You are here:

Welcome to our Physics lesson on **The Ideal Gas Law**, this is the third lesson of our suite of physics lessons covering the topic of **The Kinetic Theory of Gases. Ideal Gases**, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

The **ideal gas law** is the equation of state for an ideal gas, which establishes the relation between the four parameters of a gas sample. These four parameters are **pressure**, **volume**, **temperature** and **number of moles** of the gas sample. Given that all gases behave quite ideally at low pressures, we can calculate the unknown fourth parameter when three of them are known.

The Ideal Gas Law is an empirical law of physics. It was derived from experiment and observation rather than from theory. The experiments show that the ratio of the products

is always constant. This constant is always the same for all gas samples. It is known as the ideal gas constant and is denoted by R. For ideal gases it has a value of R = 8.31 J/mol × K.

Therefore, we can write:

R = *P × V**/**n × T*

Rearranging in order to remove the fraction, we obtain the Ideal Gas Law:

P × V = n × R × T

In chemistry, there is another unit used for the ideal constant R. It stems from the fact that in chemistry pressure is usually measured in atmospheres (atm), volume in litres (L) and temperature in Kelvin degree (K).

Find the value of ideal gas constant R in atm × L/mol × K given that its value is R = 8.31 J/mol × K.

From previous sections, we known the following conversion factors:

1 atm = 101 325 Pa (the exact value, not rounded)

1 L = 1 dm^{3} = 0.001 m^{3}

Given that

R = *P × V**/**n × T*

It is obvious that we have to convert only the units in the numerator, as those in the denominator are the same in both cases. Thus,

1 atm × 1L = 101 325 Pa × 0.001 m^{3}

= 101 325 N/m^{2} × 0.001 m^{3}

= 101.325 N × m

= 101.325 J

= 101 325 N/m

= 101.325 N × m

= 101.325 J

Therefore,

1 atm × L = 101.325 J

Thus,

8.31 J = *8.31**/**101.325* atm × L

=0.082 atm × L

=0.082 atm × L

Hence, we obtain the value of R in atm × L/mol × K equal to 0.082 atm × L/mol × K.

There is a very important quantity known as the Boltzmann Constant, k, which is used to write the Ideal Gas Law in an alternative form. It is defined by the equation:

k = *R**/**N*_{a}

Substituting the known values, we obtain for the value of Boltzmann Constant k:

k = *8.31 **J**/**mol × K**/**6.02 × 10*^{23} *particles**/**mol*

= 1.38 × 10^{-23} *J**/**K*

= 1.38 × 10

The equation of Boltzmann Constant k, helps us write the Ideal gas Law in an alternative form as stated earlier. Rearranging the last equation, we have:

N_{a} = *R**/**k*

Also, we have explained earlier that

N_{a} = *N**/**n*

where N is the total number of particles in a gas and n is the number of moles. Thus, combining the last two equations, we obtain:

or

n × R = N × k

Therefore, substituting the right part of the above expression in the equation of Ideal Gas Law P × V = n × R × T, we obtain:

P × V = N × k × T

Note the difference between the two versions of the Ideal gas law. The original equation is written in terms of moles, while this last form involves the number of gas molecules.

A gas sample exerts 2 kPa pressure on the walls of a 40 L container at 270. What is the number of gas molecules in the sample?

Clues:

P = 2 kPa = 2000 Pa

V = 40 L = 0.04 m^{3}

T = 27°C = 300 K

Also, we known that R = 8.31 J/mol × K.

Let's calculate the number of moles first. From the Ideal Gas Law, we have

P × V = n × R × T

n =*P × V**/**R × T*

=*2000 × 0.04**/**8.31 × 300*

= 0.032 moles

n =

=

= 0.032 moles

Now, let's calculate the number of molecules N in the gas sample. We have:

n = *N**/**n*_{a}

Rearranging the last equation, we obtain:

N = n × N_{a}

= 0.032 moles × 6.02 × 10^{23} *molecules**/**mol*

= 0.19264 × 10^{23} molecules

= 1.9264 × 10^{22} molecules

= 0.032 moles × 6.02 × 10

= 0.19264 × 10

= 1.9264 × 10

You have reached the end of Physics lesson **13.6.3 The Ideal Gas Law**. There are 6 lessons in this physics tutorial covering **The Kinetic Theory of Gases. Ideal Gases**, you can access all the lessons from this tutorial below.

Enjoy the "The Ideal Gas Law" physics lesson? People who liked the "The Kinetic Theory of Gases. Ideal Gases lesson found the following resources useful:

- Law Feedback. Helps other - Leave a rating for this law (see below)
- Thermodynamics Physics tutorial: The Kinetic Theory of Gases. Ideal Gases. Read the The Kinetic Theory of Gases. Ideal Gases physics tutorial and build your physics knowledge of Thermodynamics
- Thermodynamics Revision Notes: The Kinetic Theory of Gases. Ideal Gases. Print the notes so you can revise the key points covered in the physics tutorial for The Kinetic Theory of Gases. Ideal Gases
- Thermodynamics Practice Questions: The Kinetic Theory of Gases. Ideal Gases. Test and improve your knowledge of The Kinetic Theory of Gases. Ideal Gases with example questins and answers
- Check your calculations for Thermodynamics questions with our excellent Thermodynamics calculators which contain full equations and calculations clearly displayed line by line. See the Thermodynamics Calculators by iCalculator™ below.
- Continuing learning thermodynamics - read our next physics tutorial: Pressure, Temperature and RMS Speed

We hope you found this Physics lesson "The Kinetic Theory of Gases. Ideal Gases" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.

- Carnot Engine Efficiency Calculator
- Entropy Calculator
- Gas Laws Calculator
- Molecular Mean Free Path Calculator
- Translational Kinetic Energy Of Gas Calculator
- Root Mean Square Speed Calculator
- Ideal Gas Law Calculator
- Change In The Gas Internal Energy Calculator
- Radiative Heat Transfer Calculator
- Evaporative Heat Transfer Calculator
- Convective Heat Transfer Calculator
- Conductive Heat Transfer Calculator
- Final Temperature Of Mixture Calculator
- Heat Absorbed Or Released Calculator
- Thermal Expansion Calculator
- Temperature Calculator