Ideal Gas Law Applications in Chemistry

Understanding the Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas. This equation is fundamental in chemistry, particularly in calculating the behavior of gases during chemical reactions. Below are three practical examples that illustrate how the Ideal Gas Law is applied in chemical reactions.

Example 1: Calculating Gas Volume in a Reaction

In a laboratory setting, a chemist is studying the reaction between sodium bicarbonate (baking soda) and acetic acid (vinegar). This reaction produces carbon dioxide gas, which can be measured to understand the reaction’s efficiency.

To find out the volume of carbon dioxide produced at a specific temperature and pressure, the chemist uses the Ideal Gas Law.

Assuming the reaction produces 0.5 moles of CO2 at a temperature of 298 K and a pressure of 1 atm:

• Given:
  • n (moles of gas) = 0.5
  • R (ideal gas constant) = 0.0821 L·atm/(K·mol)
  • T (temperature) = 298 K
  • P (pressure) = 1 atm

Using the Ideal Gas Law:

PV = nRT
V = nRT / P
V = (0.5 mol) * (0.0821 L·atm/(K·mol)) * (298 K) / (1 atm)
V = 12.3 L

Thus, the volume of carbon dioxide gas produced is 12.3 liters under the given conditions.

Notes:

• Variations in temperature or pressure will affect the volume calculated.
• This method can be applied to various gas-producing reactions.

Example 2: Determining Moles of Gas Produced

A chemical reaction involving the decomposition of ammonium nitrate (NH4NO3) into nitrogen gas (N2), water vapor (H2O), and oxygen gas (O2) is carried out in a closed container. The chemist needs to determine how many moles of gas are produced when the reaction is complete.

For this example, let’s assume the reaction occurs at 300 K and a pressure of 2 atm, and the total volume of the container is 10 L.

Using the Ideal Gas Law:

PV = nRT
n = PV / RT
n = (2 atm) * (10 L) / (0.0821 L·atm/(K·mol) * 300 K)
n = 0.81 moles

This means that approximately 0.81 moles of gas are produced in this reaction.

Notes:

• The Ideal Gas Law is most accurate for gases at low pressures and high temperatures.
• Understanding the stoichiometry of the reaction is essential for accurate calculations.

Example 3: Predicting Pressure Change in a Reaction

A chemist is investigating a reaction that generates hydrogen gas (H2) from the electrolysis of water. The setup is in a sealed container, and the chemist wants to predict how the pressure changes as the temperature increases during the reaction.

Initially, the container holds 1 mole of gas at a temperature of 310 K with a volume of 2 L. They wish to understand how pressure will change if the temperature rises to 350 K.

Using the Ideal Gas Law:

1. Calculate initial pressure:

   • P1 = nRT / V
   • P1 = (1 mol) * (0.0821 L·atm/(K·mol)) * (310 K) / (2 L)
   • P1 = 12.76 atm

2. Calculate final pressure at 350 K:

   • P2 = nRT / V
   • P2 = (1 mol) * (0.0821 L·atm/(K·mol)) * (350 K) / (2 L)
   • P2 = 14.34 atm

The pressure increases from 12.76 atm to 14.34 atm as the temperature rises.

Notes:

• This example illustrates the direct relationship between temperature and pressure in gases.
• Real gases may deviate from ideal behavior at high pressures or low temperatures.