Gases mix homogeneously in any proportions. Each gas in a mixture will behave as if it were the only gas present. The pressure exerted by each gas in a mixture is called its partial pressure. Dalton’s Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases.
The partial pressure of a gas is proportional to its mole fraction, χ. For component A of a gas, the partial pressure and the mole fraction is
and
\(\displaystyle \chi_A\;=\;\frac{n_A}{n_{total}}\)
The mole fractions of mixture components add up to 1.
Example 1
If the total pressure is 45.5 atm, and there is 38.0 g of oxygen, 56.5 g of He, and 78.2 g of nitrogen gases, what is the partial pressure of each gas. First we convert the grams of each gas to moles.
56.5 g of He = 2.80 mole He
78.2 g of N2 = 2.79 mole N2
The total number of moles = 1.19 mole + 2.80 mole + 2.79 mole = 6.78 moles
Next, find the mole fraction of each gas.
\(\displaystyle \chi_{O_2}\;=\;\frac{1.19\;mol}{6.78\;mol}\;=\;0.176\)
\(\displaystyle \chi_{He}\;=\;\frac{2.80\;mol}{6.78\;mol}\;=\;0.413\)
\(\displaystyle \chi_{N_2}\;=\;\frac{2.79\;mol}{6.78\;mol}\;=\;0.412\)
Finally, calculate the partial pressure of each gas, PA = χAPtotal.
PO2 = χO2Ptotal = 0.176 x 45.5 atm = 8.00 atm
PHe = χHePtotal = 0.413 x 45.5 atm = 18.8 atm
PN2 = χN2Ptotal = 0.412 x 45.5 atm = 18.7 atm
For the mole fraction of N2, we could have added the first two mole fractions and then subtracted them from 1. The mole fractions of mixture components must add to one.
Example 2
Another example is for the reaction of acetylene with oxygen. The balanced equation is:
If C2H2 and O2 are mixed in the correct stoichiometric ratios, and if the total pressure of the mixture is 140. mm Hg, what are the partial pressure of the gases before the reaction occurs?
There are 2 moles of C2H2 and 5 moles of O2. The total is 7 moles of gas in the mixture. Calculate the mole fraction of C2H2.
\(\displaystyle \chi_{C_2H_2}\;=\;\frac{2\;mol}{7\;mol}\;=\;0.286\)
The mole fraction of O2 is given by: 1 – 0.286 = 0.714
The partial pressure of C2H2 is equal to 0.286 x 140. mm Hg = 40.0 mm Hg
The partial pressure of O2 is 140. mm Hg – 40.0 mm Hg = 100 mm Hg.
Collection of Gas Over Water
How does one measure the pressure of a gas that is produced in a lab experiment? One way, is by water displacement. A bottle of water is placed, open side down, into a dish of water. The gas produced from the reaction is exited through a tube that is placed under the container of water. The gas displaces water from the container, and the height of the water is measured. Water vapor is also included with the gas. The vapor pressure of the water is subtracted from the atmospheric pressure, Ptotal, to determine the gas pressure. According to Dalton’s Law, Ptotal = Pgas + PH2O. The vapor pressure of water can be found in tables for different temperatures. See the table below.
Example 3
Zinc reacts with dilute HCl to produce H2 gas. The gas is collected over water at 20°C. The total pressure is 0.987 atm and the volume is 1.486 L. Calculate the partial pressure and the mass of H2.
0.987 atm – 0.0230 atm = 0.967 atm
The temperature is 20.0°C + 273.15 = 293.15 K
Next, find the number of moles of gas using the ideal gas law.
PV = nRT and \(\displaystyle n\;=\;\frac{PV}{RT}\;=\;\frac{0.967\;atm\times\;1.486\;L}{0.0821\;\frac{L⋅atm}{mol⋅K}\times\;293.15\;K}\;=\;0.0597\;mol\;H_2\)
Convert moles to grams
\(\displaystyle 0.0597\;mol\;H_2\times\frac{2.016\;g}{mol}\;=\;0.120\;g\;H_2\)
Worksheet: Gas Mixtures and Collection of a Gas Over Water
Watch the following video before attempting exercises
Exercises
Exercise 1. A gas mixture has the following composition:
25.0% H2
2.8% HF
5.4% HCl
1.7% SO2
0.1% H2S.
What is the partial pressure of each of these gases if the total pressure of the gas mixture were 759 mmHg?
Check Answer/Solution to Exercise 1
Exercise 2. Both 1.23 mg of O2 and 0.51 mg of He are contained in a 250.00 mL flask at 18.0°C. Calculate the partial pressures of both gases. Calculate the total pressure in the flask.
Check Answer/Solution to Exercise 2
Exercise 3. A mixture of Ar and N2 gasses have a density of 1.435 g/L at STP. Calculate the mole fraction of each gas.
Check Answer/Solution to Exercise 3
Exercise 4. Chlorine, Cl2, gas can be formed by the following reaction:
2 NaCl (s) + 2 H2SO4 (l) + MnO2 (s) → Na2SO4 (s) + MnSO4 (s) + 2 H2O (g) + Cl2 (g)
A volume of 0.602 L of gas is collected over water at 28.0°C and a pressure of 758 mmHg. Calculate the mole fraction of Cl2.
Check Answer/Solution to Exercise 4
Exercise 5. Ammonium nitrate decomposes when heated to produce water vapor and N2 gas according to the following equation.
NH4NO3 (s) → 2 H2O (g) + N2 (g)
How many grams of ammonium nitrate will react if 4.26 L of nitrogen gas was collected over water at 19.3°C and 734 mmHg?
Check Answer/Solution to Exercise 5
Back to Gases: Properties and Behavior
Back to General Chemistry 1 Study Guides
Back to Home Page