Question

there are two steps in the usual industrial preparation of acrylic acid, the immediate precursor of several useful plastics.

cac₂(s) + 2h₂o(l) ⇌ c₂h₂(g) + ca(oh)₂(s) k₁

6c₂h₂(g) + 3co₂(g) + 4h₂o(l) ⇌ 5ch₂chco₂h(g) k₂

the net reaction is:

6cac₂(s) + 16h₂o(l) + 3co₂(g) ⇌ 6ca(oh)₂(s) + 5ch₂chco₂h(g) k

write an equation that gives the overall equilibrium constant k in terms of the equilibrium constants k₁ and k₂. if you need to include any physical constants, be sure you use their standard symbols, which youll find in the aleks calculator.

k = □

Explanation:

Step1: Manipulate the first reaction

Multiply the first reaction \( \text{CaC}_{2}(s)+2\text{H}_{2}\text{O}(l)
ightleftharpoons\text{C}_{2}\text{H}_{2}(g)+\text{Ca(OH)}_{2}(s) \) by 6.
When a reaction is multiplied by a factor \( n \), its equilibrium constant \( K \) is raised to the power \( n \). So the equilibrium constant for \( 6\text{CaC}_{2}(s)+12\text{H}_{2}\text{O}(l)
ightleftharpoons6\text{C}_{2}\text{H}_{2}(g)+6\text{Ca(OH)}_{2}(s) \) is \( K_{1}^{6} \).

Step2: Combine the manipulated first reaction and the second reaction

The second reaction is \( 6\text{C}_{2}\text{H}_{2}(g)+3\text{CO}_{2}(g)+4\text{H}_{2}\text{O}(l)
ightleftharpoons5\text{CH}_{2}\text{CHCO}_{2}\text{H}(g) \) with equilibrium constant \( K_{2} \).
When two reactions are added together, the equilibrium constant of the net - reaction is the product of the equilibrium constants of the individual reactions.
The net - reaction \( 6\text{CaC}_{2}(s)+16\text{H}_{2}\text{O}(l)+3\text{CO}_{2}(g)
ightleftharpoons6\text{Ca(OH)}_{2}(s)+5\text{CH}_{2}\text{CHCO}_{2}\text{H}(g) \) is obtained by adding \( 6\text{CaC}_{2}(s)+12\text{H}_{2}\text{O}(l)
ightleftharpoons6\text{C}_{2}\text{H}_{2}(g)+6\text{Ca(OH)}_{2}(s) \) and \( 6\text{C}_{2}\text{H}_{2}(g)+3\text{CO}_{2}(g)+4\text{H}_{2}\text{O}(l)
ightleftharpoons5\text{CH}_{2}\text{CHCO}_{2}\text{H}(g) \)

Answer:

\( K = K_{1}^{6}K_{2} \)