Question

2s(s) + 2o₂(g) ⇌ 2so₂(g) k₁ = 2×10¹⁰⁵
2so₂(g) + o₂(g) ⇌ 2so₃(g) k₂ = 7×10²⁴
. given the value of the equilibrium constants k₁ and k₂ for the reactions
represented above, what is the value of the equilibrium constant, k₃, for the
following reaction?
2s(s) + 3o₂(g) ⇌ 2so₃(g)
a
1×10¹³⁰
b
3×10⁸⁰
c
1×10⁶⁵
d.
2×10⁴⁰
e
7×10²⁴

Explanation:

Step1: Add the two given reactions

Adding Reaction 1 and Reaction 2 gives the target reaction:
$2S(s) + 2O_2(g) + 2SO_2(g) + O_2(g)
ightleftharpoons 2SO_2(g) + 2SO_3(g)$
Simplify: $2S(s) + 3O_2(g)
ightleftharpoons 2SO_3(g)$ (target reaction)

Step2: Multiply equilibrium constants

For added reactions, $K_3 = K_1 \times K_2$
$K_3 = (2 \times 10^{105}) \times (7 \times 10^{24}) = 14 \times 10^{129} \approx 1 \times 10^{130}$

Answer:

A. $1 \times 10^{130}$