Question

A gas occupies $70$ Litres at ${27^0}C$ . What volume will it occupy at ${273^0}C$ , pressure remaining constant.

Answer 1

Hint: The equation which gives the simultaneous effect of pressure and temperature on the volume of a gas is known as the ideal gas equation or equation of state for an ideal gas. The gas equation may be derived from Boyle’s and Charles’ law. We can use this gas equation in order to solve this question.

Complete answer:
The most common form of ideal gas equation is;
$PV = nRT$
Where, $P$= pressure
 $V$ = Volume occupied by gas
$n$ = number of moles
$T$ = temperature
$R$ = universal gas constant
In the question, it is given that the gas occupies $70L$ volume $\left( {{V_1}} \right)$ at temperature $\left( {{T_1}} \right)$ ${27^0}C$
And we have to find the volume occupied $\left( {{V_2}} \right)$ at temperature $\left( {{T_2}} \right)$ ${273^0}C$.
We’ll use the ideal gas equation to find the volume occupied.
At temperature ${T_1}$ (It is given in the question that the pressure is constant)
$P{V_1} = nR{T_1}$
At temperature ${T_2}$
$P{V_2} = nR{T_2}$
Temperatures are given in Celsius, we need to convert them in kelvin.
${T_1} = {27^0}C$
= $27 + 273 = 300K$
${T_2} = {273^0}C$
 = $273 + 273 = 546K$
On dividing the ideal gas equations at temp ${T_1}$ and ${T_2}$, we’ll get;
$\dfrac{{{V_1}}}{{{V_2}}} = \dfrac{{{T_1}}}{{{T_2}}}$
${V_2} = \dfrac{{{V_1} \times {T_2}}}{{{T_1}}}$
Putting the values;
${V_2} = \dfrac{{70 \times 546}}{{300}}$
${V_2} = 127.4L$
The volume occupied by gas at temperature ${273^0}C$ was found to be $127.4L$
Additional Information:
Gas constant $\left( R \right)$ is found to be independent of the nature of the gas and depends only on the amount of gas taken. A gas that obeys the ideal gas equation exactly is called an ideal gas.

Note:
 We used the ideal gas equation to solve the given question. An ideal gas equation is also called the equation of state because it defines the state of the gas completely when all the variables have been specified.