Question

Neon gas has a volume of $2000$mL with an atm of $1.8$, however if the pressure decreases to $1.3$ atm. What is now the volume of the neon gas?

Answer 1

Hint:To answer this question we should know the gases law, Boyle’s law. According to this law, at constant temperature, the pressure of the ideal gas is inversely proportional to the volume of the gas. We will compare Boyle's equation in two different conditions. Then by substituting all values we can determine the volume of the neon gas.

Complete solution:
The temperature is not given, so we assume that the temperature of the neon is not changing.
At constant temperature Boyle’s law gives the relation between pressure and volume.
According to Boyle’s law, at constant T, \[{\text{p}} \propto \dfrac{{\text{1}}}{{\text{V}}}\]
The relation between pressure and volume at two different condition is as follows:
${{\text{p}}_{\text{1}}}{{\text{V}}_{\text{1}}}\, = \,{{\text{p}}_2}{{\text{V}}_2}$
Where,
${{\text{p}}_{\text{1}}}$is the initial pressure
${{\text{V}}_{\text{1}}}$is the initial volume
${{\text{p}}_2}$is the final pressure
${{\text{V}}_2}$is the final volume
On substituting for$1.8$ atm ${{\text{p}}_{\text{1}}}$, $2000$mL for${{\text{V}}_{\text{1}}}$, and $1.3$atm for ${{\text{p}}_2}$,
${\text{1}}{\text{.8}}\,{\text{atm}}\, \times 2000\,{\text{ml}}\, = \,{\text{1}}{\text{.3}}\,{\text{atm}}\, \times {{\text{V}}_2}$
\[{{\text{V}}_2}\, = \,\,\dfrac{{{\text{1}}{\text{.8}}\,{\text{atm}}\, \times 2000\,{\text{ml}}\,}}{{\,{\text{1}}{\text{.3}}\,{\text{atm}}\,}}\,\]
\[{{\text{V}}_2}\, = \,\,\dfrac{{3600\,{\text{ml}}\,}}{{\,{\text{1}}{\text{.3}}\,\,}}\,\]
\[{{\text{V}}_2}\, = \,\,2769.23\,{\text{ml}}\,\]
So, the volume of the neon gas is \[2769.23\]ml.
Therefore, \[2769.23\]ml is the correct answer.

Note:The ideal gas equation is, ${\text{pV}}\,{\text{ = }}\,{\text{nRT}}$. Ideal gas law is a combination of three laws. Boyle law, according to that at constant temperature, pressure is inversely proportional to the volume. Charles’s law, at constant pressure, volume is directly proportional to the temperature. Avogadro’s law, according to that at constant temperature and pressure, volume is directly proportional to the number of moles. If we had temperature change also then we will use combined gas law. For the same gas with same number of moles, the R and n become constant so, we can write the ideal as equation as $\dfrac{{{\text{pV}}}}{{\text{T}}}\,{\text{ = }}\,{\text{nR}}$. When we compare this equation at two different conditions then we get $\dfrac{{{{\text{p}}_{\text{1}}}{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}}\, = \,\dfrac{{{{\text{p}}_2}{{\text{V}}_2}}}{{{{\text{T}}_2}}}$, that is a combined gas law.