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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