How to Calculate Density of a Gas

How to Calculate Density of a Gas Density is mass per unit volume. Finding the density of a gas is the same as finding the density of a solid or liquid. You have to know the mass and the volume of the gas. The tricky part with gases is that you are often given pressures and temperatures with no mention of volume. You have to figure it out from the other information. This example problem will show how to calculate density of a gas when given the type of gas, the pressure, and the temperature. Question: What is the density of oxygen gas at 5 atm and 27  °C? First, lets write down what we know: Gas is oxygen gas or O2.Pressure is 5 atmTemperature is 27  °C Lets start with the Ideal Gas Law formula. PV nRT whereP pressureV volumen number of moles of gasR gas constant (0.0821 L ·atm/mol ·K)T absolute temperature If we solve the equation for volume, we get: V (nRT)/P We know everything we need to find the volume now except the number of moles of gas. To find this, remember the relationship between number of moles and mass. n m/MM wheren number of moles of gasm mass of gasMM molecular mass of the gas This is helpful since we needed to find the mass and we know the molecular mass of oxygen gas. If we substitute for n in the first equation, we get: V (mRT)/(MMP) Divide both sides by m: V/m (RT)/(MMP) But density is m/V, so flip the equation over to get: m/V (MMP)/(RT) density of the gas. Now we need to insert the values we know. MM of oxygen gas or O2 is 1616 32 grams/moleP 5 atmT 27  °C, but we need absolute temperature.TK TC 273T 27 273 300 K m/V (32 g/mol  Ã‚ · 5 atm)/(0.0821 L ·atm/mol ·K  · 300 K)m/V 160/24.63 g/Lm/V 6.5 g/L Answer: The density of the oxygen gas is 6.5 g/L.