the reduction of iron(iii) oxide to iron during steel - making can be summarized by this sequence of…

the reduction of iron(iii) oxide to iron during steel - making can be summarized by this sequence of reactions: 2c(s)+o2(g)⇌2co(g) k1 fe2o3(s)+3co(g)⇌2fe(l)+3co2(g) k2 the net reaction is: 2fe2o3(s)+6c(s)+3o2(g)⇌4fe(l)+6co2(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.

the reduction of iron(iii) oxide to iron during steel - making can be summarized by this sequence of reactions: 2c(s)+o2(g)⇌2co(g) k1 fe2o3(s)+3co(g)⇌2fe(l)+3co2(g) k2 the net reaction is: 2fe2o3(s)+6c(s)+3o2(g)⇌4fe(l)+6co2(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.

Answer

Explanation:

Step1: Write equilibrium - constant expressions

For the reaction $2C(s)+O_2(g)\rightleftharpoons 2CO(g)$, the equilibrium - constant expression is $K_1=\frac{[CO]^2}{[O_2]}$ (since the concentration of solid $C$ is not included in the expression). For the reaction $Fe_2O_3(s)+3CO(g)\rightleftharpoons 2Fe(l)+3CO_2(g)$, the equilibrium - constant expression is $K_2 = \frac{[CO_2]^3}{[CO]^3}$ (since the concentrations of solid $Fe_2O_3$ and liquid $Fe$ are not included). For the net reaction $2Fe_2O_3(s)+6C(s)+3O_2(g)\rightleftharpoons 4Fe(l)+6CO_2(g)$, the equilibrium - constant expression is $K=\frac{[CO_2]^6}{[O_2]^3}$.

Step2: Manipulate the expressions for $K_1$ and $K_2$ to get $K$

First, from $K_1=\frac{[CO]^2}{[O_2]}$, we can get $[CO]^2 = K_1[O_2]$. From $K_2=\frac{[CO_2]^3}{[CO]^3}$, we can get $[CO_2]^3=K_2[CO]^3$. We want to express $K=\frac{[CO_2]^6}{[O_2]^3}$ in terms of $K_1$ and $K_2$. $[CO_2]^6=(K_2[CO]^3)^2 = K_2^2[CO]^6$. Substitute $[CO]^2 = K_1[O_2]$ into $[CO]^6=(K_1[O_2])^3$. Then $K=\frac{[CO_2]^6}{[O_2]^3}=\frac{K_2^2[CO]^6}{[O_2]^3}=\frac{K_2^2(K_1[O_2])^3}{[O_2]^3}$. Simplify the right - hand side: [ \begin{align*} \frac{K_2^2(K_1[O_2])^3}{[O_2]^3}&=\frac{K_2^2K_1^3[O_2]^3}{[O_2]^3}\ &=K_1^3K_2^2 \end{align*} ]

Answer:

$K_1^3K_2^2$