Ideal gas law/Tutorials
- All gases mentioned below are assumed to be ideal, i.e. their p, V, T dependence is given by the ideal gas law.
- Absolute temperature is given by K = °C + 273.15.
- All pressures are absolute.
- The molar gas constant R = 0.082057 atm·L/(K·mol).
Example problems
See also the tutorials on the Video subpage.
Problem 1
Determine the volume of 1 mol of ideal gas at pressure 1 atm and temperature 20 °C.
Problem 2
Compute from Charles' and Gay-Lussac's law (V/T is constant) the volume of an ideal gas at 1 atm and 0 °C (Use the final result of the previous problem). Write V_{T} for the volume at T °C, then
Problem 3
A certain amount of gas that has an initial pressure of 1 atm and an initial volume of 2 L, is compressed to a final pressure of 5 atm at constant temperature. What is the final volume of the gas?
Boyle's law (pV is constant)
or
Inserting the given numbers
Ideal gas law
The number n of moles is constant
It is given that the initial and final temperature are equal, , therefore the products RT on both sides of the equation cancel, and Eq. (1.4) reduces to Eq. (1.1).
Problem 4
How many moles of nitrogen are present in a 50 L tank at 25 °C when the pressure is 10 atm? Numbers include only 3 significant figures.
Problem 5
Given is that dry air consists of 78.1% N_{2}, 20.1% O_{2}, and 0.8% Ar (volume percentages). The atomic weights of N, O, and Ar are 14.0, 16.0 and 39.9, respectively. Compute the mass of 1 m^{3} of dry air at 1 atm and 20 °C.
Answer
Since for ideal gases the volume V is proportional to the number of moles n, a volume percentage is equal to a molar percentage. For instance, for a mixture of two gases, it is easily shown that
which states that the molar percentage of gas 1 is equal to the volume percentage of gas 1.
The mass of 1 mole of dry air is
- M = 0.781×28.0 + 0.201×32.0 + 0.008×39.9 g = 28.6192 g
In problem 1 it is found that the volume of 1 mole of ideal gas at 1 atm and 20 °C is 24.0550 L = 24.0550×10^{−3} m^{3}, or
- 1 m^{3} contains 1/(24.0550×10^{−3}) = 41.5714 mol
Hence the mass of 1 cubic meter of dry air is
- M = 28.6192 × 41.5714 = 1189.7 g = 1.1897 kg
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