# Question 2ed61

Oct 26, 2015

$\text{0.18 g}$

#### Explanation:

The idea here is that you need to use the molar volume of a gas at STP to determine what the molar mass of nitrogen gas is.

Next, you meed to use the ideal gaas law equation to find how many moles of nitrogen gas you have in that volume and at those specific conditions for pressue and temperature.

So, at STP, or Standard Temperature and Pressure, one mole of any ideal gas occupies exactly $\text{22.7 L}$ - this is known as the molar volume of a gas at STP.

This means that if $\text{28 g}$ of nitrogen gas occupy $\text{22.7 L}$ at STP, then you can say that the molar mass of nitogen gas is $\text{28 g/mol}$.

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
$V$ - its volume
$n$ - the number of moles of gas
$R$ - the universal gas constant, usually given as $0.082 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the temperature of the gas, expressed in Kelvin!

You need to find the mass of sample of nitrogen gas that

• occupies a volume of $\text{5.6 L}$
• has a pressure of $\text{38 mmHg}$
• has a temperature of ${273}^{\circ} \text{C}$

Plug in your values and solve the ideal gas law equation for $n$ - do not forget to convert the pressure from mmHg to atm and the temperature from degrees Celsius to Kelvin!

$n = \left(\frac{38}{760} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))) * 5.6color(red)(cancel(color(black)("L"))))/(0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 273)color(red)(cancel(color(black)("K}}}}\right)$

$n = \text{0.00625 moles}$

Now use nitrogen's molar mass to determine how many grams would contain this many moles

0.00625color(red)(cancel(color(black)("moles"))) * "28 g"/(1color(red)(cancel(color(black)("mole")))) = color(green)("0.18 g")#