Question

A sample of gas has a volume of 0.2 litres measured at 1 atm pressure and $\text{0}{}^\circ \text{C}$. At the same pressure, at $273{}^\circ \text{C}$, its volume will become:
(A) 0.1 litre
(B) 0.4 litre
(C) 0.8 litre
(D) 0.6 litre

Answer 1

Hint: For this problem, we have to study Charles' law according to which the volume is directly proportional to the temperature when the pressure is constant. So by putting all the values we can calculate the volume.

Complete step by step solution:
-In the given question, we have to calculate the volume when the pressure remains the same but the temperature becomes $273{}^\circ \text{C}$.
-As we know that Charles law gives us the relationship between volume and temperature when the pressure is constant.
-According to the Charle's law volume is directly proportional to the temperature such that:
\[\dfrac{{{\text{V}}_{1}}}{{{\text{V}}_{2}}}\text{ }\,\text{= }\dfrac{{{\text{T}}_{1}}}{{{\text{T}}_{2}}}\] ….. (1)
-Here, V is the volume of the gas and T is the temperature of the gas in Kelvin.
-Now, it is given that at a temperature $\text{0}{}^\circ \text{C}$ the volume of the gas is 0.2 litres so we have to find the volume of gas at temperature $273{}^\circ \text{C}$.
-So, here \[{{\text{V}}_{1}}\] is equal to 0.2 litres and \[{{\text{T}}_{1}}\] $\text{273}{}^\circ \text{C}$ or 546K is whereas the value of \[{{\text{T}}_{2}}\] is $\text{0}{}^\circ \text{C}$ or 273k and we have to calculate \[{{\text{V}}_{2}}\].
-So, we can also write the equation first as:
\[{{\text{V}}_{2}}\text{ = }\dfrac{{{\text{V}}_{1}}\text{ }\times \text{ }{{\text{T}}_{2}}}{{{\text{T}}_{1}}}\]
-Now, by putting all the values we will get:
\[{{\text{V}}_{2}}\text{ = }\dfrac{\text{0}\text{.2 }\times \text{ 546}}{273}\text{ = 0}\text{.4 litres}\]
-So, the volume of gas at $\text{0}{}^\circ \text{C}$ is equal to 0.4 litres.

Therefore, option (B) is the correct answer.

Note: Just like Charles law, Boyle's law was also given, according to which the inverse relationship between volume and pressure is given when the temperature is constant. Moreover, Gay-Lussac law was also given, according to which the pressure has a direct effect on temperature when the volume is kept constant.