## Tuesday, September 8, 2020

### Universal Gas Law and Combined Gas Law

General Chemistry Index

Where are we going with this? Getting to the current models of atomic theory didn't happen over night. This page will support the ability to use the kinetic molecular theory with the combined and ideal gas laws to explain changes in volume, pressure, moles and temperature of a gas and apply the ideal gas equation (PV = nRT) to calculate the change in one variable when another variable is changed and the others are held constant.

The Math: Universal Gas Law and Combined Gas Law
I told you there'd be math!

Universal Gas Law

When the number of molecules are included in calculations, the following formula can be used:

PV = nRT

where P is pressure, V is volume, n is number of moles, R is a number called the "gas constant", and T is temperature in Kelvin.

Just so you know… the gas constant changes depending on what units you are using. It can be Googled, such as: 82.05746  cm^3 atm / (K • mol)

Looking at the equation allows predicting how gases will behave in relationship to changing the number of molecules:

PV = nRT
(Remember, R cannot change because it is just a number like π (pi)
• if n goes up, then P and/or V have to go up unless T goes down
• if n goes down, the P and/or V have to go down unless T goes up.

The Combined Gas Law (revised)

Traditionally, the Combined Gas Law demonstrates a relationship between pressure, volume, and temperature and assumes that the number of molecules does not change.

Beginning with the Universal Gas Law, it is easy to derive the Combined Gas Law.

Divide both sides by nRT…

Using this, an equation can be set up for the "before / after" process used with Boyle's and Charles's Laws. Setting up an equation for a second state, should something from a first state change, would result in this:

Multiplying both sides by R would result in:

Now, using this equation to examine changes can result in deeper understanding. As n changes from state 1 to state 2, P, V and T must also respond in the second state as well.

It is IMPORTANT to NOTE that there are only certain combinations of P, V, T, and n that are valid because they must work with R such that.

or

If n is considered to be the same across both states, it can be omitted. Doing this will result in an equation that is identical to the commonly discussed Combined Gas Law, but including n.

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