Gas Laws

The state of a sample of gas is defined by 4 variables i.e. P, V, n & T. Gas laws are the simple relationships between any two of these variables when the other two are kept constant.

Boyle’s Law: The changes in the volume of a gas by varying pressure at a constant temperature of a fixed amount of gas was quantified by Robert Boyle in 1662. The law was named after his name as Boyle’s law. It states that:

The volume of a given mass of a gas is inversely proportional to its pressure at a constant temperature.

Mathematically

P ∝ 1/V (n, T constant)

V ∝ 1/P (n, T constant)

i.e. P = K/V (where K is the constant proportionality)

or PV = K (constant)

Let V1 be the volume of a given mass of the gas having pressure P1 at temperature T. Now, if the pressure is changed to P2 at the same temperature, let the volume changes to V2. The quantitative relationship between the four variables P₁, V₁, P₂ and V₂ is:

P1V1 = P₂V₂ (temperature and mass constant)

Graphical Representation of Boyle’s Law

• Fig. (a) show the plot of V vs P at a particular temperature. It shows that P increases
  V decreases.

• Plot (b) shows the plot of PV vs P at particular temperature. It indicates that PV value remains constant inspite of regular increase in P.

Charle’s Law: The French Scientist, Jacques Charles in 1787 found that for a fixed amount of a gas at constant pressure, the gas expands as temperature increases. The law can be stated as the volume of a given mass of a gas increases or, decrease by 1/273 of its volume at 0°C for each degree rise or, fall of temperature, provided pressure is kept constant.

Charles also found that for a given mass of a gas if pressure is kept constant, the volume increases linearly with temperature.

V = V₀ (1 + αt) or V – V0 = V₀ ∝ t

If the temperature is measured in the Celsius scale and V0 is the volume at 0°C, it is found that α = 1/273. The volume at temperature T is then;

Vt = V0

Where T = 273 + t is the temperature on the Kelvin scale, which has – 273°C as its zero point.

Let V1 be the volume of a certain mass of a gas at temperature T1 and at pressure P. If temperature is changed to T2 keeping pressure constant, the volume changes to V2. The relationship between for variables V1, T1, V2 and T₂ is:

(Pressure and Mass Constant)

Graphical Representation of Charle’s Law

COMBINED GAS EQUATION

The Boyle’s and Charles’ law can be combined to give a relationship between the three variables P, V and T. Let a certain amount of a gas in a vessel have a volume V1, pressure P1 and temperature T1. On changing the temperature and pressure to T2 and P2 respectively, the gas occupies a volume V2.

Then we can write

The above relation is called the combined gas law.

Avogadro’s Law: The Avogadro’s law states that at a given temperature and pressure, the volume of a gas is directly proportional to the amount of gas i.e.

V ∝ n (P and T constant)

or V = constant × n

Where n is the amount of the substance

It was said that 1 mol of any gas at 0°C and under 1 atm pressure occupies 22.4 × 10–3 m3 or 22.4 litre.

Avogadro further generalised the statement that a mole of any substance contains 6.022 × 1023 particles (molecules, atoms or any other entities).

IDEAL GAS EQUATION

A gas that would obey Boyle’s and Charle’s law under the conditions of temperature and pressure is called an ideal gas.

Here, we combine four measurable variables P, V, T and n to give a single equation.

V ∝ n [P, T constant] Avogadro’s law

V ∝ T [n, P constant] Charle’s law

V ∝ 1/P [n, T constant] Boyle’s law

The combined gas law can be written as V ∝ nT/P or PV ∝ nT

PV = nRT

this is called ideal gas equation

where R is the constant of proportionality or universal gas constant

The value of R was found out to be

R = 8.314 J mol–1 K^–1

R = 0.0821 litre atm K–1 mol^–1

R = 2 cal K^–1 mol^–1

Relation between molar mass and density (From ideal gas equation)

n = W/M

P = nRT/V

Increase in volume of air = 640 – 600 = 40

Gay Lussac’s Law (temperature pressure law)

It state that pressure of the given of mass a gas is directly proportional to the Kelvin temperature at constant volume

P ∝ T (n.v. are constant)