Calculate the temperature of a substance given the pressure, volume, and amount of substance through the ideal gas law.

## Ideal Gas Law Formula

The follow equation is used to define ideal gasses:

pV = nRT

- Where p is the pressure in Pascals (Pa)
- V is the volume of gas in cubic meters (m^3)
- n is the number of moles of substance
- R is the ideal gas constant = 8.3144598 (J/mol*K)
- and T is the temperature of the gas in Kelvin (K)

## Ideal Gas Definition

An ideal gas is a form of gas that follows a set of conditions. These conditions mean that the ideal gas can be evaluated in simplified conditions that help with modeling and solving equations. The following is the set of parameters that define an ideal gas

- They obey Newton’s laws of motion
- They don’t interact except with collisions. I.E. no chemical reactions
- Collisions are elastic
- They are modeled as point particles (take up no space)
- It’s a large amount of substance.

If all of these criteria are met, then this gas can be modeled by the ideal gas law and corresponding equation.

## How to calculate ideal gas properties

The properties of a so-called ideal gas all follow the equation outlined above. Since the gas constant is already known, only 3 out of 4 properties must be known in order to calculate the missing property. For instance, if you know the pressure, volume, and amount of substance you can calculate the temperature. If you know the pressure, temperature, and volume, you can calculate the amount of substance. Simply re-arrange the equation and you are off and running.

The following example will go over the steps to calculating the properties of an ideal gas. In this case, specifically, we will solve for pressure.

- First, we must rearrange the ideal gas equation to solve for pressure. We can simply do this by dividing both sides by volume. The result is the following: p = nrT/V.
- Now that we have pressure solved for in the equation, we need to find or measure the 3 other variables. This would be a number of moles, temperature, and volume. For this example, we will assume 1 mole, 1 degree C temperature, and 1 cubic meter of volume.
- Finally, enter all of that information into the formula and you can find your pressure in pascals.