Ideal Gas Equation Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which law describes how molecules influence gas characteristics such as temperature and pressure?

1. Kepler’s law
2. Newton’s laws of motion
3. Faraday’s laws of electromagnetism
4. Kinetic theory of gases

Ans. The correct answer is d. Kinetic theory of gases

Explanation: The behavior of gases is explained by the kinetic theory of gases.

Ques. Temperature is measured in the unit of _____.

1. Kelvin
2. Radians
3. Volt
4. Luminosity

Ans. The correct answer is a. Kelvin

Explanation: Temperature is measured in kelvins, denoted by the letter K.

Ques. One mole of an ideal gas at STP occupies how many liters?

1. 21.4 liters
2. 20.4 liters
3. 23.4 liters
4. 22.4 liters

Ans. The correct answer is d. 22.4 liters

Explanation: One mole of an ideal gas occupies 22.4 liters at normal pressure and temperature.

Ques. Which of the following is the ideal gas equation?

1. P + V = nRT
2. PV = nRT
3. PV = n + R + T
4. PV = 2nRT

Ans. The correct answer is b. PV = nRT

Explanation: The equation for an ideal gas can be expressed by the formula PV = nRT.

Ques. As per the kinetic theory of gases, when molecules collide with each other ______

1. No energy is lost
2. No energy is gained or lost
3. No energy is gained
4. None of the above

Ans. The correct answer is b. No energy is gained or lost

Explanation: According to the kinetic theory of gas, no energy is gained or lost when molecules collide.

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Short Answers Questions [2 Marks Questions]

Ques. State ideal gas law.

Ans. According to the ideal gas law, the product of the pressure and volume of one gram of an ideal gas is equal to the product of the gas's absolute temperature and the universal gas constant.

Ques. What is the empirical formula for the ideal gas law?

Ans. The empirical formula for the ideal gas law is given by

PV = nRT

Where

• P is the pressure.
• V is the volume.
• n is the amount of substance.
• R is the universal gas constant.

Ques. How is the ideal gas law used in everyday life?

Ans. Assume an engineer wants to keep 500 g of oxygen at 1 atm and 125 degrees Fahrenheit in a container. The Ideal Gas Law is used to calculate the capacity of a container that must be constructed for the purpose.

Ques. Why is the ideal gas inaccurate?

Ans. The hypothesis of the ideal gas is only valid under ideal conditions. At high pressure and low temperature, the ideal gas law practically fails because molecule size and intermolecular forces become crucial aspects to consider and are no longer negligible.

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Long Answers Questions [3 Marks Questions]

Ques. What is the volume occupied by 2.34 grams of carbon dioxide gas at STP?

Ans. The ideal gas equation is given by

PV = nRT

Where

• n is the number of moles
• T is the absolute temperature
• P is the pressure of the gas
• V is the volume of the gas
• R is the universal gas constant

The volume occupied by 2.34 grams of carbon dioxide gas at STP is given by

V = nRT/P

⇒ V = [(2.34 g /44 g mol^-1) x 0.08206 L atm mol^-1 K^-1 x 273 K] / 1 atm

⇒ V = 1.19 L

Ques. Calculate the temperature at which 0.654 moles of neon gas occupy 12.30 liters at 1.95 atmospheres.

Ans. The ideal gas equation is given by

PV = nRT

Where

• n is the number of moles
• T is the absolute temperature
• P is the pressure of the gas
• V is the volume of the gas
• R is the universal gas constant

The temperature at which 0.654 moles of neon gas occupy 12.30 liters at 1.95 atmospheres is given by

T = PV/nR

⇒ T = (1.95 atm x 12.30 L) / (0.654 mol x 0.08206 L atm mol^-1 K^-1)

⇒ T = 447 K

Ques. What are the fundamental assumptions underlying the ideal gas law?

Ans. The following assumptions act as the foundation for the ideal gas law, which was developed from the kinetic theory of gases.

• The gas is composed of a large number of randomly moving molecules that follow Newton's equations of motion.
• The molecules have a negligible volume relative to the space taken up by the gas.
• In gases, intermolecular forces are negligible.
• Gases collide completely elastically.
• The absolute temperature of a gas affects its average kinetic energy.

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Very Long Answers Questions [5 Marks Questions]

Ques. A person’s lungs might hold 6.0 L of air at body temperature (310 K) and atmospheric pressure (101 kPa). Given that the air contains 21% oxygen, find the number of oxygen molecules in the lungs.

Ans. Assume that the air in the lungs is ideal gas, then we can apply the ideal gas equation i.e.

PV = NK_BT

Where

• N is the number of molecules in the air
• K_B is the Boltzmann’s constant
• T is the absolute temperature
• P is the pressure of the gas
• V is the volume of the gas

Given

• P = 101 kPa = 1.01 x 10⁵ Pa
• V = 6 L = 6 x 10^-3 m^-3
• T = 310 K
• K_B = 1.381 x 10^-23 JK^-1

On substituting the values, the number of air molecules is given by

N = PV/K_BT

⇒ N = (1.01 x 105 x 6 x 10^-3) / (1.381 x 10^-23 x 310)

⇒ N = 1.4 x 10²³ air molecules

Hence, the number of oxygen molecules (n) is given by

n = 21% of N = 21% of 1.4 x 10²³

⇒ n = 2.94 x 10²² oxygen molecules

Ques. One mole of each of hydrogen, oxygen, and nitrogen is mixed in a closed container of volume 10 liters and temperature 27 ℃. Calculate the pressure exerted by the mixture.

Ans. Let P be the pressure exerted by the mixture, then According to Dalton’s law of partial pressure, we have

P = P₁ + P₂ + P₃

Where

• P is the pressure exerted by the mixture
• P₁ is the pressure exerted by hydrogen
• P₂ is the pressure exerted by oxygen
• P₃ is the pressure exerted by nitrogen

Using the ideal gas equation

P = nRT/V + nRT/V + nRT/V = 3nRT/V

Given

• n = 1 mole
• V = 10 liters = 10 x 10^-3 m³
• T = 270 ℃ = 27 + 273 = 300 K
• R = 8.314 J mol^-1 K^-1 (Universal gas constant)

On substituting the values, we get

P = (3 x 1 x 8.314 x 300) / (10 x 10^-3)

⇒ P = 7.48 x 10⁵ N/m²

Ques. At the top of a mountain, a thermometer reads 7 ℃ and a barometer reads 70 cm of Hg. At the bottom of the mountain, they read 27 ℃ and 76 cm of Hg. If the density of the air at the top and bottom of the mountain is rt and rb respectively, then find the value of rt : rb. Neglect the variation in molecular mass.

Ans. For an ideal gas, we have

PV = nRT

⇒ PV = MRT/M₀

Where

• M is the mass of the gas molecule
• M₀ is the molar mass

⇒ PM₀ = MRT/V

But M/V = ρ (density)

⇒ PM₀ = ρRT

⇒ ρ = PM₀ / RT

⇒ ρ ∝ P/T

⇒ ρ₁ / ρ₂ = (P₁/T₁) x (T₂/P₂)

Given

• P₁ = 70 cm of Hg
• P₂ = 76 cm of Hg
• T₁ = 7 ℃ = 7 + 273 = 280 K
• T₂ = 27 ℃ = 27 + 273 = 300 K
• ρ₁ = r_t
• ρ₂ = r_b

On substituting the values, we get

r_t / r_b = (70/280) x (300/76) = 75/76

Hence r_t : r_b = 75:76

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