Laws related to Gases

Gas Laws:

The precise statements which correlates multiple parameters of gases like (volume, absolute temperature, pressure etc.) are called gas laws.

1-Boyle’s law: In 1662, Robert Boyle proposed his gaseous law, according to which;

Statement:  “At constant temperature, the volume of given mass of a gas is inversely proportional to its pressure.”

Mathematical representation:

Let ‘V’ be the volume of given mass of a gas and ‘P’ be its pressure, then according to the Boyle’s law;

V ∝ 1/ P   (at constant temperature)

Or         V = K / P

Or          PV = K    ---------------- (1)

Where K is the proportionality constant and is independent of the variables.

From equation (1) the law can also be stated as;

“At constant temperature, the product of pressure and volume of given mass of a gas is always remain constant.”

Where K is same as amount of given gas.

n the given diagram, mass of a gas at constant temperature shows increase in volume by decrease in pressure. On the other hand increase in pressure decreases volume. But the product of pressure and volume is constant in both cases.

If P1 and V1 be the initial pressure and volume and P2 and V2 be the final states,

then,     P$_1$V$_1$ =   K

And      P$_2$V$_2$ =   K

Or       P$_1$V$_1$ = P$_2$V$_2$ -------------- (2)

Boyle’s law (K.M.T):

According to kinetic molecular theory, at constant temperature whenever the pressure of the gas increases the intermolecular distances decrease as a result of which volume of a gas reduces, vice versa.

Graphical representation:

The graph between volume and pressure of a gas is an iso-thermal curve because it is plotted at same temperature.

2-Charles’s law:

In 1787, J. Charles proposed his gaseous law, according to which;

Statement:  “At constant pressure, the volume of given mass of a gas is inversely proportional to absolute temperature.”

Mathematical representation:

Let ‘V’ be the volume of given mass of a gas and ‘T’ be its absolute temperature, then according to the Charles’s law;

For example, that if you double the temperature of a gas from 300 K to 600 K, at constant pressure, the volume of a fixed mass of the gas will become double.

V∝ T (at constant pressure)

Or       V = K x T

Or       V / T = K    ---------------- (1)

Where K is the proportionality constant and is independent of the variables.

From equation (1) the law can also be stated as;

“At constant pressure, the quotient of volume and absolute temperature of given mass of a gas is always remain constant.”

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

Then,                     V$_1$ / T$_1$=   K

And                        V$_2$ / T$_2$ =   K

Or                         V$_1$ / T$_1$= V$_2$ / T$_2$ -------------- (2)

Charles’s law (K.M.T):

According to kinetic molecular theory, at constant pressure whenever the absolute temperature of the gas increases the intermolecular distances increases along with kinetic energy of gas particles as a result of which volume of a gas reduces, vice versa.

Graphical representation:

The graph between volume and absolute temperature of a gas is an iso-baric gradient (slope) because it is plotted at same pressure.

Absolute scale:

The scale for the measurement of temperature, in which the reference standard unit of temperature is Kelvin “K”, is termed as Absolute scale or Kelvin scale.

Absolute Temperature:

The temperature which is measured in Kelvin scale, is called absolute temperature.

Absolute zero:

A theoretical reference temperature, in which the volume of a gas becomes zero and whose value is -2730 C or 0 k, is termed as Absolute zero.

In actual practice, gases change their states into liquids and solids.