# Question fe72d

Mar 9, 2016

$\text{510 mmHg}$

#### Explanation:

Pressure and volume have an inverse relationship when temperature and number of moles of gas are kept constant - this is known as Boyle's Law.

As you know, gas pressure is caused by the collisions that take place between the molecules of gas and the walls of the container.

When you increase the volume of gas while keeping the average kinetic speed of its molecules, i.e. the temperature, constant, you essentially reduce the frequency with which the gas particles collide with the walls of the container.

Since the molecules are not hitting the walls of the container as often as they did before you increased the volume, you can say that the pressure will decrease. So, when volume increases, pressure decreases, and when volume decreases, pressure increases.

Mathematically, this is written 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 the equation to solve for ${P}_{2}$

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

Plug in your values to get

P_2 = (2.00color(red)(cancel(color(black)("L"))))/(3.00color(red)(cancel(color(black)("L")))) * "761 mmHg" = "507.33 mmHg"#

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

${P}_{2} = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{510 mmHg} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

As predicted by Boyle's Law, an increase in volume resulted in a decrease in pressure.