# Question 20ca9

Jul 16, 2015

Volume: 1.8 L.

#### Explanation:

In order to determine the volume occupies by your sample of carbon dioxide gas, you need to use the ideal gas law equation

$P V = n R T$, where

$P$ - the pressure of the gas;
$V$ - the volume it occupies;
$n$ - the number of moles of gas;
$R$ - the ideal gas constant, expressed in atm L/mol K;
$T$ - the temperature of the gas, expressed in Kelvin.

Before using the ideal gas law equation, use carbon dioxide's molar mass to determine how many moles of gas you have in your 2.5-g sample

2.5cancel("g") * ("1 mole "CO_2)/(44.01cancel("g")) = "0.0568 moles"# $C {O}_{2}$

So, isolate the volume of the gas on one side of the equation and plug in your values - do not forget to convert the presure to atm and the temperature to Kelvin!

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

${V}_{C {O}_{2}} = \left(0.0568 \cancel{\text{moles") * 0.082(cancel("atm") * "L")/(cancel("mol") cancel("K")) * (273.15 + 77)cancel("K"))/(700/760cancel("atm}}\right)$

${V}_{C {O}_{2}} = \text{1.771 L}$

I'll leave the answer rounded to two sig figs, despite the fact you only gave one sig fig for the pressure of the sample

${V}_{C {O}_{2}} = \textcolor{g r e e n}{\text{1.8 L}}$