Dalton's Law of Partial Pressures

in a mixture of gases, the total pressure is the sum of the partial pressures of all the gases present. The partial pressure is the pressure a gas in a mixture would exert if it alone occupied the space of volume

Taken from Dictionary of Science

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Dalton's Law of Partial Pressure:

The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.

Mathematically, this can be represented as:

Pressure_Total = Pressure₁ + Pressure₂ ... Pressure_n

Explanation and Discussion:

Dalton's Law explains that the total pressure is equal to the sum of all of the pressures of the parts. This only is absolutely true for ideal gases, but the error is small for real gases. This may at first seem a trivial law, but it can be very valuable in the chemistry lab.

Let's say you want to collect hydrogen gas. To do this, you set up a system that uses a pneumatic trough, a test tube that has a pipetted stopped, a cable that connects the pipett into the pneumatic trough, and a test tube above the cable that collects the hydrogen. Warning: Do not conduct this experiment unless you are under the direction of a chemist or your chemistry teacher. It is dangerous and involves a Bunsen burner and dangerous materials. You submerge the test tube that will collect the hydrogen, and tilt it up so it only contains water. By placing zinc and acid in the pipetted test tube and heating it, hydrogen gas is given off. This gas pumps through the water and enters into the collection test tube. After the first few seconds, the gas will be pure hydrogen. Image of start of hydrogen generation. When the water level is equal in the test tube and the trough, turn off the generator. The pressure inside the test tube will be equal to the atmospheric pressure. Image of pressure equalibrium in hydrogen generator. Now you can use the ideal gas law to determine the number of hydrogen moles in the test tube, right? Not quite.

You see, the water you collected the hydrogen over has vapor pressure that will distort the equation if not accounted for. Because of the Dalton's Law of partial pressure, you know that the pressure in the test tube is from both the hydrogen and the water. To find just the hydrogen, you would have to subtract the vapor pressure of the water. Vapor pressure of water is published in most chemistry books as a table in the appendix, and varies by the temperature of the water.

Calculations with Dalton's Law:

Let's try that last experiment with real numbers. In our lab, the atmospheric pressure is 102.4 kPa. The temperature of our water is 25°C. We used a 250 mL beaker instead of a test tube to collect the hydrogen. Let's find the pressure of the hydrogen, and then find the moles of hydrogen using the ideal gas law.

Step 1: We need to know the vapor pressure of the water. A common table lists the pressure at 25°C as 23.76 torr. A torr is 1 mm of mercury at standard temperature. In kilopascals, that would be 3.17 (1 mm mercury = 7.5 kPa). We should also convert the 250 mL to .250 L and 25°C to 298 L.

Step 2: We can use Dalton's Law to find the hydrogen pressure. It would be:

P_Total = P_Water + P_Hydrogen
102.4 kPa = 3.17 kPa + P_Hydrogen

So the pressure of Hydrogen would be: 99.23 kPa or 99.2 kPa.

Step 3: We use the Ideal Gas Law to get the moles. Recall that the Ideal Gas Law is:

PV=nRT

where P is pressure, V is volume, n is moles, R is the Ideal Gas Constant (0.0821 L-atm/mol-K or 8.31 L-kPa/mol-K), and T is temperature.

Therefore, our equation would be:

99.2 kPa x .250 L = n x 8.31 L-kPa/mol-K x 298 K

This can be re-arranged so:

n = 99.2 kPa x .250 L / 8.31 L-kPa/mol-K / 298 K
n = .0100 mol or 1.00 x 10^-2 mol Hydrogen

Taken from Thinkquest