# Question 68dd9

Mar 18, 2016

$\text{3300 torr}$

#### Explanation:

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

When this is the case, pressure and volume have an inverse relationship - this is known as Boyle's Law.

Simply put, when pressure increases, volume decreases, and when pressure decreases, volume increases. This means that right from the start, you can look at the fact that the volume of the gas decreases and say that the pressure must increase.

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

Rearrange to solve for the pressure of the gas at the final state, ${P}_{2}$

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

Plug in your values to get

P_2 = (6.00 color(red)(cancel(color(black)("L"))))/(1.40color(red)(cancel(color(black)("L")))) * "760 torr" = "3257.1 torr"#

Rounded to two sig figs, the number of sig figs you have for the initial pressure of the gas, the answer will be

${P}_{2} = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{3300 torr} \textcolor{w h i t e}{\frac{a}{a}} |}}}$