partial+pressure

Dalton's law of partial pressures deals only with a mixture of ideal gases. Essentially, it states that in a mixture, all gases exert their own pressures (called partial pressures); the sum of all of these pressures is equal to the total pressure of the gas mixture.

Here is the equation: P(total) = P(gas 1) + P(gas 2) + ... etc.

The best example is air, which is primarily a mixture of nitrogen gas and oxygen gas:



Suppose a 1.00 liter sample of air at 25 C has a pressure of 1.00 atm.
 * The total pressure of the mixture is 1.00 atm. P(total) = 1.00 atm
 * Air is about 78% nitrogen (N2), 21% oxygen (O2), and the remainder argon (Ar).
 * To determine the partial pressure of each gas, multiply its percent in decimal form by the total pressure:
 * For P(N2): 0.78 x 1.00 = 0.78 atm
 * For P(O2): 0.21 x 1.00 = 0.21 atm
 * For P(Ar): 0.01 x 1.00 = 0.01 atm
 * So, P(total) = P(N2) + P(O2) + P(Ar) = 0.78 atm + 0.21 atm + 0.01 atm = 1.00 atm!

The ideal gas law can then be used, if enough information is provided, to determine the amount (in moles) of each gas in the mixture.

PV = nRT

Individual partial pressures can be used to determine the amounts of individual gases:

P(N2)V = n(N2)RT

(0.78 atm)(1.00 L) = n(N2)(0.08206)(298 K)

Solving for n(N2) yields 0.032 mole N2 in the air sample.

Example:

A 2.0 L steel cylinder contains a mixture of gases at 20 C and 10.0 atm. The mixture is composed of 3.0 moles of N2, 2.0 moles of O2, and 1.0 mole of CO2. Calculate the partial pressure of each gas in the cylinder.

Step 1: Find the percent composition of the mixture.
 * The total number of moles of gases is 3.0 mol + 2.0 mol + 1.0 mol = 6.0 mol
 * To find the percentage in decimal form, divide the individual mole amounts by the total moles:
 * For N2: 3.0/6.0 = 0.50 = 50%
 * For O2: 2.0/6.0 = 0.33 = 33%
 * For CO2: 1.0/6.0 = 0.17 = 17%

Step 2: multiply the mole fractions by the total pressure to get the individual partial pressures:
 * For N2: 0.50 x 10.0 atm = 5.0 atm
 * For O2: 0.33 x 10.0 atm = 3.3 atm
 * For CO2: 0.17 x 10.0 atm = 1.7 atm

To check, use Dalton's Law of partial pressures:
 * P(total) = P(N2) + P(O2) + P(CO2) = 5.0 atm + 3.3 atm + 1.7 atm = 10.0 atm.

Here are some worksheets: