Question

Consider the following two equilibria and their respective equilibrium constants: (1) NO(g) + ½O2(g) NO2(g) (2) 2NO2(g) 2NO(g) + O2(g) Which one of the following is the correct relationship between the equilibrium constants K1 and K2?
K2 = 1/(2 K1)

K2 = 2/K1

K2 = 1/(2K1)2

K2 = (1/K1)2

K2 = –K1/2

Answer 1

Answer:

The fourth option is correct K2 = (1/K1)2

Explanation:

Step 1: Data given

(1) NO(g) + ½O2(g) ⇆ NO2(g)  

(2) 2NO2(g) ⇆ 2NO(g) + O2(g)

Step 2: Calculate K1

K1 = [NO2] / [NO][O2]^0.5

Step 3: Calculate K2

K2 = [NO]²[O2]/[NO2]²

Step 4: When we square the first equation

K1² = [NO2]² / [NO]²[O2]

Step 5: Calculate the reverse reaction

1/K1² = [NO]²[O2] / [NO2]² = K2

So K2 = 1/K1²  = 1²/K1²

The fourth option is correct K2 = (1/K1)2

Answer 2

Answer:

The answer is K2 = (1/K1)2

Explanation:

For the first reaction:

NO + 1/2O₂ = NO₂

$K_{1} =\frac{[NO_{2}] }{[NO][O_{2}]^{1/2} }$

For the second reaction:

2NO₂ = 2NO + O₂

$K_{2} =\frac{[NO]^{2}[O_{2}] }{[NO_{2}]^{2} }=\frac{[NO][O_{2}]^{1/2} }{[NO_{2}]^{2} } =(\frac{1}{K_{1} } )^{2}$