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Ideal Gas Equation - Ideal Gas Law, Derivation, Universal Gas Constant, Practice Problems and FAQs

Ideal Gas Equation - Ideal Gas Law, Derivation, Universal Gas Constant, Practice Problems and FAQs

Do you know how airbags in the vehicle work when the vehicle undergoes a sudden collision? Ideal gas laws are used in the working of airbags. When the vehicle collides, airbags in the vehicle get inflated quickly by nitrogen gas produced from a chemical reaction to save a person's life. In 1834, Benoît Paul Émile Clapeyron stated the relation between pressure, volume, temperature and amount of substances by combining different laws which include Boyle’s law, Charles’s law, Gay- Lussac’s law and Avogadro’s law known as Ideal gas equation.

Table of Content

  • Ideal Gas Law
  • Derivation of Ideal Gas Equation
  • Values and Units of Universal Gas Constant
  • Practice Problems
  • Frequently Asked Questions - FAQ

Ideal Gas Law

It stated the relationship between pressure, volume, temperature and amount of gas present by combining different gas laws and helps in determining the approximate behaviour of the gas.


Derivation of Ideal Gas Equation

According to Boyle’s law, the pressure of the gas is inversely proportional to the volume occupied by the gas when temperature and amount of gas are assumed to be constant.

Mathematically, 

Where represents the pressure of the gas, represents the volume occupied by the gas.

According to Charles’s law, which states that the volume of the gas is directly proportional to the temperature when the pressure exerted by the gas and amount of the gas is assumed to be constant.

Mathematically,

Where represents the volume of the gas, represents the temperature of the gas in Kelvin scale. 

According to Gay-Lussac’s law, which states that the pressure of the gas is directly proportional to the temperature when the volume of the gas and amount of the gas is assumed to be constant

Mathematically,

Where represents the pressure of the gas, represents the temperature of the gas in Kelvin scale. 

According to Avogadro’s law, which states that volume of the gas is directly proportional to the amount of gas present when the pressure and temperature of the gas are assumed to be constant.

Mathematically,

Where represents the volume of the gas, represents the number of moles of gas. 

Combining the above laws and equations we get,

 

So, the equation is known as Ideal gas equation. 

Where, 

Pressure of the gas

Volume of the gas

Number of moles of gas

Temperature of the gas in kelvin scale

Universal gas constant

Let’s consider two different conditions where; 


Initial pressure of the gas

Initial volume of the gas

Initial temperature of the gas

Initial no. of moles of the gas  

Final pressure of the gas

Final volume of the gas

Final temperature of the gas  

Final no. of moles of the gas  

Using the ideal gas equation for initial and final conditions we get,

Using equation and we get, 

Values and Units of Universal Gas Constant

Universal gas constant can be expressed in various units, the values of are as follows: 

Practice problems

Q. Calculate the volume () occupied by of gas at and pressure. Consider that gas behaves ideally at a given temperature and pressure.

Solution:

According to the given data;

Volume of the gas

Number of moles of gas

Temperature of the gas

Pressure of the gas =

According to the ideal gas equation;

 

Putting the values given in above equation, we get;

 

Q. Gas is heated in an open container from to Calculate the of gas escaped out from the container. Assume that gas behaves ideally.

Solution:

We know in the case of an open container, pressure and volume will remain constant.

Using the ideal gas equation we get,

Or,

Percentage of gas escaped out from the container =

Putting the value of in the above equation, we get; 

Percentage of gas escaped out from the container

Percentage of gas escaped out from the container =

Q. If a of a gas is filled in a container at a temperature of and at a pressure of . Calculate the number of moles of gas present in a container at a given temperature and pressure. Assume that gas behaves ideally.

a. 
b. 
c. 
d. 

Answer: (B)

According to the given data,

Volume of the gas

Number of moles of gas

Temperature of the gas

Pressure of the gas in container

Using ideal gas equation, we get;

Q. At and , if of gas is filled in a cylinder-piston arrangement which occupies a volume of . What will be the volume occupied by the same amount of gas when it is heated to and pressure is increased to ? Assume the gas behaves ideally.

A)
B)
C)
D)

Answer: (C)

According to the given data, 

Initial pressure of the gas

Initial volume of the gas

Initial temperature of the gas

Final pressure of the gas

Final temperature of the gas  

Let the final volume of the gas be .

Using the ideal gas equation for initial and final conditions we know,

Frequently Asked Questions-FAQ

Q.How density of an ideal gas can be calculated using the ideal gas equation?

Answer: 

We know that according to the ideal gas equation,

  

is the given mass of the substance and is the molar mass of the substance)

But, the density of the substance

Density of the gas

 Q. How to determine the molar volume at STP condition?

Answer: 

STP stands for standard temperature and pressure which corresponds to pressure and

temperature equals to . Molar volume is the volume occupied by one mole of the gas. 

So, the number of moles of gas

Temperature of the gas

Pressure of the gas

Let’s assume the molar volume of the gas be .

Using ideal gas equation we get,

 

 Therefore, at STP condition one mole of any gas occupies the volume of known as molar volume of gas at STP.

Q. What are the assumptions for gas to behave ideally?

Answer: Few assumptions for gas to behave ideally include there should be no interactions between the 

gas particles present in the container, the volume of the individual particle should be negligibly 

small in comparison to the volume of the container and the collision between the particles 

should be perfectly elastic in nature. 

Q. Why ideal gas is generally said as theoretical gas?

Answer: Ideal gas is a theoretical gas because it is not possible to have no interaction between the 

particles. Moreover, there is always a loss in the kinetic energy during the collision of particles 

and with the wall of the container.

Related topics

Charles's Law Gay-Lussac’s Law
Avogadro’s Law Dalton's Law of Partial Pressure
Boyle’s law Real Gas

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