Using the ideal gas formula, calculate the volume of 1.50 moles of a gas at 115 kPA and a temperature of 298K?

using the ideal gas formula, calculate the volume of 1.5omoles of a gas at 115kPA and a temperature of 298k?

Mar 17, 2016

$\text{32.3 L}$

Explanation:

This is a pretty straightforward ideal gas law equation practice problem, so make sure that you're familiar with the aforementioned ideal gas law equation

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

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas
$R$ - the universal gas constant, usually given as $0.0821 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the absolute temperature of the gas

Now, the most important thing to do at this point is make sure that the units given to you match those used in the expression of the ideal gas constant.

As you can see, the pressure of the gas is given to you in kPa, but you actually need it to be expressed in atm. This means that you're going to have to convert it by using the conversion factor

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 atm " = " 101.325 kPa}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Rearrange the ideal gas law equation to solve for $V$, the volume of the gas

$P V = n R T \implies V = \frac{n R T}{V}$

Plug in your values to get

V = (1.50color(red)(cancel(color(black)("moles"))) * 0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 298color(red)(cancel(color(black)("K"))))/(115/101.325color(red)(cancel(color(black)("atm")))) = color(green)(|bar(ul(color(white)(a/a)"32.3 L"color(white)(a/a)|)))

The answer is rounded to three sig figs.