Typical numericals on Kinetic Theory of Gases & Equation of Ideal Gas for JEE and CBSE board exams:

1. Question: A gas occupies 500 cm³ at 273 K and 760 mm Hg. Calculate its volume at STP.

Shortcut Method:

Volume at STP = V1 * (273 K / T1)

Plug in the given values:

Volume at STP = 500 cm³ * (273 K / 273 K)

Volume at STP = 500 cm³

2. Question: Calculate the pressure exerted by 0.5 moles of an ideal gas at a temperature of 373 K when confined to a volume of 10 litres.

Shortcut Method:

Pressure = (n / V) * R * T

Plug in the given values:

Pressure = (0.5 moles / 10 L) * (8.314 J/mol K) * (373 K)

Pressure = 1532.53 Pa

3. Question: A sample of gas has a pressure of 2 atm, a volume of 3.5 L, and a temperature of 400 K. Calculate the number of moles of gas present.

Shortcut Method:

Number of moles = pressure * volume / (temperature * ideal gas constant)

Plug in the given values:

Number of moles = 2 atm * 3.5 L / (400 K * 0.08206 L atm/mol K)

Number of moles = 0.216 moles

4. Question: A cylinder contains 10 g of oxygen gas at a pressure of 10 atm and a temperature of 25°C. Calculate the volume occupied by the gas.

Shortcut Method:

Volume = (weight of gas) * (ideal gas constant) * (temperature) / (pressure) * (molecular weight)

Plug in the given values:

Volume = (10 g) * (8.314 J/mol K) * (298 K) / (10 atm) * (32 g/mol)

Volume = 0.782 L

5. Question: A balloon is filled with 100 L of helium gas at a pressure of 1.5 atm and a temperature of 300 K. Calculate the number of moles of helium gas present in the balloon.

Shortcut Method:

Number of moles = volume * pressure / (ideal gas constant) * (temperature)

Plug in the given values:

Number of moles = 100 L * 1.5 atm / (8.314 J/mol K) * (300 K)

Number of moles = 6.098 moles