Question

A gas has a volume of 22.4 L at 0.853 atm. What pressure is needed to change the volume to 24.0L?

Answer 1

The pressure needed to change the volume to 24 L is 0.796 atm.

Explanation:

It is known by Boyle's law that the pressure experienced by the gas molecules will be inversely proportional to the volume occupied by the molecules.

$P =\frac{1}{V}$

So as the initial volume is said to be 22.4 L, consider it as V₁ = 22.4 L. Then the initial pressure is said to be 0.853 atm, so P₁ = 0.853 atm. So we have to determine the new pressure P₂ when the volume is changed to V₂ = 24 L.  As there is increase in the volume, the pressure should be decreased due to Boyle's law. Thus, as per Boyle's law, the two pressures and their volumes can be related as

$P_{1} V_{1} = P_{2} V_{2}$

$0.853*22.4 = P_{2}*24\\\\P_{2} = \frac{0.853*22.4}{24} = 0.796 atm$

Thus, the pressure gets decreased to 0.796 atm on increase in the volume to 24 L.

So the pressure needed to change the volume to 24 L is 0.796 atm.