# How many grams of helium are contained in a "2.0-L" balloon at 30.0^@"C" and at "735 mmHg" ?

Dec 20, 2017

$\text{0.31 g}$

#### Explanation:

The idea here is that you can use the ideal gas law equation to find the number of moles of helium present in your sample and the molar mass of the gas to convert that to grams.

You could also rewrite the ideal gas law equation in terms of the mass of helium present in the sample to get the answer directly.

So, you know that the ideal gas law equation looks like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{P V = n R T}}}$

Here

• $P$ is the pressure of the gas
• $V$ is the volume it occupies
• $n$ is the number of moles of gas present in the sample
• $R$ is the universal gas constant, equal to $0.0821 \left(\text{atm L")/("mol K}\right)$
• $T$ is the absolute temperature of the gas

You also know that the mass of the gas, let's say $m$, can be expressed in terms of its molar mass, let's say ${M}_{M}$, and the number of moles.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{m = \frac{n}{M} _ M}}}$

This means that you can rewrite the ideal gas law equation as

$P V = \frac{m}{M} _ M \cdot R T$

Rearrange to solve for $m$

$m = {\overbrace{\frac{P V}{R T}}}^{\textcolor{b l u e}{\text{the number of moles}}} \cdot {M}_{M}$

Finally, plug in your values to find the mass of the sample--do not forget to convert the temperature from degrees Celsius to Kelvin and the pressure from mmHg to atmospheres!

m = ( 735/760 color(red)(cancel(color(black)("atm"))) * 2.0color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (30.0 + 273.15)color(red)(cancel(color(black)("K")))) * "4.003 g" color(red)(cancel(color(black)("mol"^(-1))))

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{m = \text{0.31 g}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the volume of the gas.