Question

Which of the following statements are correct?
I. Rise in compressibility factor $Z$ with increase in pressure is due to '$a$'.
II. Rise in compressibility factor $Z$ with increase in pressure is due to '$b$'.
III. Ideal gas do not exist but is a useful concept.
IV. For 1 mole of a van der Waal's gas,
$Z=1+\frac{bP}{RT}-\frac{a}{RTV}+\frac{ab}{RT{V}^2}$

• A. I, II, III, IV
• B. II, III, IV
• C. I, III, IV
• D. I, IV

Answer 1

The correct option is B II, III, IV

According to van der Waal's equation, $(P+\frac{n^{2}a}{V^2})(V-nb)=nRT$
$Z=1+\frac{bP}{RT}-\frac{a}{RTV}+\frac{ab}{RT{V}^2}$
So, rise in compressibility factor $Z$ with increase in pressure is due to '$b$'.
Ideal gas assumptions,

Gases are composed of many particles that behave like hard spherical objects in a state of constant, random motion.

These particles move in a straight line until they collide with another particle or the walls of the container.

These particles are much smaller than the distance between particles, therefore the volume of a gas is mostly empty space and the volume of the gas molecule themselves is negligible.

There is no force of attraction between gas particles or between the particles and the walls of the container.

Collisions between gas particles or collisions with the walls of the container are elastic. That is, none of the energy of the gas particle is lost in a collision.