Dalton’s Law of Partial Pressure Collecting Gas over Water

Dalton’s Law of Partial Pressure allows us to determine the pressure (and from that, concentration) of a gas produced in a chemical reaction by collecting the gas over water.

collecting-gas-over-water

When gas is collected over water, the gas displaces the water in the flask as depicted above. The volume the gas displaces the water is the volume of the gas collected. If the flask is adjusted so that the water level inside the flask is equal to the water level outside of the flask, we know that the gas pressure inside the flask is equal to the gas pressure outside of the flask.

p-total

However, the gas in the flask is a combination of two gases really, the pressure of the gas PLUS the pressure of the water vapor, because water is in a continual state of vaporization and condensation.

p-atm

The value of the partial pressure of the water vapor can be found in a reference table, given that you know the temperature and atmospheric pressure. To determine the pressure of the gas, solve for Pgas:

p-gas

This experimental method only works for gases that are insoluble in water. If the gas were soluble in water then the amount of gas collected in the gaseous state would be less, as some of it would be dissolved in the water. In that case, the partial pressure of the gas collected would be less than the total amount of gas produced. Examples of gases that are soluble in water, and therefore cannot be collected in this way, are ammonia NH3 and hydrogen chloride HCl.

Let’s look at a sample problem.

Sample Problem

21.4 mL of hydrogen gas were collected over water at 15 ºC and 756.0 mm Hg. How many moles of hydrogen gas were collected? (vapor pressure of H2O at 15 ºC is 12.8 mm Hg).

From the volume and pressure of hydrogen gas, we can determine the number of moles of hydrogen gas collected using the ideal gas law. We know that the volume collected is 21.4 mL. To determine the pressure of gas collected, we must realize that the 756.00 mm Hg of gas collected over water is a mixture of hydrogen gas and water vapor. We’re given the partial pressure of water vapor as 12.8 mm Hg. We know that the total pressure in the flask is a sum of the partial pressure of hydrogen gas and the partial pressure of water vapor:

p-total-h2

Rewriting to solve for the partial pressure of hydrogen gas:

p-h2

Plugging in our values:

743

The pressure of the hydrogen gas collected is 743.2 mm Hg.

We want to now find the number of moles of hydrogen gas produced.

These are our givens:

P = 743.2 mm Hg

V = 21.4 mL

T = 15 ºC

And the ideal gas law is:

ideal-gas-law-small

 

We need to make sure the units of our variables match those of Rydberg’s constant R, L-atm-K-1-mol-1.

Pressure must be in the unit atmospheres, volume must be in the unit Liters and temperature must be in the unit Kelvin.

978atm

 

214L

 

288K

 

Rewriting the ideal gas law to solve for moles, n:

 

nPV

 

And plugging in our values for the variables P, V and T:

 

885mol

 

8.85 x 10-4 mol of H2 gas was collected.

Sample Problem

A 27.7 mL sample of CO2 was collected over water at 25.0 ºC and 1.00 atm. How many moles of CO2(g) were collected? (The vapor pressure of water at 25.0 ºC is 23.8 torr.)

Again, we are asked to solve for moles of gas. We will ultimately use the ideal gas law to do this. Keep in mind that a problem could go beyond the ideal gas law, and require us to use the calculated moles of a gas in a stoichiometric problem. This current problem does not go into stoichiometry.

We are given a total pressure of gas collected as 1.00 atm, and that the water vapor pressure is 23.8 torr. We know that the total pressure is the sum of the partial pressures of the gas and water vapor.

p-total-co2

Solving for the partial pressure of CO2:

p-co2

 

Since the total pressure is given in atm, and the vapor pressure of water is given in the unit torr, we need to first convert vapor pressure to atmospheres.

313atm

 

 

 

97atm2

 

We want to find mol CO2, n, and we’re given:

P = 0.97 atm

V = 27.7 mL

T = 25.0 ºC

We need to convert the unit of volume to Liter and the unit of temperature to Kelvin.

277L

 

298K

 

The Ideal Gas Law is:

ideal-gas-law-small

 

Rewriting to solve for n:

nPV

 

And, plugging in our variables for P, V and T:

 

11mol

 

0.0011 mol CO2 was collected.