Question

A $20$ ${\text{litre}}$container at $400K$ contains $C{O_2}(g)$ at pressure $0.4atm$ 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: $SrC{O_3}(s) \rightleftarrows SrO(s) + C{O_2}$, ${K_p} = 1.6atm$)
A. $2$litre
B. $5$litre
C. $10$litre
D. $4$litre

Answer 1

The relation between pressure and volume at constant temperature is given by Boyle. The relation is known as Boyle’s law which states that at constant temperature the product of pressure and volume is constant.

Complete step by step answer:
There are three relations between pressure, volume, temperature and number of moles.
Let us talk about that.
Charles law: In this law the relation between volume and temperature is given at constant pressure and number of moles. The equation is as: At constant pressure and number of moles the volume is inversely proportional to the temperature.
Boyle’s law: In this law the relation between volume and pressure is given at constant temperature and number of moles. The equation is as: At constant temperature and number of moles the pressure is inversely proportional to the volume of the gas.
Avogadro law: In this law the relation between volume and number of moles is given at constant pressure and temperature. The relation is as: At constant pressure and temperature the volume of gas is directly proportional to the number of moles of the gas.
In the question we are given the volume and pressure in a closed vessel i.e. the number of moles of gas is constant at constant temperature. In the initial state we are given with pressure $0.4atm$ and volume $20L$. So these quantities will be as
${P_1} = 0.4atm \\\ {V_1} = 20L \\\$
When the piston is moved to decrease the volume then it is given that ${K_p}$(pressure constant) is $1.6atm$. This will be the final pressure of the solution. Hence it will be treated as ${P_2}$and finally we have to find ${V_2}$(final volume of the gas). And we know that at constant temperature and number of moles then the product of pressure and volume is constant. So the relation is:${P_1}{V_1} = {P_2}{V_2}$
$0.4 \times 20 = 1.6{V_2} \\\ {V_2} = 5L \\\$
So volume after the piston is moved will be $5L$.

So, the correct answer is Option B.

Note:
By using the three we see above i.e. Charles law, Boyle’s law and Avogadro’s law, the ideal gas equation also known as ideal gas law is derived. Ideal gas law is as: $PV = nRT$ where $P$ is pressure, $V$ is the volume, $n$ is number of moles of gas, $T$is the temperature and $R$is gas constant.