Ideal Gas Law Example Problem

Find Moles of Gas Using the Ideal Gas Law

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At low temperatures, real gases act like ideal gases. Tetra Images/Jessica Peterson/Getty Images

The ideal gas law is an equation of state the describes the behavior of an ideal gas and also a real gas under conditions of ordinary temperature and low pressure. This is one of the most useful gas laws to know because it can be used to find pressure, volume, number of moles, or temperature of a gas.

The formula for the ideal gas law is:

PV = nRT

P = pressure
V = volume
n = number of moles of gas
R = ideal or universal gas constant = 0.08 L atm / mol K
= absolute temperature in Kelvin

Sometimes, you may use another version of the ideal gas law:

PV = NkT

where:

N = number of molecules
k = Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K

Ideal Gas Law Example

One of the easiest applications of the ideal gas law is to find the unknown value, given all the others.

6.2 liters of an ideal gas are contained at 3.0 atm and 37 °C. How many moles of this gas are present?

Solution

The ideal gas law states

PV = nRT

Because the units of the gas constant are given using atmospheres, moles, and Kelvin, it's important to make sure you convert values given in other temperature or pressure scales. For this problem, convert °C temperature to K using the equation:

T = °C + 273

T = 37 °C + 273
T = 310 K

Now, you can plug in the values. Solve ideal gas law for number of moles

n = PV / RT

n = ( 3.0 atm x 6.2 L ) / ( 0.08 L atm /mol K x 310 K)
n = 0.75 mol

Answer

There are 0.75 mol of the ideal gas present in the system.