# Question 1df7b

Dec 11, 2015

$\text{2.1 L}$

#### Explanation:

As you know, pressure and volume have an inverse relationship when number of moles and temperature are kept constant - this is known as Boyle's Law.

That happens because gas pressure is caused by the collisions between the gas molecules and the walls of the container.

If temperature, which is actually a measure of the average kinetic energy of the gas molecules, is kept constant, increasing the volume of the container will result in less frequent collisions.

Simply put, the molecules will have more room to move about in, so they won't hit the walls of the container as often $\to$ pressure will decrease.

Likewise, decreasing the volume means giving the molecules less room to move in. As a result, they'll hit the walls of the container more often $\to$ pressure will increase.

Mathematically, this is expressed as

$\textcolor{b l u e}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}} \text{ }$, 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

Notice that in your case, the pressure of the gas increased from $\text{3.0 atm}$ to $\text{7.0 atm}$. This tells you that the volume must have decreased in the process.

Plug in your values and solve for ${V}_{2}$ to confirm that this is indeed the case

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

V_2 = (3.0 color(red)(cancel(color(black)("atm"))))/(7.0color(red)(cancel(color(black)("atm")))) * "5.0 L" = color(green)("2.1 L")#

The answer is rounded to two sig figs.