Gas Laws

GAS LAWS

Gases have certain properties which differentiate them from solids and liquids.Gas laws are certain rules which a gas  follows when subjected to a change in temperature , pressure and volume. 

Volume of the gas undergoes significant change -if its temperature or pressure is slightly changed.

Temperature: 

                     an indicator of the average kinetic energy possessed by the molecule.(Kelvin)

Pressure:

                  Average force exerted by the gas molecule on the walls of a container per unit area of the container. 1atm =76cm of Hg or 760 mm of Hg

Volume: 

             Space occupied by the fixed mass of the gas.(Litre)

Boyle's law, also referred to as the Boyle–Mariotte law, is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases. A modern statement of Boyle's law is:

The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.

Mathematically, Boyle's law can be stated as:

{\displaystyle P\propto {\frac {1}{V}}}

Pressure is inversely proportional to the volume

Or    V α  1/p

         PV = k

Pressure multiplied by volume equals some constant {\displaystyle k}

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

The equation states that the product of pressure and volume is a constant for a given mass of confined gas and this holds as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as:

{\displaystyle P_{1}V_{1}=P_{2}V_{2}.}P₁ V₁ = P₂V₂ =k

This equation shows that, as volume increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases.

Boyle's Law Graph[ Volume Vs Pressure]

Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.

This relationship of direct proportion can be written as:

V α T

So this means:

{\displaystyle {\frac {V}{T}}=k,\quad or\quad V=kT} V/T = k

where:

V is the volume of the gas,

T is the temperature of the gas (measured in kelvins),

and k is a non-zero constant.

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}\qquad {\text{or}}\qquad {\frac {V_{2}}{V_{1}}}={\frac {T_{2}}{T_{1}}}\qquad {\text{or}}\qquad V_{1}T_{2}=V_{2}T_{1}.}V1/T1   =   V2/T2  = k

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

At absolute zero temperature the gas possesses zero energy and hence the molecules restrict motion

Charle's Law Graph[ Volume vs temperature in degree Celsius]

Combined gas law

Combining the laws of Charles, Boyle and Gay-Lussac gives the combined gas law, which takes the same functional form as the ideal gas law save that the number of moles is unspecified, and the ratio of {\displaystyle PV}PV  to {\displaystyle T}T  is simply taken as a constant.

PV/T   = k

{\displaystyle {\frac {PV}{T}}=k,}

where P {\displaystyle p} is the pressure of the gas, V{\displaystyle V} is the volume of the gas, T{\displaystyle T} is the absolute temperature of the gas, and {\displaystyle k}k is a constant. When comparing the same substance under two different sets of conditions, the law can be written as

P1V1/T1  = P2V2/T2   = k