Kaplan MCAT General Chemistry Review

Ours is a highly aromatic world. The smells and aromas of food, flowers, exhaust, rot, wet dog, and skunk are instantly recognizable and elicit in us reactions of delight or disgust. In our introduction to Chapter 4, Compounds and Stoichiometry, we explained that our sense of smell depends upon the interactions between vaporized compounds and the chemical receptors of the olfactory epithelium located inside our nasal cavities. The rate at which those gaseous compounds travel will determine what we’d smell first: a flower or a skunk.

The movement of gas molecules through a mixture (such as air) is called diffusion. The kinetic molecular theory of gases predicts that heavier gases diffuse more slowly than lighter ones do because of their differing average speeds. (Because all gas particles have the same average kinetic energy at the same temperature, it must be that particles with greater mass travel at a slower average velocity.) In 1832, Thomas Graham showed mathematically that under isothermal and isobaric conditions, the rates at which two gases diffuse are inversely proportional to the square root of their molar masses. Thus,

where r₁ and r₂ are the diffusion rates of gas 1 and gas 2, respectively, and MM₁ and MM₂ are the molar masses of gas 1 and gas 2, respectively. You know by now that the MCAT commonly tests students’ understanding of ratios. From this equation, you can see that a gas that has a molar mass four times that of another gas will travel half as fast as the lighter gas.

Key Concept

Diffusion: When gases mix with one another. Effusion: When a gas moves through a small hole under pressure. Both will be slower for larger molecules.

Effusion is the flow of gas particles under pressure from one compartment to another through a small opening. Graham used the kinetic molecular theory of gases to show that for two gases at the same temperature, the rates of effusion are proportional to the average speeds. He then expressed the rates of effusion in terms of molar mass and found that the relationship is the same as that for diffusion:

Latex balloons are often filled with a 60/40 mixture of helium and air. Latex is a fairly porous material that allows for the effusion of the gas mixture contained inside. Since the weighted average molar mass of air (consisting of about 78% N₂ and 21% O₂) is about 29 grams/mole and the molar mass of helium is 4 grams/ mole, the helium gas will effuse almost three times faster than the air. This is why helium balloons have such a fleeting life span and perhaps explains in part their ability to enchant us.

Ideal Gas Behavior

The ideal gas law was first stated in 1834 by Benoît Paul Émile Clapeyron, more than 170 years after Sir Robert Boyle has pesrformed his experimental studies on the relationship between pressure and volume in the gas state. In fact, by the time the ideal gas law found its expression, Boyle’s law, Charles’ law, and even Dalton’s law had already been well established. Historical considerations aside, it will benefit us to examine the ideal gas law first so that we can then understand the other laws, which had been “discovered” first, to be only special cases of the ideal gas law.

One more important discovery that preceded Clapeyron’s formulation of the ideal gas law was Amedeo Avogadro’s formulation in 1811, known as Avogadro’s principle, that all gases at a constant temperature and pressure occupy volumes that are directly proportional to the number of moles of gas present. Equal amounts of all gases at the same temperature and pressure will occupy equal volumes. For example, one mole of any gas, irrespective of its chemical identity, will occupy 22.4 liters at STP.

where n₁ and n₂ are the number of moles of gas 1 and gas 2, respectively, and V₁ and V₂ are the volumes of the gases, respectively.

IDEAL GAS LAW.

The ideal gas law shows the relationships among four variables that define a sample of gas: pressure (P), volume (V), temperature (T ), and number of moles (n). The law combines the mathematical relationships earlier determined by the work of Boyle, Charles, and Gay-Lussac with Avogadro’s principle and is represented by this equation:

PV = nRT

where R is a constant known as the gas constant, which has a value of 8.21 × 10^-2 (L•atm)/(mol•K). Be aware that the gas constant can be expressed in other units.

MCAT Expertise

PV = nRT. Knowing this equation means we can derive others based on the answer we are looking to find.