States Of Matter

It is the Boyle temperature At Boyle temperature, the first virial coefficient (B) vanishes and real gas approaches ideal behaviour.

Here, a and bare van der Waals' constants.

The two types of speeds are defined as;
Root mean square speed
Average speed
For the same gas, at a given temperature, M and T are same, therefore

According to kinetic theory, average kinetic energy
where, is Boltzmann- constant. Since, it is independent of molar mass, it will be same for He and at a given temperature.

According to postulates of kinetic theory, there is no intermolecular attractions or repulsions between the molecules of ideal gases.

According to Graham's Law of diffusion of gases, the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass

Pressure is inversely proportional to volume at constant temperature, hence (a) is correct.
Average kinetic energy of a gas is directly proportional to absolute temperature, hence (b) is correct.
Expansion at constant temperature cannot change the number of molecules, hence (d) is incorrect.

HCl will diffuse at slower rate than ammonia because rate of effusion
Therefore, ammonia will travel more distance than HCl in the same time interval and the two gas will first meet nearer to HCl end

PV = nRT
PV =
= d
(A) d =
(B) d =
(C) d =
(D) d =
will be minimum when numerator is minimum and denominator is maximum. Thus, (C) is the correct choice for the answer.

2 a (say), - a


= 4 or = 64

The mean translational kinetic energy of an ideal gas is
Absolute temperature, i.e

Let x g of each gas is mixed.
Mole of ethane

Mole fraction of hydrogen
Mole fraction of hydrogen

The correct answer is C:1
Expression of rms is,

For a gas to show ideal behaviour, the attractive force between the gas molecules must be negligible.

Also, at high temperature and low pressure, the attractive forces between the gas molecules becomes negligible.

1L = 1000 mL = 1000
Mass = Density volume
= (0.0006 g (1000 )
= 0.6 g
18 g of water = 18
0.6 g of water = 0.6
0.6 g of water = 0.6
Actual volume occupied by molecules = 0.6

Root mean square speed

Option (a) is correct because in the limit of large volume, both intermolecular force and molecular volume becomes negligible in comparison to volume of gas.
Option (b) is wrong statement because in the limit of large pressure Z > 1.
Option (c) is correct statement. For a van der Waals' gas, van der Waals' constants a and b are characteristic of a gas, independent of temperature
Option (d) is wrong statement because Z can be either less or greater than unity, hence real pressure can he less or greater than ideal pressure.

In the van der Waals' equation

The additional factor in pressure, i.e. corrects for intennolccular force while b corrects for molecular volume.

(a) According to a postulate of kinetic theory of gases, collision between the molecules as well as with the wall of container is perfectly elastic in nature.
(b) If a gas molecule of mass m moving with speed u collide to the wall of container, the change in momentum is p = - 2mu. Therefore, heavier molecule will transfer more momentum to the wall as there will be greater change in momentum of the colliding gas molecule. However, this is not postulated in kinetic theory.
(c) According to Maxwell-Boltzmann distribution of molecular speed, very few molecules have either very high or very low speeds. Most of the molecules moves in a specific, intermediate speed range.
(d) According to kinetic theory of gases, a gas molecule moves in straight line unless it collide with another molecule or to the wall of container and change in momentum is observed only after collision.

The van der Waals equation of state is

For one mole and when b = 0, the above equation condenses to


E (i) is a straight equation between pV and whose slope is -
- a'. Equating with slope of the straight line given in the graph.

Average kinetic energy depends only on absolute temperature
K = Boltzmann constant



Using above formulae, correct statements are (A, C, D).

To solve the problem of finding the ratio of root mean square velocities of two ideal gases X and Y, we use the root mean square (RMS) velocity formula: where is the gas constant, is the temperature, and is the molar mass of the gas. At a constant temperature , the ratio of the RMS velocities for gases X and Y can be calculated as:

From the ideal gas law , we know that at constant temperature and volume and for the same gas constant , the pressure is proportional to moles . Initially, 10 g of gas X exerts a pressure of 2 atm. When 80 g of gas Y is added, the pressure becomes 6 atm.

The additional moles contributed by gas Y increase the total pressure from 2 atm to 6 atm, thus the pressure due to gas Y alone is 4 atm. The pressure is directly proportional to the number of moles, so the moles of gas X and Y can be written as:

Using the ideal gas law, number of moles can be expressed as . Hence:

Thus, .

The ratio of the RMS velocities is:

Therefore, the ratio of root mean square velocities is .

Correct answer: 2:1