Ideal Gas Law Example Problem 1

The ideal gas law describes the behavior of an ideal gas, but can also be used when applied to real gases under a wide variety of conditions. This allows us to use this law to predict the behavior of the gas when the gas is subjected to changes in pressure, volume or temperature.

The Ideal Gas Law is expressed as

PV = nRT
where
P = Pressure
V = Volume
n = number of moles of gas particles
T = Absolute Temperature in Kelvin
and
R is the Gas Constant.

The Gas Constant, R, while a constant, depends on the units used to measure pressure and volume. Here are a few values of R depending on the units.

R = 0.0821 liter·atm/mol·K
R = 8.3145 J/mol·K
R = 8.2057 m³·atm/mol·K
R = 62.3637 L·Torr/mol·K or L·mmHg/mol·K

This ideal gas law example problem shows the steps needed to use the Ideal Gas Law equation to determine the amount of gas in a system when the pressure, volume, and temperature are known.

Problem

A cylinder of argon gas contains 50.0 L of Ar at 18.4 atm and 127 °C. How many moles of argon is in the cylinder?

Solution

The first step of any Ideal Gas Law problem is to convert temperatures to the absolute temperature scale, Kelvin. At relatively low temperatures, the 273 degree difference makes a very large difference in calculations.

To change °C to K, use the formula

T = °C + 273

T = 127 °C + 273
T = 400 K

The second step is to choose the ideal gas constant value of R suitable for our units. Our example has liters and atm. Therefore, we should use

R = 0.0821 liter·atm/mol·K

Our example wants us to find the number of moles of gas.

PV = nRT

solve for n

plug in our values

n = 28.0 mol

Answer

There are 28.0 moles of argon in the cylinder.

There are two important factors to keep in mind when doing this type of problem. First, the temperature is measured as absolute temperature. Second, use the correct value of R for your problem. Using the correct units of R will avoid embarrassing unit errors.