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Kinetic Theory - Multiple Choice Questions

 

Q1. The height of a water barometer meauring atmospheric pressure at the surface of a lake is 10 m.

A diving bell of internal volume 6.0 m3 is lowered into the fresh water lake until the volume of the contained air is 4.0 m3.

Assuming the temperature of the air in the bell does not change, find how deep in metres the surface of the water in the bell is below the lake's surface.

A
5
B
20/3
C
15
D
50/3
E
25

P1 = 6.0 m3

V2 = 4.0 m3

P1 = 10 m H2O

P1V1 = P2V2

10 x 6.0 = P2 x 4.0

P2 = 15 m H2O

However the air suffers not only the pressure from the water but also atmospheric prssure. Therefore the 15 m H2O pressure is composed of 10 m H2O from the atmosphere and 5 m H2O from the water it is immersed in - so the answer is therefore choice A.

Q2. A gas molecule of mass m moving at velocity u collides at right angles with the side of a container and rebounds elastically.

Which one of the following statements concerning the motion of the molecule is incorrect?

A
The magnitude of the change in momentum of the molecule is zero.
B
The magnitude of the change in momentum of the molecule is 2mu.
C
The force exerted by the molecule on the side of the container is equal to the force exerted by the container on the molecule.
D
The change in kinetic energy of the molecule is zero.

 

Q3. The composition of a carbon dioxide (CO2) molecule is one atom of and two atoms of .

What is the number of molecules of CO2 in 2.2 kg of the gas?

A
 1.0 × 1022
B
3.0 × 1022
C
3.0 × 1025
D
4.7 × 1025

 

A mole of gas contains the Avagadro number of molecules.

A mole of gas contains 'the mass in grammes' of the atomic weight of the molecule.

Atomic weight = 12 + (2 x 16) = 44

So 44g of CO2 contains NA (the Avagadro number of) molecules.

2.2 kg = 2200 g

2200/44 = 50

∴ 2.2 kg contain 50NA molecules

50NA = 50 x 6.02 x 1023 = 3.0 x 1025

Choice C

 

 

Q4. What is the total internal energy of 2.4 mol of an ideal gas which has a temperature of 15 °C?

A
 6.0 × 10−21 J
B
1.4 × 10−20 J
C
4.5 × 102 J
D
8.6 × 103 J

 

Each molecule has an energy of 3/2kT

Each mole has NA molecules

∴ 2.4 mol has an energy of 2.4 x 3/2kTNA

T = 15oC

T = 15 +273K

T = 288K

E = 2.4 x 1.5 x 1.38 x 10-23 x 288 x 6.02 x 1023

E = 8660 J

Choice D