# Question 43d81

May 23, 2017

$5.48 \times {10}^{5} \text{mL}$

#### Explanation:

We'll be using the pressure-volume relationship of gases illustrated by Boyle's law:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Solving for ${V}_{2}$:

${V}_{2} = \frac{{P}_{1} {V}_{1}}{{P}_{2}}$

We need to have consistent units for the pressure, so let's convert the $575 \text{mm Hg}$ to atmospheres:

575cancel("mmHg")((1"atm")/(760cancel("mmHg"))) = 0.757"atm"

Plugging in known variables, the final volume, in $\text{mL}$, is

V_2 = ((0.757cancel("atm"))(1.00 xx 10^6 "mL"))/(1.38cancel("atm")) = color(red)(5.48 xx 10^5"mL"#