# Question #e8fd6

Apr 5, 2017

Using Boyle's Law (from the combined Ideal Gas Law), we find that the new volume is 1.409 liters. (See explanation)

#### Explanation:

We can solve this by using a variation of the Ideal Gas Law (PV = nRT). This variation is the combined Ideal Gas Law:

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$, which allows us to compare the changes made to pressure, volume, and temperature.

Since temperature is constant, ${T}_{1} = {T}_{2}$, so our new comparison would be: (Boyle's Law)

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

We need to find the new volume, ${V}_{2}$, so we rearrange the equation:
${V}_{2} = \frac{{P}_{1} {V}_{1}}{P} _ 2$

These are the values we have:
${V}_{1} = 3$ L
${P}_{1} = 101$ kPa
${P}_{2} = 215$ kPa

Plug in and solve:
${V}_{2} =$ $\frac{\left(101 k P a\right) \left(3 L\right)}{215 k P a} = 1.409 L$