# Question bc2ab

Nov 20, 2015

$\text{4.6 L}$

#### Explanation:

The idea here is that keeping the temperature and the number of moles of gas constant will allow you to use Boyle's Law to calculate how the volume of the gas will change following that increase in pressure.

As you know, Boyle's Law states that when temperature and number of moles of gas are kept constant, pressure and volume have an inverse relationship.

Simply put, when pressure increases, volume decreases, and when pressure decreases, volume increases. Mathematically, Boyle's Law can be written like this

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

Plug your values and solve this equation for ${V}_{2}$, but do not forget to convert the final pressure from mmHg to atm by using the conversion factor

$\text{1 atm " = " 760 mmHg}$

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

V_2 = (1.50color(red)(cancel(color(black)("atm"))))/(1240/760color(red)(cancel(color(black)("atm")))) * "5.0 L" = color(green)("4.6 L")#

Notice how the volume decreased as a result of the increase in pressure.