If kc = 7.04 * 10-2 for the reaction: 2 hbr (g) ⇌h2 (g) + br2 (g), what is the value of kc for the reaction: 1/2 h2 (g) + 1/2 br2 ⇌hbr (g)

At the first reaction when 2HBr (g) ⇄ H2 (g) + Br2 (g)

So Kc = [H2] [Br2] / [HBr]^2

7.04X10^-2 = [H2][Br] / [HBr]^2

at the second reaction when 1/2 H2 (g) + 1/2 Br2 (g) ⇄ HBr

Its Kc value will = [HBr] / [H2]^1/2*[Br2]^1/2

we will make the first formula of Kc upside down:

1/7.04X10^-2 = [HBr]^2/[H2][Br2]

and by taking the square root:

∴ √ (1/7.04X10^-2) = [HBr] / [H2]^1/2*[Br]^1/2

∴ Kc for the second reaction = √ (1/7.04X10^-2) = 3.769