A mixture of gases has a pressure of 1.6 atm. The mixture is analyzed and found to contain 0.200g of H2, 4.00g of CO2, and 1.45g of N2. What is the partial pressure of each gas in the mixture?
Dalton's Law states that the total pressure of a system is equal to the sum of the partial pressures of the individual gasses present. So the total pressure of the mixture (1.6 atm) is equal to the sum of the partial pressures of hydrogen, carbon dioxide, and nitrogen. Stated mathematically:
P(total) = 1.6 atm = p(H2) + p(CO2) + p(N2)
The partial pressure for any individual gas is equal to the total pressure of the system multiplied by the mole fraction for that particular gas. And the mole fraction for any particular gas is the number of moles of that gas divided by the total number of moles of all of the gasses in the system. So we need to calculate the mole fraction for each gas in order to find their partial pressures.
First, let's convert each gas from grams to moles.
0.2 g H2 * (1 mole / 2 g) = 0.1 moles H2
4.0 g CO2 * (1 mole / 44 g) = 0.091 moles CO2
1.45 g N2 * (1 mole / 28 g) = 0.052 moles N2
Adding all of these together gives 0.1+0.091+0.052=0.243 moles of gas total. Now we can find the mole fraction of each gas:
0.1 moles / 0.243 moles = 0.41 = mole fraction of H2
0.091 moles / 0.243 moles = 0.37 = mole fraction of CO2
0.052 moles / 0.243 moles = 0.21 = mole fraction of N2
Note that the mole fractions should add up to 1 and they do (accounting for rounding). Now we can calculate the partial pressures of each gas by multiplying each mole fraction by the total pressure of the system (1.6 atm):
0.41 * 1.6 atm = 0.656 atm = partial pressure of H2
0.37 * 1.6 atm = 0.592 atm = partial pressure of CO2
0.21 * 1.6 atm = 0.336 atm = partial pressure of N2
That is how to calculate the partial pressure of each gas in the mixture.
Since Dalton's Law states that the individual pressures of gases in a mixture add up to the total pressures, we can use the fact that the total pressure of all 3 gases equals 1.6 atm.
In order to determine the individual partial pressures, we basically need to find out what % of the gas is H2, CO2, and N2. This can be done using the equation for a mole fraction.
Mole fraction = moles of a particular gas/total moles of gas
Since we have the amounts of each gas in grams, we need to convert it to moles.
(0.2 g H2)/(2 g/mol) = 0.10 moles H2
(4.0 g CO2)/(44 g/mol) = 0.091 moles CO2
(1.45 g N2)/(28 g/mol) = 0.052 moles N2
Adding up the moles, 0.10 + 0.091 + 0.052 = 0.243 moles of gas. Now, we can determine the mole fraction of each gas.
H2 - 0.1/0.243 = 0.41
CO2 - 0.091/0.243 = 0.37
N2 - 0.052/0.243 = 0.21
What the mole fraction describes is the percentage of each gas in the mixture (if you add up the decimals you should get a value that is very close to 1).
Now, we can simply multiply the mole fraction by the total pressure, 1.6 atm to get the individual pressures.
0.41*1.6 = 0.66 atm H2
0.37*1.6 = 0.60 atm CO2
0.21*1.6 = 0.34 atm N2