Need help preparing for the General Chemistry section of the MCAT? MedSchoolCoach expert, Ken Tao, will teach everything you need to know about the Ideal Gas Law . Watch this video to get all the mcat study tips you need to do well on this section of the exam!
Ideal gases do not exist in nature. However, under conditions of high temperatures and low pressures, real gases may approximate ideal gases. Several equations of note on the MCAT can only be used to reason about ideal gases. Therefore, assuming that a gas is ideal allows us to use these equations in order to understand the properties of the gas under consideration.
Ideal Gas Law
The ideal gas law equation is PV = nRT. Here P represents the gaseous pressure, V the volume, n the moles of gas, R the gas constant (0.08 L ⋅atm ⋅mol-1 ⋅K-1), and T the temperature in Kelvin. By manipulating each variable of this equation, we can begin to understand how the various properties of a gas affect one another. Note that ideal gas calculations using these formulae must always be carried out with temperature in Kelvin, not degrees Celsius, else the answers obtained will be incorrect. While we can use the ideal gas law to solve many questions about ideal gases, it is often convenient to use simplified versions of the equation. For instance, Boyle's law, Charles’ law, and Avogadro's law. In these equations, a subset of the variables are held constant.
Boyle’s law
Boyle's law examines ideal gases when the temperature and number of moles of gas are held constant. Therefore, the whole right side of the equation is a constant value.
nRT = constant value
Extrapolating further, the product of pressure and volume must be a constant.
PV = (nRT)constant
Therefore, if you want to increase the pressure of a gas examined under Boyle’s law, then you have to decrease the volume, and vice versa. Boyle’s law thus illustrates that pressure is inversely related to the volume when the number of moles of gas and temperature are constant.
Consider one gas held under differing conditions of pressure and volume. If you increase the volume of its container, the gas molecules now have to travel a greater distance from one wall to collide with the other wall. The result of this is more infrequent collisions, producing a lower pressure. This can be expressed in equation form as
P1V1 = P2V2 = (nRT)constant
Charles’ Law
Charles’ law examines ideal gases when the number of moles of gas are constant and when the pressure is constant. If pressure and the number of moles of gas are constant, then volume is directly proportional to temperature.
V/T = (nR/P)constant
If temperature of gas molecules increases, they have more kinetic energy and collide more often with the container walls - implying a greater gaseous pressure. However, a requirement for Charles’ law is that the pressure stays constant. Therefore, when the temperature is raised, the increased pressure causes the volume to expand. The volume expanding lowers the pressure. Overall, there is no change in the pressure, but a proportional change in temperature and volume. This can be described by the equation
V1/T1 = V2/T2 = (nR/P)constant
Avogadro’s Law
Avogadro's law examines ideal gases when the temperature is constant and the pressure is constant. The directly proportional relationship between volume and number of moles of gas is depicted as
V/n = (RT/P)constant
At STP, one mole of a gas occupies a volume of 22.4 liters. If you have two moles of gas, the gas occupies twice that volume - 44.8 liters. This directly proportional relationship is depicted by the equation
V1/n1 = V2/n2 = (RT/P)constant
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