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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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