Ideal Gas Law:
Substituting in variables, the formula is:
Explanation and Discussion:
The Ideal Gas Law may be the largest and most complex of the gas laws. This is in part because of the number of variables in the equation, and in part to the abstraction of an "ideal" gas that the law is built on. The Ideal Gas Law is also designed as a sort of umbrella for Boyle's, Charles', and Avogadro's laws.
First, we'll go over the parts of the equation, PV=nRT. P is pressure. Pressure can be in either atmospheres (atm) or kilopascals (kPa). V is volume in liters (L). n is the number of moles of the gas. Because moles of a substance are determined by mass divided by molecular mass, it can create an interesting variant we will discuss later. R is the Ideal Gas Constant. Depending on whether atmosphers or kilospascals were used, the value is either 0.0821 L-atm/mol-K or 8.31 L-kPa/mol-K, respectively. Temperature is in absolute degrees Kelvin.
An interesting aspect of the Ideal Gas Law is its flexibility. It
contains elements that allow you to solve for other quantities, such as
density or molecular mass. To solve for molecular mass:
We can also see density in that last equation, m/V (grams/liter). The
same equation, but with density(d) in place of mass per volume (m/V),
To solve just for density, the equation would become:
So far, we have been skirting the concept of an ideal gas. What exactly is an ideal gas? An ideal gas is one that exactly conforms to the kinetic theory. The kinetic theory, as stated by Rudolf Clausius in 1857, has five key points. These are:
The Kinetic Theory makes several assumptions about an ideal gas. These cause problems because real gases are not ideal. The main causes of error are related to pressure and temperature.
At high pressures, the behavior of real gases changes dramatically from that predicted by the Ideal Gas Law. Under 10 atmospheres of pressure or less, Ideal Gas Law predictions are very close to real amounts and do not generate serious error.
When the temperature of a gas is close to its liquefaction point, the behavior is very different from Ideal Gas Law predictions. With increasing temperatures, the Ideal Gas Law predictions become close to real values.
The answer is simple: ideal gases have molecular volume and show no attraction between molecules at any distance; real gas molecules have volume and show attraction at short distances. Let us first consider what pressure does. Pressure at high degrees will bring the molecules very close together. This causes more collisions and also allows the weak attractive forces to come into play. With low temperatures, the molecules do not have enough energy to continue on their path to avoid that attraction.
The van der Waals Equation
In order to overcome the errors in the Ideal Gas Law, Johannes van der
Waals developed an equation to predict the behavior of real gases.
Johannes van der Waals' equation included corrections for the finite
volume of the molecules of the gas and the attractive forces between the
molecules. Two new constants, a and b, were added. The corrected
The correction nb subtracts the volume of the molecules. b is measured in liters/mole. The correction with a reflects the strength of attraction and is measured in liters2-atmosperes per moles2.
The equation is generally put in the form:
Values of a and b are different for each gas. The values of a and b generally increase with increased mass of the molecule and complexity of the molecule.
For an example calculation, check the Dalton's Law of Partial Pressure page.
You can test yourself.
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