Ideal gas law formula

The ideal gas law formula, which is expressed as P V = n R T, provides a relationship between the pressure, volume, temperature, and the number of moles of a given quantity of gas. In this formula, P represents pressure, V represents volume, n represents the number of moles, T represents temperature, and R represents the gas constant. This formula is widely used in physics and chemistry to calculate the properties of gases under different conditions.

Contents

Practice problems

Problem #1

Find the number of moles of hydrogen gas in a cylinder with a volume of 4 L, pressure of 2 atm, and temperature of 30 ℃. Use the ideal gas constant value, R = 0.0821 L atm/mol K.

Solution

Given data:

• Number of moles of the gas, n = ?
• Volume of the gas, V = 4 L
• Pressure of the gas, P = 2 atm
• Temperature of the gas, T = 30 ℃ = 303 K
• Ideal gas constant, R = 0.0821 L atm/mol K

Applying the formula:

• P V = n R T
• 2 × 4 = n × 0.0821 × 303
• 8 = n × 24.8763
• n = 0.32 mol

Therefore, the number of moles of the gas is 0.32 mol.

Problem #2

A rubber tire has 0.45 moles of air at a pressure of 12 atm and a temperature of 25 ℃. Calculate the volume of air in the tire. Use the ideal gas constant value, R = 0.0821 L atm/mol K.

Solution

Given data:

• Number of moles of the air, n = 0.45 mol
• Pressure of the air, P = 12 atm
• Temperature of the air, T = 25 ℃ = 298 K
• Volume of the air, V = ?
• Ideal gas constant, R = 0.0821 L atm/mol K

Applying the formula:

• P V = n R T
• 12 × V = 0.45 × 0.0821 × 298
• 12 × V = 11.0096
• V = 1.08 L

Therefore, the volume of the air present in a rubber tyre is 1.08 L.

Problem #3

A cylinder contains 0.3 moles of argon gas and has a volume of 2 L. If the pressure of the gas in the cylinder is 4 atm, what is the temperature of the gas? Use the value of the ideal gas constant, R = 0.0821 L atm/mol K.

Solution

Given data:

• Number of moles of the gas, n = 0.3 mol
• Volume of the gas, V = 2 L
• Pressure of the gas, P = 4 atm
• Temperature of the gas, T = ?
• Ideal gas constant, R = 0.0821 L atm/mol K

Applying the formula:

• P V = n R T
• 4 × 2 = 0.3 × 0.0821 × T
• 8 = 0.0246 × T
• T = 325.20 K

Therefore, the temperature of the gas is 325.20 K.

Problem #4

A container is filled with 6 L of gas containing 1.5 moles of helium gas at a temperature of 20 ℃. Calculate the pressure of the gas in the container. Take the value of the ideal gas constant, R = 0.0821 L atm/mol K.

Solution

Given data:

• Volume of the gas, V = 6 L
• Number of moles of the gas, n = 1.5 mol
• Temperature of the gas, T = 20 ℃ = 293 K
• Pressure of the gas, P = ?
• Ideal gas constant, R = 0.0821 L atm/mol K

Applying the formula:

• P V = n R T
• P × 6 = 1.5 × 0.0821 × 293
• P × 6 = 36.0829
• P = 6.01 atm

Therefore, the pressure of the gas in the container is 6.01 atm.