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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:
Rearranging in order to remove the fraction, we obtain the Ideal Gas Law:
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 dm3 = 0.001 m3
Given that
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,
Therefore,
Thus,
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:
Substituting the known values, we obtain for the value of Boltzmann Constant k:
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:
Also, we have explained earlier that
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
Therefore, substituting the right part of the above expression in the equation of Ideal Gas Law P × V = n × R × T, we obtain:
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 m3
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
Now, let's calculate the number of molecules N in the gas sample. We have:
Rearranging the last equation, we obtain:
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.
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