The temperature of the gas is raised from 27°C to 927°C, the root mean square velocity is

\(\sqrt{927/27}\) time the earlier value
same as before
halved
doubled

Solution

Which of the following gases will have highest rate of diffusion?

CO₂
NH₃
O₂
N₂

Solution

\(Rate \; of \; dif\!fusion \propto \frac{1}{\sqrt{density}} \propto \frac{1}{\sqrt{molality}}\)

NH₃ has the highest rate of diffusion as it is the lightest molecule.

Internal energy and pressure of a gas per unit volume are related as :

P = ²⁄₃E
P = ³⁄₂E
P = ¹⁄₂E
P = 2E

Solution

PV = ¹⁄₃mnu² = ¹⁄₃Mu²

= ²⁄₃.¹⁄₂ mnu² = ²⁄₃E or p = ²⁄₃E per unit vol.

In a closed flask of 5 litres, 1.0 g of H₂ is heated from 300 to 600 K. Which statement is not correct?

Pressure of the gas increases
The rate of collision increases
The number of moles of gas increases
The energy of gaseous molecules increases

Solution

Here volume is constant. Again the mass of H₂ is fixed so the number of moles of the gas do not change. As temperature increases the pressure also increases. The rate of collision among the gas molecules and their energy also increases.

Which of the following is not a property of liquid state?

Inter molecular force of attraction in a liquid is quite large
All liquids accompanied by cooling on evaporation
Lower the boiling point of a liquid, greater is its vapour pressure at room temperature
A liquid boils at high temperature at the top of a mountain than at the sea level

Solution

A liquid boils at lower temperature at the top of a mountain.

Root mean square velocity of a gas molecule is proportional to

m^1/2
m⁰
m^-1/2
m

Solution

According to kinetic gas equation

PV = ¹⁄₂mNu², u = root mean square velocity

⇒ \(u^{2} = \frac{3PV}{mN}\) or \(u \propto \frac{1}{\sqrt{m}}\)

i.e u ∝ m^{^-1⁄₂}

The ratio between most probable velocity, mean velocity and r.m.s velocity is :

√2 : √(8/π) : √3
√2 : √3 : √(8/π)
1 : 2 : 3
1 : √2 : √3

Solution

The inversion temperature T_i(K) of hydrogen is (given vander Waal’s constants a and b are 0.244 atm L²mol^-2 and 0.027 Lmol^-1 respectively)

Solution

Gases become cooler during Joule Thomson’s expansion only if they are below a certain temperature known as inversion temperature (T_i). The inversion temperature is characteristic of each gas and is given by

T_i = ^2a⁄_bR, where R is gas constant

Given a = 0.244 atm L²mol^-2

b = 0.027 L mol^-1

R = 0.0821 L atm deg^-1mol^-1

∴ \(T_{i} = \frac{2 \times 0.244}{0.027 \times 0.0821} = 220\; K\)

X mL of H₂ gas effuses through a hole in a container in 5 seconds. The time taken for the effusion of the same volume of the gas specified below under identical conditions is :

10 seconds : He
20 seconds : O₂
25 seconds : CO
55 seconds : CO₂

Solution

The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is

64.0
32.0
4.0
8.0

Solution

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