Question

A gas mixture contains 0.150 mol of oxygen ( O 2 ) gas, 0.419mol of nitrogen ( N 2 ) gas. and 0.211 mol of argon ( Ar ) gas in a 0.250L flask at 298K . What is the total pressure of the mixture?

Answer 1

77.3 bar

Explanation:

We can use the Ideal Gas Law to calculate the individual gas pressures and then use Dalton’s Law of Partial pressures to calculate the total pressure.

Step 1. Calculate the individual gas pressures.

pV = nRT Divide both sides by V

p = (nRT)/V = n(RT/V)

For ease of typing, let’s call oxygen Gas 1, nitrogen Gas 2, and argon Gas 3.

For all three gases,

R = 0.083 14 bar·L·K⁻¹mol⁻¹

T = 298 K

V = 0.250 L

Let’s calculate the value of (RT)/V.

(RT)/V = (0.083 14 × 298)/0.250

(RT)/V = 24.78/0.250

(RT)/V = 99.10 bar·mol⁻¹

So,

p = 99.10n Calculate p₁

———

p₁ = 99.10 × 0.150

p₁ = 14.87 bar Calculate p₂

———

p₂ = 99.10 × 0.419

p₂ = 41.52 bar Calculate p₃

———

p₃ = 99.10 × 0.211

p₃ = 20.91 bar

===============

Step 2. Calculate the total pressure

According to Dalton’s Law,

p = p₁ + p₂ + p₃

p = 14.87 + 41.52 + 20.91

p = 77.3 bar