Gas laws

Gas pressure

Pressure is defined as the force per unit area acting on the surface.

The unit of pressure is Newton per metre squared [N/m2]. (or Pascal[[Pa]: 1Pa=1 N/m2)

The gas molecules are in random and continuous motion. They exert a force on the wall of container when they collide to it. Since the force is exerted over an area, pressure is produced.

The pressure of a gas of constant volume increases when;

- there are more molecules in the gas

- the molecules move faster

- the molecules have a greater mass.

Boyle’s law

Law For a fixed mass of a dry gas at constant temperature, The product of its volume and pressure is constant.

Formula for Boyle’s law

PV = constant

P: Pressure [N/m2]

V: Volume [m3]

If the initial pressure and volume are P1 and V1, and the final ones are P2 and V2,

P1 V2 = P2 V2

Example

A gas occupies a volume of 2m3 at 25oC and pressure of 200N/m2. What would be the volume of the gas if the pressure is reduced to 100N/m2 at the same temperature?

Solution

P1 V2 = P2 V2

Given that

P1 = 200N/m2

V1 = 2m3

P2 = 100N/m2

V2 = ?

200 × 2 = 100 × V2

400 = 100V2

100V2 100 = 400 100

Answer: V = 4m 3

Kelvin temperature scale

SI unit of temperature is Kelvin [K].

- The size of the degree in Kelvin is the same as in Celsius.

- According to the calculations (Charle’s law), a gas would contract as it cools until at -273 oC. Then, the gas has no volume at -273 oC.

- -273 oC is called absolute zero (0K).

- 273 must be added to convert Celsius into Kelvin.

Formula to find temperature in Kelvin

Tk = Tc + 273

Tk: Temperature in Kelvin scale [K]

Tc: Temperature in Celsius scale [oC]

Example

Convert (a) 0 oC and (b)100 oC into K.

Solutions

(a) TK = 0 oC + 273 = 273K

(b) TK = 100 oC + 273 = 373K

Charles’ law

Law The volume of a fixed mass of a gas at constant pressure is directly proportional to its Kelvin temperature.

Formula for Charles’ law

V T = constant

V: Volume [m3]

T: temperature [K]

If the initial volume and temperature are V1 and T1, and the final ones are V2 and T2,

V1 T1 = V2 T2

Example

The sun heats 15m3 of dry air at 27 oC until its volume increases to 16 m3 under the atmospheric pressure. Calculate the temperature of the air.

Solution

V1 T1 = V2 T2

V1 = 15m3

T1 = 27oC = 300k (= 27 + 273)

V2 = 16m3

T2 = ?

15 300 = 16 T2

Cross multiply

15T2 = 16 × 300

15T2 = 4800

15T2 15 = 4800 15

T2 = 320K

Answer: TC = TK – 273 = 320 –273 = 47 oC

Combination of Boyle’s and Charles’ laws

Formula for Boyle’s and Charles’ laws

P1 V1 T1 = P2 V2 T2

This equation is called the general gas equation.

Example

15m3 of gas is at a pressure of 70N/m2 and a temperature of 27 oC. Find its volume when it is at a temperature of 127oC and a pressure of 35N/m2.

Solution

P1 V1 T1 = P2 V2 T2

Given that

P1 = 70N/m2

V1 = 15m3

T1 = 27 oC = 300K (= 27 + 273)

P2 = 35N/m2

V2 = ?

T2 =127 oC = 400K (= 127 + 273)

70 (15) 300 = 35(V2) 400

1050 300 = 35V2 400

Cross multiply

1050(400) = (300)35V2

10500V2 = 420000

10500V2 10500 = 420000 10500

V2 = 40m 3