Editing Stoichiometry (section)

== Gas stoichiometry ==
''Gas stoichiometry'' is the quantitative relationship (ratio) between reactants and products in a [[chemical reaction]] with reactions that produce [[gases]]. Gas stoichiometry applies when the gases produced are assumed to be [[ideal gas|ideal]], and the temperature, pressure, and volume of the gases are all known. The ideal gas law is used for these calculations. Often, but not always, the [[standard temperature and pressure]] (STP) are taken as 0&nbsp;°C and 1 bar and used as the conditions for gas stoichiometric calculations.

Gas stoichiometry calculations solve for the unknown [[volume]] or [[mass]] of a gaseous product or reactant. For example, if we wanted to calculate the volume of gaseous {{chem2|NO2}} produced from the combustion of 100&nbsp;g of {{chem2|NH3}}, by the reaction:
: {{chem2|4 NH3 (g) + 7 O2 (g) -> 4 NO2 (g) + 6 H2O (l)}}
we would carry out the following calculations:
: <math>100\, \mathrm{g\, NH_3}\cdot\frac{1\, \mathrm{mol\, NH_3}}{17.034\, \mathrm{g\, NH_3}}=5.871\, \mathrm{mol\, NH_3} </math>

There is a 1:1 molar ratio of {{chem2|NH3}} to {{chem2|NO2}} in the above balanced combustion reaction, so 5.871&nbsp;mol of {{chem2|NO2}} will be formed. We will employ the [[ideal gas law]] to solve for the volume at 0&nbsp;°C (273.15&nbsp;K) and 1 atmosphere using the [[gas constant|gas law constant]] of ''R''&nbsp;=&nbsp;0.08206 L·atm·K<sup>−1</sup>·mol<sup>−1</sup>:
: <math>\begin{align}
PV&= nRT\\
V&= \frac{nRT}{P}\\
&= \frac{5.871\text{ mol}\cdot 0.08206\,\frac{\mathrm{L\cdot atm}}{\mathrm{mol\cdot K}}\cdot 273.15\text{ K}}{1\text{ atm}}\\
&= 131.597\, \mathrm{L\, NO_2}
\end{align}</math>

Gas stoichiometry often involves having to know the [[molar mass]] of a gas, given the [[density]] of that gas. The ideal gas law can be re-arranged to obtain a relation between the [[density]] and the [[molar mass]] of an ideal gas:
: <math>\rho = \frac{m}{V}</math> &nbsp;&nbsp; and &nbsp;&nbsp; <math>n = \frac{m}{M}</math>
and thus:
: <math>\rho = \frac {M P}{R\,T}</math>
where:
* ''P''&nbsp;= absolute gas [[pressure]]
* ''V''&nbsp;= gas [[volume]]
* ''n''&nbsp;= amount (measured in [[mole (unit)|moles]])
* ''R''&nbsp;= universal ideal gas law constant
* ''T''&nbsp;= absolute gas [[temperature]]
* ''ρ''&nbsp;= gas density at ''T'' and ''P''
* ''m''&nbsp;= mass of gas
* ''M''&nbsp;= molar mass of gas