# A sample of gas has a volume of 200 mL at a pressure of 700 mm Hg. What will be its pressure if its volume is reduced to 100 mL?

Nov 19, 2015

The new pressure will be $\text{1000 L}$, rounded to one significant figure.

#### Explanation:

Boyle's law states that when a gas is held at a constant temperature and mass in a closed container, the volume and pressure vary inversely. The equation to use is ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

Given
${V}_{1} = 200 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.2 L}}$
${P}_{1} = \text{700 mmHg}$
${V}_{2} = 100 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.1 L}}$

Unknown
${P}_{2}$

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

Solution
Rearrange the equation to isolate ${P}_{2}$ and solve.

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

P_2=((700"mmHg"xx0.2cancel"L"))/(0.1cancel"L")="1400 L", which must be rounded to $\text{1000 L}$ because all of the measurements have only one significant figure.
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