Answer:
a. pNO₂ = 1 atm pN₂O₄ = 4 atm
b. pNO₂ = 1 atm pN₂O₄ = 4 atm
c. It does not matter.
Explanation:
From the information given in this question we know the equilibrium involved is
N₂O₄ (g) ⇄ 2 NO₂ (g)
with Kp given by
Kp = p NO₂²/ p N₂O₄ = 0.25
We know that if we place 4.5 atm of N₂O₄ is placed in a flask, a quantity x is going to be consumed producing 2x atm of NO₂ and we can setup the following equation:
0.25 = p NO₂²/ p N₂O₄ = (2x)² / (4.5 - x)
0.25 x (4.5 - x) = 4x²
4x² + 0.25 x - 1.125 = 0
after solving this quadratic equation, we get two roots
x₁ = 0.5
x₂ = -0.56
the second root is physically impossible, and the partial pressures for x₁ = 0.5 will be
pNO₂ = 2 x 0.5 atm = 1.0 atm
pN₂O₄ = (4.5 - 0.5) atm = 4.0 atm
Similarly for part b, we get the equilibrium equation
0.25 = (9- 2x)² / x
0.25x = 81 - 36x + 4x²
the roots of this equation are:
x₁ = 5.0625
x₂ = 4
the first root is physically impossible since it will give us a negative partial pressure of N₂O₄ :
p N₂O₄ = 9 - 2(5.0625) = -1.13
the second root give us the following partial pressures:
p N₂O₄ = (9 - 2x4) atm = 1 atm
p NO₂ = 4 atm
The partial pressures are the same, it does not matter from which direction an equilibrium position is reached since what is essential is that the partial pressures of the gasses N₂O₄ and NO₂ obey the equilibrium equation.
