Kinetic Theory of Gases and Related Laws Quiz

Answer: True

Solids possess the least compressibility and thermal expansion, liquids have more, and gases the most.

Many of the beginner fluid and classical mechanics' equations overlook compressibility in solids and liquids as being negligible.

Answer: Graham's Law of Effusion

The gas law not mentioned here but also useful for the cause, is Gay-Lussac's Law. This establishes that the pressure of a given mass of gas is directly proportional to its temperature in the KELVIN scale, or P/T = k.

Boyle's Law establishes that the pressure of a gas at a given temperature is inversely proportional to the volume of the gas, or PV = k.

Charles' Law establishes that the volume of a gas is directly proportional to the temperature of the concerned gas in Kelvins, or V/T = k.

We can easily derive the ideal gas equation hence, PV = nRT, where R is the universal gas constant. These gas laws form the basis of kinetic gas theory as well.

Answer: All gaseous molecules move towards the walls of the container

On the contrary, the postulates of the kinetic theory of gases state that each gas molecule moves randomly, causing it to be also called the 'Dynamic Particle Theory'. It also states that the pressure of a gas is derived from the gaseous molecules colliding with the walls of a container.

From these postulates, the kinetic gas equation is derived:

Pv = (mnc^2)/3

where P is the pressure of the gas, V the volume, m mass of each gaseous molecule, n the total number of molecules and c the Root Mean Square speed of the gas.

Answer: 4k/3

To solve this question, you can apply Dalton's Law of Partial Pressures, which states that if you mix two such gases that do not react with each other, the total pressure exerted is equal to the sum of the partial pressures of the respective gases mixed together.

A partial pressure is the amount of pressure the gas would exert when occupying the new volume. This may be found by using Boyle's law.

Answer: Hydrogen

According to Graham's law of effusion/diffusion, the rate of diffusion/effusion of gases is inversely proportional to the square root of the respective densities of the gases.

Hydrogen is the lightest gas among the four listed, and in fact among all the gases, and hence has the quickest rate of diffusion.

Answer: Gaseous molecules move randomly in all directions

It must be noted that ideal gases are 'ideal and hypothetical' - and may not be very accurate when gases are actually modelled experimentally. It was observed through experimental results that pressure-volume graphs weren't a straight line, but instead a curve.

Deviations caused by the factors in the answer options are higher in gases that can be liquefied or are soluble in water. In such gases, the molecules tend to be closer together, increasing deviations caused by attraction or repulsion between them.

These faulty assumptions have the least effect when the pressure is low and the temperature is high. However, under high pressure and at low temperature, the molecules come closer - due to which the intermolecular forces of attraction and repulsion between molecules may not be negligible anymore, and neither will be the volume of the gas compared to the volume occupied by its molecules.

The extent of deviations from ideal gas behaviour is measured by the quantity Z, or compressibility factor, represented by z = (PV)/(NRT).

For an ideal gas , the value of Z is 1. If the value of Z is less than 1, negative deviation has been shown and the gas is more compressible than expected behavior. If the value of Z is more than 1, positive deviation has been shown and the gas is less compressible than expected behavior.
Noted as 'certain conditions' in the question, real gases do act like ideal gases at a certain temperature and Z =1. This temperature is known as the Boyle's Point of the concerned gas.

Answer: Most probable speed

The y-axis represents the number of molecules and the x-axis represents the molecular speed. Consequently , the x-coordinate at the peak would show the speed at which you will find the maximum amount of molecules.

The most probable speed can be found by using the following formula:

c* = square root of ( 2*R*T/M) where R is the universal gas constant, T is the temperature and M is the molar mass of the gas species concerned.

Answer: Van Der Waals

The Dutch physicist J.D. Van Der Waals won his Nobel Prize in 1910 for these advancements.

This is the modified Van Der Waals' equation:

(P + an^2/V^2)(V-nb) = nRT

The constant 'a' corrects for differing intermolecular forces of attraction while 'b' corrects for the effective size of the molecules. (Its value is four times the actual volume of the molecules).

The values of these constants vary according to the nature of the gas.

Answer: 22.4 L of chlorine

At conditions of STP ( 273 Kelvin temperature and 1 atmosphere pressure) , one mole of any gas has a volume of 22.4 L. (You can always find it using the ideal gas equation if you don't remember.)

The mass of 22.4 L of chlorine = mass of 1 mol of chlorine = 35.5 g
Mass of 89.6 L of hydrogen gas = mass of 4 mol of hydrogen gas = 16 g
Mass of oxygen is directly given -> 30 g
Mass of 1.5 mol of fluorine gas = 1.5 * 19 = 28.5 g

Answer: It stays the same

This question requires the application of the combined gas law. Since 'n' remains equal and R is a constant, we can bring it down to this equation:

Initial Pressure * Initial Volume/ Initial temperature = Final Pressure * Final Volume/ Final temperature

Given that final temperature = 2 * initial temperature and final pressure = 2 * initial pressure, the required ratio may be found using appropriate substitution in the given equation.