Question

300ml of a gas at ${{2}}{{{7}}^{{o}}}{{c}}$ is cooled to ${{ - }}{{{8}}^{{o}}}{{c}}$ at constant pressure. The final volume is:
A) ${{150ml}}$
B) ${{300ml}}$
C) ${{265ml}}$
D) ${{380ml}}$

Answer 1

Hint: Combined gas law is the combination of three laws i.e., Charles law, Boyle’s law, and Gay-Lussac’s law. Combined gas law shows that: Pressure is inversely proportional to the volume. Pressure is directly proportional to the temperature and The Volume is directly proportional to the measure of temperature.

Complete step by step answer:
Here we can follow Charles Law or simply we can follow combined gas law:
According to Charle’s law ${{V\alpha T}}$ at constant pressure
So we get $\dfrac{{{{{V}}_1}}}{{{{{V}}_2}}}{{ = }}\dfrac{{{{{T}}_1}}}{{{{{T}}_2}}}$ where the initial values are given by ${{{V}}_1}{{,}}{{{T}}_1}$and final values are given by ${{{V}}_2}{{,}}{{{T}}_2}$
Or
According to Combined Gas Law $\dfrac{{{{{P}}_1}{{{V}}_1}}}{{{{{T}}_1}}}{{ = }}\dfrac{{{{{P}}_2}{{{V}}_2}}}{{{{{T}}_2}}}$
Since pressure is constant, ${{{P}}_1}{{ = }}{{{P}}_2}$
So we get here, $\dfrac{{{{{V}}_1}}}{{{{{T}}_1}}}{{ = }}\dfrac{{{{{V}}_2}}}{{{{{T}}_2}}}$ where the initial values are given by ${{{V}}_1}{{,}}{{{T}}_1}$ and final values are given by ${{{V}}_2}{{,}}{{{T}}_2}$.
Given: Initial volume ${{{V}}_1}{{ = 300ml}}$
Initial temperature, ${{{T}}_1}{{ = 2}}{{{7}}^{{o}}}{{C = 27 + 273 = 300 K}}$ (when we convert into kelvin i.e.,${{k}}$)
Final volume, ${{{V}}_2}{{ = ?}}$
Final temperature, ${{{T}}_2}{{ = - }}{{{8}}^{{o}}}{{C}}$
${{ = - 8 + 273 = 265K}}$
Applying these values in the formula $\dfrac{{{{{V}}_1}}}{{{{{V}}_2}}}{{ = }}\dfrac{{{{{T}}_1}}}{{{{{T}}_2}}}$we get,
$\dfrac{{{{300}}}}{{{{300}}}}{{ = }}\dfrac{{{{{V}}_2}}}{{{{265}}}}$
So, ${{{V}}_2}{{ = }}\dfrac{{{{300 \times 265}}}}{{{{300}}}}{{ = 265}}$
The final volume is ${{265ml}}$.

So, the correct answer is Option C.

Additional Information:
Derivation of Combined Gas Law:
Boyle’s Law ${{PV = K}}$,
Charles Law $\dfrac{{{V}}}{{{T}}}{{ = K}}$,
and Gay- Lussac’s Law $\dfrac{{{P}}}{{{T}}}{{ = K}}$
Since Combined Gas Law is the combination of these three laws, the formula for combined gas law is $\dfrac{{{{PV}}}}{{{T}}}{{ = K}}$ where ${{P}}$ = pressure, ${{T}}$= temperature, ${{V}}$ = volume and ${{K}}$ is constant.

Note: The temperature should always be in kelvin for the purpose of calculation. So, if the units are given in Celsius scale, it must be converted to kelvin by adding ${
{273}}$ to a particular unit. We can adjust the formula of the Combined Gas Law to compare two different conditions in one substance.