Question

Nitrogen forms a surprising number of compounds with oxygen. A number of these, often given the collective symbol NOx (for "nitrogen x oxygens") are serious contributors to air pollution. They can often be interconverted, sometimes by reaction with oxygen or ozone (O3) in the air.
An atmospheric scientist decides to study the reaction between nitrogen monoxide and oxygen that produces nitrogen dioxide. He fills a stainless steel reaction chamber with 4.9atm of nitrogen monoxide gas and 5.1atm of oxygen gas and raises the temperature considerably. At equilibrium he measures the mole fraction of nitrogen dioxide to be 0.52.

Calculate the pressure equilibrium constant Kp for the equilibrium between nitrogen monoxide, oxygen, and nitrogen dioxide at the final temperature of the mixture. Round your answer to 2 significant digits.

Answer 1

Answer:

9.2

Explanation:

Let's do an equilibrium chart of this reaction:

2NO(g) + O₂(g) ⇄ 2NO₂(g)

4.9 atm    5.1 atm    0       Initial

-2x             -x           +2x    Reacts (stoichiometry is 2:1:2)

4.9-2x      5.1-x        2x      Equilibrium

The mole fraction of NO₂ (y) can be calculated by the Raoult's law, that states that the mole fraction is the partial pressure divided by the total pressure:

y = 2x/(4.9 - 2x + 5.1 -x + 2x)

0.52 = 2x/(10 - x)

2x = 5.2 -0.52x

2.52x = 5.2

x = 2.06 atm

Thus, the partial pressure at equilibrium are:

pNO = 4.9 -2*2.06 = 0.78 atm

pO₂ = 5.1 - 2.06 = 3.04 atm

pNO₂ = 2*2.06 = 4.12 atm

Thus, the pressure equilibrium constant Kp is:

Kp = [(pNO₂)²]/[(pNO)²*(pO₂)]

Kp = [(4.12)²]/[(0.78)²*3.04]

Kp = [16.9744]/[1.849536]

Kp = 9.2