**Ideal gas law formula** describes the relationship between **pressure **(P), **volume** (V), **temperature** (T), and the **number of moles** (n) of a given quantity of gas. Here’s the formula of ideal gas law: **P V = n R T**

Let’s solve some problems based on this formula, so you’ll get a clear idea.

## Ideal Gas Law Practice Problems

**Problem 1:** Calculate the number of moles of the gas present in the cylinder which contains 4 L of hydrogen gas at 2 atm pressure and 30 °C temperature. (Take the value of ideal gas constant, 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 °C = 303 K

Ideal gas constant, R = 0.0821 L atm/mol K

Using the formula of ideal gas law,

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 tyre contains 0.45 moles of air at 12 atm pressure and 25 °C temperature. Calculate the volume of the air present in a rubber tyre. (Take the value of ideal gas constant, 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 °C = 298 K

Volume of the air, V = ?

Ideal gas constant, R = 0.0821 L atm/mol K

Using the formula of ideal gas law,

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 is filled with 2 L of gas and it contains 0.3 moles of argon gas. If the pressure of the gas in the cylinder is 4 atm, then what is the temperature of the gas? (Take the value of ideal gas constant, R = 0.0821 L atm/mol K)

Solution:

Given data:

Volume of the gas, V = 2 L

Number of moles of the gas, n = 0.3 mol

Pressure of the gas, P = 4 atm

Temperature of the gas, T = ?

Ideal gas constant, R = 0.0821 L atm/mol K

Using the formula of ideal gas law,

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 6 L of gas containing 1.5 moles of helium gas is released in an empty container at 20 °C temperature. Calculate the pressure of the gas in the container. (Take the value of 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 °C = 293 K

Pressure of the gas, P = ?

Ideal gas constant, R = 0.0821 L atm/mol K

Using the formula of ideal gas law,

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**.

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