# If a gas sample in a balloon had a volume of 100 and a pressure of 3 atm. It mL was then compressed to a pressure of 10 atm, what would be its volume?

May 12, 2017

The final volume of the gas will be $\text{30 mL}$.

#### Explanation:

Boyle's gas law will allow us to find the answer. Boyle's law states that the volume of a given amount of gas varies inversely with the applied pressure, as long as temperature and mass are held constant. The equation for this law is:

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

Given
${P}_{1} = \text{3 atm}$
${V}_{1} = \text{100 mL}$
${P}_{2} = \text{10 atm}$

Unknown: ${V}_{2}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Insert the given data and solve.

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

V_2=(3color(red)cancel(color(black)("atm"))xx100"mL")/(10color(red)cancel(color(black)("atm")))="30 mL"