Gas Mixtures and Density

The Ideal Gas Law and its subsidiary laws are useful in some respects on their own, but it may be difficult to see how they apply to chemistry. In this last section, we will build off the Ideal Gas Law to solve chemistry problems involving molecular mass. We will also learn about Dalton's Law of Partial Pressures, which is frequently used in chemistry lab settings, including your lab for this week.

Molecular Mass of Gases

The molecular mass of a substance is a very useful thing to know. It can be used (since it is equal to the molar mass) to convert between grams and moles. It can also be used to confirm the identity of an unknown compound.

A common way to find a compound's molecular mass (if the formula is unknown) is to take a sample of the compound, weigh it to find its mass m, and use some other technique to find the moles present in the sample n. The molecular mass is then equal to m divided by n.

Finding the number of moles in a sample is sometimes difficult; however, if you can get your sample into the gas phase and measure its temperature, pressure, and volume, the Ideal Gas Law allows you to easily calculate n.

Suppose, for example, that 25.0 g of a gas occupies a volume of 3.0 liters at 27 ^oC and a pressure of 4.0 atm. What is the molecular mass of the gas?

The Ideal Gas Law allows us to calculate the moles of gas in the sample, and gives a value of 0.49 mol. We can then take the mass of the sample (25.0 g) and divide it by 0.49 mol, which gives a molar mass of 51 g/mol.

Gas Density

Combining the Ideal Gas Law with the equation for molecular mass allows us to develop an equation for predicting the density of a gas, which can be useful in many settings. Below at left, you can see a rearrangement of the IGL, with the equation for molecular mass at right (where M is the molecular mass). The expression m/M is plugged in for n. Then both sides are multiplied by M, and the expression m/V is collapsed to give d, the gas density (since density is mass over volume).

For example, we can use this equation to calculate the density of a gas like ammonia (M = 17.03 g/mol) at STP, meaning a pressure of 1.0 atm and a temperature of 273 K. It's important to remember that if you use the R value of 0.082, it has units of liters in it, so the density comes out in g/L. In this case, the density of ammonia at STP would be 0.76 g/L.

Dalton's Law of Partial Pressure

One of the assumptions of the Kinetic Molecular Theory is that gas particles simply bounce off of each other without interacting in any way. This means that the identity of the gas particles does not influence their PVT behavior.

Many gases are, like air, homogeneous mixtures of several gases. Because the gas particles do not interact in any way other than bouncing off each other, each gas particle has exactly the same influence on the gas law properties (P, V, T, and n) of the gas. One mole of nitrogen will exert the same pressure as a mixture of a tenth of a mole each of ten different gases under the same conditions of temperature and volume, assuming, of course, that the gases all behave like ideal gases (which is generally a good assumption).

This led John Dalton to propose that, in a mixture of two or more gases, each one behaves just as if it were the only one in the container, exerting a pressure called its partial pressure. The total pressure in the container is then just the sum of these partial pressures. This is called Dalton’s Law of Partial Pressures.

Theoretical Background

The partial pressure of a gas is the pressure it would exert if it were the only gas in the container; and, in fact, this is the pressure that it does exert. This is a behavior of gases which obey the Ideal Gas Law. As long as the assumptions of the Kinetic Molecular Theory are valid, Dalton’s Law describes the behavior of mixtures of gases.

Each gas in a mixture obeys the Ideal Gas Law just as if it were the only gas in the container. For example, in a mixture of two gases, gas 1 and gas 2, P₁ and P₂ are their partial pressures, and n₁ and n₂ are the numbers of moles of the two gases, respectively. Since they are mixed together, each one occupies the entire volume of the container, V, and they are always at the same temperature, T.

Each gas can occupy the entire volume of the container only if the other gas molecules take up no room at all. This, if you remember, is one of the assumptions of the Kinetic Molecular Theory. Dalton’s Law would also not be valid if the molecules of one gas bound to or reacted with those of another gas in the mixture; but this, too, would violate one of the assumptions of the Kinetic Molecular Theory.

We can write the Ideal Gas Law for each gas separately. That is, each gas in a mixture obeys the Ideal Gas Law. Its volume is the entire volume of the container, which is the same for every gas in the mixture. Its temperature is the same as the temperature of all the other gases. The pressure and the number of moles, however, are the values that apply only to that gas, and so have subscripts in the Ideal Gas Law indication which gas we mean.

Dalton's Law in the Lab

Dalton's law very commonly gets used in laboratory settings like the lab you will perform for this lesson; that is, settings where a gas is collected over water. Gas generated by a reaction can be bubbled through water and trapped in a container above the water's surface as shown below. This is a convenient way to capture a gas sample, and allows for measurement of the temperature and volume of the sample pretty easily. However, measuring the sample's pressure comes with a complication.

As shown here, in addition to the gas produced by the reaction, the space above the water will also contain a (usually small) amount of gaseous water, AKA water vapor. Both the gas of interest and the water vapor exert a partial pressure (P₁ and P₂), with the total pressure P equal to P₁ + P₂.

Most methods of measuring pressure in the container cannot distinguish between partial pressures of gases in a mixture, and instead can only measure the total pressure P. If we are interested specifically in the pressure of the gas of interest, we must calculate it by subtracting the partial pressure of the water vapor, as shown below.

Fortunately, the partial pressure of water in a container is always the same at a given temperature, and the values are well-documented and can be easily looked up. It doesn't matter what size container we use for collection, how much gas we are generating, or what the identity of our gas of interest is; if we can measure the temperature, we can look up the partial pressure of water and subtract it from the total pressure to calculate our gas pressure.

Google Sites

Report abuse