Complete Guide to Chemistry Derivations and Formula Proofs

Ideal gas Law 

Ideal gas law is based on behavior of ideal gas. It is an approximation of the behavior of many real gases under many conditions. It is actually a combination of Boyle’s law, Charles’ Law and Avogadro’s law. 

Charles’ Law and Avogadro’s law. 

To understand the ideal gas law first you need to know Boyle’s law, Charles law, Avogadro’s law and Gay-Lussac’s Law. 

Boyle’s law – Boyle’s law states that the absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if temperature and amount of gas remain unchanged within a closed system. 

Mathematical expression of Boyle’s law - P1V 

where P is the pressure of the gas and V is the volume.

Charle’s Law – Charle’s Law states that when the pressure on a sample of a dry gas is held constant, the kelvi the voln temperature and volume will be in direct proportion. 

Mathematical equation can be written as follows – V T,

where V is the volume of the gas and T is the temperature of the gas.

Gay-Lussac’s Law – Gay-Lussac’s law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant. 

Mathematically it can be expressed as follows – P T ,

where P is pressure of the gas and T is temperature of the gas.

Avogadro’s law- Avogadro’s law states that at the same temperature and pressure, equal volumes of gases contain equal numbers of moles. 

Mathematically it can be expressed as follows – V n ,

where V is volume of gas and n is number of moles of the gas 

Now, let’s understand ideal gas law. Ideal gas law is expressed by the general gas equation which is a thermodynamics equation relating state variables such as pressure, volume and temperature with ideal gas. 

Ideal gas law can be easily expressed by – PV = nRT

Ideal Gas Equation 

Ideal gas law is expressed by an ideal gas equation.

The ideal gas equation is written as – PV = nRT

Where P = pressure of the gas 

V = volume of the gas 

n= number of moles of the ideal gas 

R = Gas constant or ideal gas constant 

T = temperature 

Molar form of the ideal gas can be written as follows – 

‘n’ number of moles of the gas is equal to the total mass of the gas divided by its molar mass. So, we can write n= m/M

 Now let’s put the value of n in the above gas equation -PV = mMRT

Where m = total mass of the gas in kg 

             M = Molar mass (in kilograms per mole)

Derivation of Ideal Gas equation 

If V = volume of the gas, P = pressure on gas and T = temperature then – 

According to Boyle’s Law-

V 1P    at constant T or temperature………………………………………. (I)

According to Charle’s Law-

V T   at constant P or pressure……………………………………………… (II)

According to Avogadro’s Law-

V n   at constant T and P………………………………………………………..(III)

Where n = number of moles of the gas 

From equations (I), (II) and (III) we can write – 

V ∝ 1P ×T ×n

We can write the above equation as – 

V = R1P ×T×n , where R is the Universal Gas Constant and its value is 8.314 Jmol-1K-1

V = RTnP

After rearranging the above equation – 

PV = nRT

Universal Gas Constant 

Universal gas constant is also known as gas constant or ideal gas constant. It is denoted by ‘R’. it is an experimentally derived number that is used in ideal gas equations and other equations. 

Ideal gas constant and its experimental values in different units are given below – 

Applications of Ideal Gas Law 

• It is largely used in thermodynamics. 

• It can be used in stoichiometry problems. 

• It can be used to determine densities of gases. 

• Ideal gas law is used in the working mechanics of airbags which are used in vehicles. 

• Using ideal gas equations, we are able to use coolant gases in refrigerators, air conditioners etc. 

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