At low pressure the van der Waal’s equation is reduced to

\(Z = \frac{PV_{m}}{RT} = 1 - \frac{ap}{RT}\)
\(Z = \frac{PV_{m}}{RT} = 1 + \frac{b}{RT}p\)
pV_m = RT
\(Z = \frac{PV_{m}}{RT} = 1 - \frac{a}{RT}\)

Solution

The van der Waal’s constant ‘a’ for four gases P, Q, R and S are 4.17, 3.59, 6.71 and 3.8 atm L²mol^-2 respectively. Therefore,the ascending order of their liquefaction is

R < P < S < Q
Q < S < R < P
Q < S < P < R
R < P < Q < S

Solution

Easily liquefiable gases have greater intermolecular forces which is represented by high value of 'a'. The greater the value of 'a' more will be liquefiability. So, the order is Q < S < P < R.

Gas deviates from ideal gas nature because molecules

are colouress
attaract each other
contain covalent bond
show Brownian movement.

Solution

Due to intermolecular interactions appreciable at high P and low T, the ideal gas deviates from ideal behaviour.

Rate of diffusion of NH₃ is twice that of X. What is the molecular mass of X?

Solution

A gas described by van der Waal’s equation

(i) behaves similar to an ideal gas in the limit of large molar volume

(ii) behaves similar to an ideal gas in the limit of large pressure

(iii) is characterised by van der Waal’s coefficients that are dependent on the identity of the gas but are independent of the temperature

(iv) has the pressure that is lower than the pressure exerted by the same gas behaving ideally

(i) and (ii)
(i) and (iii)
(i), (ii) and (iii)
(ii) and (iv)

Solution

(i) At very large molar volume

P + ^a⁄_{V²_m} = P and V_m - b = V_m

(iii) According to van der Waals equation 'a' and'b' are independent of temperature.

Graph between P and V at constant temperature is

straight
curved increasing
straight line with slope
none of these

Solution

P ∝ ¹⁄_V (at constant T)

∴ PV = constant.

The compressibility factor for an ideal gas is

Solution

The compressibility factor of a gas is defined as \(Z = \frac{PV_{m}}{RT}\)

For an ideal gas, pV_m = RT. Hence Z = 1

In van der Waal’s equation of state for a non-ideal gas, the term that accounts for intermolecular forces is

(V - b)
RT
(P + ^a⁄_V²)
(RT)^-1

Solution

(P + ^a⁄_V²)(V – b) = RT; Here (P + ^a⁄_V²) represents the intermolecular forces.

The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is

critical temperature
Boyle temperature
inversion temperature
reduced temperature

Solution

The temperature at which a real gas behaves like an ideal gas is called Boyle’s temperature or Boyle’s point.

Value of universal gas constant(R) depends upon

Number of moles of gas
Volume of gas
Temperature of gas
None of these

Solution

Value of gas constant depends only upon units of measurement.

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