Question

A 20 litre container at 400 K contains $C{O_2}$ (g) at pressure $0.4{\text{ atm}}$ and an excess of SrO (neglect the volume of solid SrO). The volume of the container is now decreased by moving the movable piston fitted in the container. The maximum volume of the container, when pressure of $C{O_2}$ attains its maximum value, will be
Given that:
$SrC{O_3}(s) \rightleftharpoons SrO\left( s \right) + C{O_2}\left( g \right)$
${K_p} = 1.6{\text{atm}}$
(A) 5 litres
(B) 10 litres
(C) 4 litres
(D) 2 litres

Answer 1

To solve this question, we shall be using the ideal gas equation. Then we shall write the equilibrium equation and then with moles of carbon dioxide we will find the volume.

Formula used: We are going to use the ideal gas equation:
$PV = nRT$
Here, $P$ is the pressure of the gas
$V$ is the volume of the gas
$n$ is the number of moles
$R$ is the universal gas constant
$T$ is the temperature of the gas.

Complete step by step solution:
Volume of the container is 20 L and at 400K.
By using Ideal gas equation,
$PV = nRT$
Putting the values:
$0.4 \times 20 = {n_{C{O_2}}} \times R \times 400{\text{K}}$
${n_{C{O_2}}} = \dfrac{{0.2}}{R}$
These are the initial moles of carbon dioxide.
After reaching equilibrium:
$SrC{O_3}(s) \rightleftharpoons SrO\left( s \right) + C{O_2}\left( g \right)$
All pressure is because of $C{O_2}$
Again, applying the ideal gas equation:
${P_2}{V_2} = nRT$
On putting the values:
$1.6 \times {V_2} = \dfrac{{0.2}}{R} \times R \times 400$
${V_2} = 5{\text{L}}$

Thus, the pressure of $C{O_2}$ ​is maximum at $1.6{\text{atm}}\;$ and the volume is 5L.

Note:
The ideal gas law $PV = nRT$ was discovered by physicist and engineer Clapeyron in 1834.The term ideal gas refers to a hypothetical gas composed of molecules which follow a few rules: Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision upon impact with each other or an elastic collision with the walls of the container.
The ideal gas law is a valuable tool in understanding state relationships in gaseous systems. For example, in a system of constant temperature and pressure, the addition of more gas molecules results in increased volume.
The real gas that acts most like an ideal gas is helium. This is because helium, unlike most gases, exists as a single atom, which makes the van der Waals dispersion forces as low as possible. Another factor is that helium, like other noble gases, has a completely filled outer electron shell.