ - 1}}{K^{ - 1}}\]
Here, Hydrogen gas behaves ideally. So, it obeys the ideal gas equation, pV = nRT.

Then,
\[ \Rightarrow - p.dV = nRT\]
\[ \Rightarrow - pdV = 0.895moles \times 8.314Jmo{l^{ - 1}}{K^{ - 1}} \times 298K\]
\[ \Rightarrow - pdV = 2218.05Jmo{l^{ - 1}}\]

So, the work done by the gas during the expansion is -2218.05\[Jmo{l^{ - 1}}\] .

Note: While attending to the question, one must note down the given values and the value which is to be found out. Here, we had to find out the work done, but only the amount of pressure was given. Thus, we had to use the ideal gas equation to find out the work done. The temperature was given and the no.of moles can be found from the given data. The temperature in this question is given in Celsius and must be converted to Kelvin. One must mention the unit of work while writing the steps of the reaction.