The Ideal Gas Law is a fundamental equation in chemistry that relates pressure, volume, temperature, and the number of moles of a gas. It is expressed as:
\[PV = nRT\]
Where:
In stoichiometric calculations, the Ideal Gas Law helps us determine the amounts of reactants and products in gaseous reactions. Here are three practical examples.
In a laboratory experiment, 5 grams of propane (C₃H₈) is completely combusted in a closed container, producing carbon dioxide (CO₂) and water (H₂O). To find the moles of CO₂ produced, we first need to determine the balanced reaction:
\[C₃H₈ + 5O₂ → 3CO₂ + 4H₂O\]
From the balanced equation, we see that 1 mole of propane produces 3 moles of carbon dioxide. The molar mass of propane is approximately 44.1 g/mol.
First, calculate the moles of propane:
\[n_{C₃H₈} = \frac{mass}{molar \ mass} = \frac{5 g}{44.1 g/mol} ≈ 0.113 mol\]
Using the stoichiometric ratio, we can find the moles of CO₂ produced:
\[n_{CO₂} = 0.113 mol \times \frac{3 mol \ CO₂}{1 mol \ C₃H₈} ≈ 0.339 mol\]
Notes: This example demonstrates how to apply stoichiometry in conjunction with the Ideal Gas Law to find the amount of a product formed during a reaction.
Consider a reaction where 4 moles of ammonia (NH₃) decompose at a temperature of 300 K and a pressure of 2 atm. The reaction is:
\[2NH₃(g) → N₂(g) + 3H₂(g)\]
To find the volume of gas produced (N₂ and H₂), we first determine the total moles of gas produced:
From the balanced equation, 2 moles of NH₃ yield 1 mole of N₂ and 3 moles of H₂:
Total moles produced = 1 (N₂) + 3 (H₂) = 4 moles.
Now, we can apply the Ideal Gas Law to find the volume:
Using the equation: \[V = \frac{nRT}{P}\]
Substituting the values:
\[V = \frac{4 mol \times 0.0821 L·atm/(K·mol) \times 300 K}{2 atm} ≈ 49.26 L\]
Notes: This example illustrates how to use the Ideal Gas Law to determine the volume of gases produced in a reaction, showcasing practical stoichiometric calculations.
Suppose you have a container that holds a mixture of 2 moles of nitrogen gas (N₂) and 1 mole of oxygen gas (O₂) at a temperature of 350 K. To find the total pressure exerted by the gas mixture, we can use the Ideal Gas Law, keeping in mind that the total number of moles is:
Total moles, n = 2 (N₂) + 1 (O₂) = 3 moles.
Now we can calculate the total pressure using the Ideal Gas Law:
\[P = \frac{nRT}{V}\]
Assuming the volume of the container is 10 L:
\[P = \frac{3 mol \times 0.0821 L·atm/(K·mol) \times 350 K}{10 L} ≈ 8.65 atm\]
Notes: This example highlights how to calculate the pressure of a gas mixture using the Ideal Gas Law, emphasizing the importance of understanding the behavior of multiple gas types in a single system.