# Question #932eb

Apr 23, 2015

The new pressure must be 238 torr.

You have two parameters that remain constant after the change is made - temperature and number of moles.

Since only pressure and volume will be changed, you can use Boyle's Law to solve for the pressure needed to get your sample from 190. mL. to 600. mL.

According to Boyle's Law, an ideal gas' pressure and volume have an inverse relationship when temperature and number of moles are kept constant.

In other words, the higher the pressure, the smaller the volume. LIkewise, the lower the pressure, the bigger the volume.

Mathematically, this is written as

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$, where

${P}_{1}$, ${V}_{1}$ - the pressure and temperature of a gas at an initial state;
${P}_{2}$, ${V}_{2}$ - the pressure and temperature of a gas at a final state.

So, you know the initial volume and pressure, and the final volume, which means that you can solve for the final pressure by

${P}_{2} = {V}_{1} / {V}_{2} \cdot {P}_{1}$

${P}_{2} = \left(\text{190."cancel("mL"))/("600."cancel("mL")) * "750. torr" = color(green)("238 torr}\right)$

Notice that the magnitude of the final pressure is given by the ratio between the two volumes.

Since ${V}_{1} / {V}_{2} < 1$ (volume increases), you have ${P}_{2} < {P}_{1}$ (pressure decreases). Likewise, if

${V}_{1} / {V}_{2} > 1$ (volume decreases), then ${P}_{2} > {P}_{1}$ (pressure increases).