# Gas Stoichiometry

## Gas Stoichiometry

At standard temperature and pressure, one mole of any gas will occupy a volume of 22.4 L.### Learning Objectives

Calculate volumes of gases consumed/produced in a reaction using gas stoichiometry.### Key Takeaways

#### Key Points

- At Standard Temperature and Pressure (STP), 1 mole of any gas will occupy a volume of 22.4 L.
- The Ideal Gas Law, along with a balanced chemical equation, can be used to solve for the amount, either in volume or mass, of gas consumed or produced in a chemical reaction.

#### Key Terms

**stoichiometry**: the study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations)

### Stoichiometric Calculations Involving Ideal Gases at STP

Stoichiometric calculations involving gases allow us to convert between mass, number of moles, and most importantly,*volume*of gases. The following relationship makes this possible:

- 1 mole of
*any*gas at standard temperature and pressure (273 K and 1 atm) occupies a volume of 22.4 L.

While the above relationship is an estimation, it is a relatively good approximation at STP, and can be used reliably in calculations.

### Example

$4\;NH_3(g)+7\;O_2(g)\rightarrow4\;NO_2(g)+6\;H_2O(l)$

- According to the above reaction, what volume of NO
_{2}(*g*) is produced from the combustion of 100 g of NH_{3}(*g*), assuming the reaction takes place at standard temperature and pressure? - From the periodic table, we can determine that the molar mass of ammonia, NH
_{3}(*g*), is 17 g/mol, and perform the following stoichiometric calculation: - $\left(\frac{\text{100 g }NH_3}{ }\right)\times\left(\frac{\text{1 mol }NH_3}{\text{17 }g}\right)\times \left(\frac{\text{4 mol }NO_2}{\text{4 mol }NH_3}\right)\times \left(\frac{\text{22.4 }L}{\text{1 mol }NO_2}\right)=\text{132 L }NO_2(g)$

Note the final conversion factor. Because we are told that the reaction takes place at STP, we can relate volume, 22.4 L, to 1 mol NO

_{2}.