Partial pressure is the pressure exerted by a component gas within a mixture.
According to Dalton's law of partial pressures, the total pressure is the sum of the partial pressures of each component.
This relationship can be explained using Kinetic Molecular Theory.
Pressure is caused by collisions of gas particles with a surface.
We can add together the pressure from collisions of individual components in a gas mixture to get the total pressure.
The partial pressure of a gas is proportional to the mole fraction of that gas in the mixture.
Mole fraction of gas "A" in a mixture would be equal to the moles of gas "A" divided by the total moles of gas in the mixture.
Let's practice using Dalton's law of partial pressures.
Our problem reads, "A 1500 milliliter mixture of oxygen, nitrogen, and carbon dioxide has a total pressure of 751 torr at 305 Kelvin.
The partial pressures of oxygen and carbon dioxide are 315 torr and 125 torr, respectively.
For part A, what is the mole fraction of nitrogen in the mixture?
For part B, what mass of nitrogen gas is present in the mixture?"
We'll start with Dalton's law of partial pressures:
the total pressure is equal to the partial pressure of oxygen plus the partial pressure of nitrogen plus the partial pressure of carbon dioxide.
Rearranging the equation for the partial pressure of nitrogen, and substituting in our values from the problem,
we get the partial pressure of nitrogen is 311 torr.
Next we can use our equation for the partial pressure of a gas within a mixture.
The partial pressure of nitrogen is equal to the mole fraction of nitrogen times the total pressure.
We can rearrange the equation to solve for the mole fraction of nitrogen.
Substituting in our values and completing the calculation, we get 0.414.
Mole fraction is a unitless number between zero and one.
To solve part B, we can start with the ideal gas law and rearrange it to solve for moles of gas.
Since we want moles of just nitrogen gas, we can use the partial pressure of nitrogen gas in the ideal gas law.
We'll need to convert the partial pressure of nitrogen from torr to atmospheres using the conversion factor one atmosphere is 760 torr.
We also need to convert 1500 milliliters into liters.
Completing our calculation, we should get 0.0245 moles of nitrogen.
Our last step is to convert from moles to grams using the molar mass of nitrogen.
Completing the calculation, we should get 0.687 grams of nitrogen gas in the mixture.
One common application of Dalton's law of partial pressures is when we experimentally collect a gas by the displacement of water.
If we wanted to collect hydrogen gas from the reaction of zinc metal and hydrochloric acid,
we could use this apparatus to easily determine the volume of gas, the total pressure of gas (which is just atmospheric pressure),
and the temperature.
Using this information we could calculate moles of gas.
However, we need to be aware that when collecting a gas over water, we'll also have some pressure of water vapor above the water,
which is included in the total pressure.
Using Dalton's law of partial pressures,
we can subtract out the vapor pressure of water at a given temperature to get the pressure of hydrogen gas.
Let's practice with this type of problem.
The problem reads, "The reaction of zinc metal with hydrochloric acid produces hydrogen gas and aqueous zinc chloride.
When the reaction is performed with a certain amount of zinc metal, 256 milliliters of gas is collected over water at 25° C.
Assume the gas is a mixture of hydrogen and water vapor.
The mixture has a total pressure of 753 torr, and the vapor pressure of water a 25° C is 23.8 torr.
Calculate the mass of zinc needed for this reaction."
Our first step is to write a balanced chemical equation for the reaction.
We can calculate the mass of zinc using dimensional analysis if we have the moles of hydrogen gas that were produced.
To determine the moles of hydrogen, we'll use the ideal gas law rearranged for moles of gas.
Notice that if we just want the moles of hydrogen gas, we'll need to use the partial pressure of hydrogen gas instead of the total pressure.
So we'll need Dalton's law of partial pressures to calculate the partial pressure of hydrogen gas.
Rearranging this equation to solve for the partial pressure of hydrogen gas, and substituting in our values from the problem, we get 729.2 torr.
We can substitute this into our ideal gas law equation, but we need to convert it from torr to atmospheres using 1 atmosphere is 760 torr.
We also need to convert our volume from milliliters to liters and temperature from degrees Celsius to Kelvin.
Completing the calculation, we should get 0.1004 moles of hydrogen.
Our last step is to convert moles of hydrogen gas produced to grams of zinc metal using dimensional analysis.
We can convert from moles of hydrogen to moles of zinc using the coefficients in the balanced chemical equation.
And we can convert from moles of zinc to grams of zinc using its molar mass.
Completing the calculation, we get 0.657 grams of zinc.