Gas Laws explained with Presentation

 Gas Laws

The gas laws are a group of laws that govern the behavior of gases by providing relationships between the  following:

The volume is occupied by gas.

The pressure is exerted by a gas on the walls of its container.  The absolute temperature of the gas.

The amount of gaseous substance (or) the number of moles of gas.

The gas laws were developed towards the end of the 18th century by numerous scientists (after whom, the individual laws are named).

The five gas laws are:

 Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.

 Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature. 

Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.

 Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.

The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.

 

Boyle’s Law

Boyle’s law gives the relationship between the pressure of a gas and the volume of the gas at a constant  temperature. Basically, the volume of a gas is inversely proportional to the pressure of a gas at a constant  temperature.

Boyle’s law equation is written as:

V ∝ 1/P

Or

P ∝ 1/V

Or

PV = k₁

Where V is the volume of the gas, P is the pressure of the gas and K₁ are the constant.

Boyle’s Law can be used to determine the current pressure or the volume of gas and can be represented also as;

P₁V₁ = P₂V₂

 

Charle’s Law

Charle’s law states that at constant pressure, the volume of a gas is directly proportional to the temperature (in Kelvin) in a  closed system. Basically, this law describes the relationship between the temperature and volume of the gas.

Mathematically, Charle’s law can be expressed as;

V ∝ T

Where, V = volume of gas, T = temperature of the gas in Kelvin.

Another form of this equation can be written as;  V₁ / T₁ = V₂ / T₂

 

Gay-Lussac Law

Gay-Lussac law gives the relationship between temperature and pressure at constant volume.

The law states that at a constant volume, the pressure of the gas is directly proportional to the temperature for a given gas.

If you heat up a gas, the molecules will be given more energy, they move faster.  If you cool down the molecules, they slow down and the pressure decreases.

The change in temperature and pressure can be calculated using Gay-Lussac law and it is mathematically represented

as;

P ∝ T  Or

P / T = k₁  or

P₁ / T₁ = P₂ / T₂

 

Avogadro’s Law

Avogadro’s law states that if the gas is an ideal gas, the same number of molecules exists in the system.

The law also states that if the volume of gases is equal it means that the number of the molecule will be the same as the ideal gas only when it has equal volume.

The above statement can be mathematically expressed as;  V / n = constant

Or

V1 / n1 = V2 / n2

Where V is the volume of an ideal gas and n in the above equation represents the number of gas molecules.

 

Combined Gas Law

The combined gas law is also known as a general gas equation is obtained by combining three gas laws which  include Charle’s law, Boyle’s Law and Gay-Lussac law.

The law shows the relationship between temperature, volume and pressure for a fixed quantity of gas.

The general equation of combined gas law is given as;  PV / T = k

If we want to compare the same gas in different cases, the law can be represented as;  P1V1 / T1 = P2V2 / T2

 

Graham’s Law:

Graham’s Law which is popularly known as Graham’s Law of Effusion, was formulated by Thomas Graham in the year 1848.  Thomas Graham experimented with the effusion process and discovered an important feature: gas molecules that are  lighter will travel faster than the heavier gas molecules.

According to Graham’s Law, at constant pressure and temperature, molecules or atoms with lower molecular mass will effuse faster than the higher molecular mass molecules or atoms. Thomas even found out the rate at which they escape through diffusion. In other words, it states that the rate of effusion of a gas is inversely proportional to the square root of its molecular mass. This formula is generally used while comparing the rates of two different gases at equal pressures and temperatures. The formula can be written as 

M1 is the molar mass of gas 1  M2 is the molar mass of gas 2

Rate1 is the rate of effusion of the first gas

Rate2 is the rate of effusion for the second gas

It states that the rate of diffusion or effusion is inversely proportional to its molecular mass.

 

Numerical Problems

1.) Boyle’s Law related problem

An 18.10mL sample of gas is at 3.500 atm. What will be the volume if the pressure becomes 2.500

atm, with a fixed amount of gas and temperature?.

2.) Charle’s law-related problem

A sample of Carbon dioxide in a pump has a volume of 21.5 mL and it is at 50.0 oC. When the amount of gas and pressure remain constant, find the new volume of Carbon dioxide in the pump if the temperature is increased to 75.0 oC.

3.) Gay-Lussac Law related problem

Determine the pressure change when a constant volume of gas at 2.00 atm is heated from 30.0 °C to

40.0 °C.

4.) Avogadro’s Law

At constant temperature and pressure, 6.00 L of a gas is known to contain 0.975 mol. If the amount of gas is increased to 1.90 mol, what will be the new volume?.

Solution for 1.):

By solving with the help of Boyle’s law equation  P1V1 = P2V2

V2 = P1V1 / P2

V2 = (18.10 * 3.500atm)/2.500atm  V2 = 25.34 mL

Solution for 2.)

V2 = V1T2/T1

V2 = 21.5*348.15/323.15  V2 = 23.16 mL

 

Solution for 3.) :

P1/T1 = P2/T2

P2 = (P1*T2)/T1 = ((2*(313.15))/(303.15)= 626.3/303.15  P2 = 2.0659

Solution for 4.):

V1/n1 = V2/n2

V2 = (6*1.90)/0.975  V2=              11.69L