Calculate the number of atoms and volume of 1 gallon of helium gas at stp.

Monday, February 13, 2012

Calculate the number of atoms and volume of 1 gallon of helium gas at stp.

Hello!

STP means standard temperature and pressure. Denote the temperature as $\displaystyle{T}$ (in Kelvin) and the pressure as $\displaystyle{P}.$ They may be different for different standards.

The formula we need is $\displaystyle{P}{V}={n}{R}{T},$ where $\displaystyle{V}$ is the volume of a gas, $\displaystyle{n}$ is the number of moles and $\displaystyle{R}$ is the ideal gas constant, about $\displaystyle{8.3}\frac{{J}}{{{m}{o}{l}\cdot{K}}}.$ The volume is also given, it is $\displaystyle{1}{g{{a}}}{l}{l}{o}{n}\approx{3.8}\cdot{{10}}^{{-{3}}}{{m}}^{{3}}.$

From all this data we can find the quantity of helium in moles: $\displaystyle{n}=\frac{{{P}{V}}}{{{R}{T}}}.$ The number of atoms in each mole is a constant called Avogadro's constant, $\displaystyle{N}_{{A}}\approx{6}\cdot{{10}}^{{{23}}}{{\left({m}{o}{l}\right)}}^{{-{1}}},$ so the number of atoms is $\displaystyle{n}\cdot{N}_{{A}}=\frac{{{P}{V}}}{{{R}{T}}}\cdot{N}_{{A}}.$

Let $\displaystyle{T}={273}{K}$ and $\displaystyle{P}={{10}}^{{5}}{P}{a},$ then the number of atoms is about

$\displaystyle\frac{{{{10}}^{{5}}\cdot{3.8}\cdot{{10}}^{{-{3}}}\cdot{6}\cdot{{10}}^{{{23}}}}}{{{8.3}\cdot{273}}}\approx{0.01}\cdot{{10}}^{{{25}}}={{10}}^{{23}}.$

This is the answer.

Ninenotes

Monday, February 13, 2012

Calculate the number of atoms and volume of 1 gallon of helium gas at stp.

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