A sample of solid NH4NO3 was placed in an evacuated container and then heated so that it decomposed explosively according to the following equation:

NH4NO3 (s) N2O (g) + 2H2O (g)

At equilibrium, the total pressure in the container was found to be 2.72 bar at a temperature of 500.°C. Calculate Kp.

a.

1.64

b.

0.822

c.

2.98

d.

80.5

e.

0.745

The correct answer is C (Kp = 2.98)

Explanation:

Step 1: Data given

The total pressure in the container was found to be 2.72 bar at a temperature of 500°C

2.72 barr = 2.684431 atm

Step 2: The balanced equation

NH4NO3 (s) → N2O (g) + 2H2O (g)

Step 3: Calculate partial pressure N2O

Partial Press N2O = 1/3 * 2.72 = 0.907 bar

Step 4: Calculate partial pressure H2O

Partial Press, H2O = 2/3 * 2.72 = 1.813 bar

Kp = p (NO2) * p (H2O) ²

Kp = 0.907 * 1.813²

Kp = 2.98

The correct answer is C (2.98)

Kp is 2.98 (option c.)

Explanation:

The decomposition is:

NH₄NO₃ (s) → N₂O (g) + 2H₂O (g)

Total pressure at equilibrium is 2.72 bar so, in order to determine Kp we need the partial pressure and we only have total pressure.

According to stoichiometry, nitrogen oxide increase by 1, the partial pressure and water vapor, by 2.

Total pressure is: Partial pressure N₂O + Partial pressure H₂O

2.72 bar = X + 2X → X = 2.72 bar / 3 = 0.91 bar

Partial pressure N₂O = 0.91 bar

Partial pressure H₂O = 1.81 bar

We make the expression for Kp = Partial pressure N₂O. (P. pressure H₂O) ²

Kp = 0.91. 1.81² = 2.98

We do not consider the ammonium nitrate, because it is solid