# A sample of a gas has a volume of 2.0 liters at a pressure of 1.0 atmosphere. What will the pressure be when the volume increases to 4.0 liters at constant temperature?

Jun 12, 2017

$\text{0.50 atm}$

#### Explanation:

The idea here is that the pressure of a gas and the volume it occupies have an inverse relationship when the temperature and the number of moles of gas, i.e. the amount of gas present in the sample, remain constant $\to$ this is known as Boyle's Law. Simply put, when the temperature and the number of moles of gas are constant, a decrease in the volume of the gas will cause an increase in its pressure and an increase in the volume of the gas will cause a decrease in its pressure.

In your case, you know that the volume is increasing

$\text{2.0 L " -> " 4.0 L}$

so you should expect the volume to decrease

${\text{1.0 atm " > " P}}_{2}$

Your tool of choice here will be this equation

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}}}}$

Here

• ${P}_{1}$ and ${V}_{1}$ represent the pressure and volume of the gas at an initial state
• ${P}_{2}$ and ${V}_{2}$ represent the pressure and volume of the gas at a final state

Rearrange to solve for ${P}_{2}$

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

and plug in your values to find

V_2 = (2.0 color(red)(cancel(color(black)("L"))))/(4.0color(red)(cancel(color(black)("L")))) * "1.0 atm" = color(darkgreen)(ul(color(black)("0.50 atm")))

The answer is rounded to two sig figs.