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

The answer is K2 = (1/K1)2

Step-by-step explanation:

For the first reaction:

NO + 1/2O₂ = NO₂

`K_(1) =([NO_(2)] )/([NO][O_(2)]^(1/2) )`

For the second reaction:

2NO₂ = 2NO + O₂

`K_(2) =([NO]^(2)[O_(2)] )/([NO_(2)]^(2) )=([NO][O_(2)]^(1/2) )/([NO_(2)]^(2) ) =((1)/(K_(1) ) )^(2)`

Answer 2

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

Step-by-step 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