# A 89.9 g sample of dinitrogen monoxide is confined in a 3.65-L vessel. What is the pressure (in atm) at 110 degrees Celsius?

Nov 10, 2015

$\text{18 atm}$

#### Explanation:

All you have to do here is use nitrous oxide's molar mass to determine how many moles you have in that sample, then use the ideal gas law equation to find its pressure.

Nitrous oxide, $\text{N"_2"O}$, has a molar mass of $\text{44.013 g/mol}$. This tells you that one mole of nitrous oxide will have a mass of $\text{44.013 g}$. In your case, that sample of nitrous oxide will contain

89.9color(red)(cancel(color(black)("g"))) * ("1 mole N"_2"O")/(44.013color(red)(cancel(color(black)("g")))) = "2.043 moles N"_2"O"

Now, the ideal gas law equation looks like this

$\textcolor{b l u e}{P V = n R T} \text{ }$, where

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas
$R$ - the universal gas constant, equal to $0.082 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the temperature of the gas - expressed in Kelvin

Plug in your values and solve for $P$ - make sure that you convert the temperature from degrees Celsius to Kelvin

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

$P = \left(2.043 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * 0.082("atm" * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 110)color(red)(cancel(color(black)("K"))))/(3.65color(red)(cancel(color(black)("L}}}}\right)$

$P = \text{17.59 atm}$

Rounded to two sig figs, the number of sig figs you have for the temperature of the gas, the answer will be

$P = \textcolor{g r e e n}{\text{18 atm}}$