17.6: Gas Mixtures

Learning Objective

• Learn Dalton's law of partial pressures.

One of the properties of gases is that they mix with each other. When they do so, they become a solution—a homogeneous mixture. Some of the properties of gas mixtures are easy to determine if we know the composition of the gases in the mix.

In gas mixtures, each component in the gas phase can be treated separately. Each component of the mixture shares the same temperature and volume. (Remember that gases expand to fill the volume of their container; gases in a mixture continue to do that as well.) However, each gas has its own pressure. The partial pressure of a gas, P_i, is the pressure that an individual gas in a mixture has. Partial pressures are expressed in torr, millimeters of mercury, or atmospheres like any other gas pressure; however, we use the term pressure when talking about pure gases and the term partial pressure when we are talking about the individual gas components in a mixture.

Dalton's law of partial pressures states that the total pressure of a gas mixture, P_tot, is equal to the sum of the partial pressures of the components, P_i:

\[P_{tot}=P_{1}+P_{2}+P_{3}+...=\sum_{\#of\, gases}P_{i}\nonumber \]

Although this law may seem trivial, it reinforces the idea that gases behave independently of each other.

Example \(\PageIndex{1}\):

A mixture of H₂ at 2.33 atm and N₂ at 0.77 atm is in a container. What is the total pressure in the container?

Solution

Dalton's law of partial pressures states that the total pressure is equal to the sum of the partial pressures. We simply add the two pressures together:

P_tot = 2.33 atm + 0.77 atm = 3.10 atm

Exercise \(\PageIndex{1}\)

N₂ and O₂. In 760 torr of air, the partial pressure of N₂ is 608 torr. What is the partial pressure of O₂?

Answer

152 torr

 

Food and Drink Application: Carbonated Beverages

Carbonated beverages—sodas, beer, sparkling wines—have one thing in common: they have CO₂ gas dissolved in them in such sufficient quantities that it affects the drinking experience. Most people find the drinking experience pleasant—indeed, in the United States alone, over 1.5 × 10⁹ gal of soda are consumed each year, which is almost 50 gal per person! This figure does not include other types of carbonated beverages, so the total consumption is probably significantly higher.

All carbonated beverages are made in one of two ways. First, the flat beverage is subjected to a high pressure of CO₂ gas, which forces the gas into solution. The carbonated beverage is then packaged in a tightly-sealed package (usually a bottle or a can) and sold. When the container is opened, the CO₂ pressure is released, resulting in the well-known hiss of an opening container, and CO₂ bubbles come out of solution. This must be done with care: if the CO₂ comes out too violently, a mess can occur!

Figure \(\PageIndex{1}\) Carbonated beverage © Thinkstock. If you are not careful opening a container of a carbonated beverage, you can make a mess, as the CO₂ comes out of solution suddenly.

The second way a beverage can become carbonated is by the ingestion of sugar by yeast, which then generates CO₂ as a digestion product. This process is called fermentation. The overall reaction is

C₆H₁₂O₆(aq) → 2C₂H₅OH(aq) + 2CO₂(aq)

When this process occurs in a closed container, the CO₂ produced dissolves in the liquid, only to be released from solution when the container is opened. Most fine sparkling wines and champagnes are turned into carbonated beverages this way. Less-expensive sparkling wines are made like sodas and beer, with exposure to high pressures of CO₂ gas.

Summary

• The pressure of a gas in a gas mixture is termed the partial pressure.
• Dalton's law of partial pressure says that the total pressure in a gas mixture is the sum of the individual partial pressures.