# Question d42dd

Jun 29, 2017

$\text{2 L}$

#### Explanation:

The thing to remember here is that every time the temperature of a gas and the number of moles of gas are kept constant, the pressure and the volume of the gas have an inverse relationship described by Boyle's Law.

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

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

In your case, the pressure of the gas is increasing

$\text{118 kPa " -> " 214 kPa}$

so you should expect the volume of the gas to decrease

$\text{4 L } > \textcolor{w h i t e}{.} {V}_{2}$

Rearrange the equation to solve for ${V}_{2}$

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

Plug in your values to find

V_2 = (118 color(red)(cancel(color(black)("kPa"))))/(214color(red)(cancel(color(black)("kPa")))) * "4 L" = color(darkgreen)(ul(color(black)("2 L")))#

The answer must be rounded to one significant figure, the number of sig figs you have for the initial volume of the gas.