# Question e70ce

Apr 19, 2016

$\text{1540 mL}$

#### Explanation:

Notice that the problem doesn't mention temperature or number of moles of gas, which means that they are being kept constant.

When that is the case, volume and pressure have an inverse relationship described by Boyle's Law.

Boyle's Law tells you that when pressure Increases, volume decreases, and when pressure decreases, volume increases.

Mathematically, this is expressed as

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {P}_{1} {V}_{1} = {P}_{2} {V}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$, where

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

In your case, the pressure decreases from $4.4$ atm to $1.0$ atm, which means that you should expect the volume of the gas to increases.

Rearrange the above equation and 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 get

V_2 = (4.4 color(red)(cancel(color(black)("atm"))))/(1.0color(red)(cancel(color(black)("atm")))) * "350 mL" = color(green)(|bar(ul(color(white)(a/a)"1540 mL"color(white)(a/a)|)))#

The answer is rounded to three sig figs.