# What is the volume occupied by a mole of an ideal gas, if the pressure is 626 mm Hg and the temperature is 25.0 degrees Celsius?

May 31, 2018

$V = \text{29.7 L}$

#### Explanation:

We can use the Ideal Gas Law to calculate the volume:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange the Ideal Gas Law to get

$V = \frac{n R T}{p}$

In this problem,

$n = \text{1 mol}$
R = (25.0 + 273.15) K = 298.15 K"

p = 626 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760color(red)(cancel(color(black)("mmHg")))) = "0.8237 atm"

V = (1 color(red)(cancel(color(black)("mol"))) × "0.082 06 L"·color(red)(cancel(color(black)("atm"·"K"^"-1"·"mol"^"-1"))) × 298.15 color(red)(cancel(color(black)("K"))))/(0.8237 color(red)(cancel(color(black)("atm")))) = "29.7 L"