To find the equilibrium constant ($K_c$) for the reaction, we need to use the equilibrium concentrations of the reactants and products. The reaction is given by:

$\text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons 3\text{H}_2(g) + \text{CO}(g)$

The equilibrium constant expression for this reaction is:

[ K_c = \frac{[\text{H}_2]^3 [\text{CO}]}{[\text{CH}_4] [\text{H}_2\text{O}]} ]

Given:

• Volume of the reaction container = 3.00 L
• Amount of $\text{H}_2$ at equilibrium = 1.8 mol
• Amount of $\text{CO}$ at equilibrium = 0.60 mol
• Amount of $\text{CH}_4$ at equilibrium = 0.40 mol
• Amount of $\text{H}_2\text{O}$ at equilibrium = 0.20 mol

First, we need to convert these amounts to concentrations (molarity, $M$), which is moles per liter (mol/L):

$[\text{H}_2] = \frac{1.8 \text{ mol}}{3.00 \text{ L}} = 0.60 \text{ M}$ $[\text{CO}] = \frac{0.60 \text{ mol}}{3.00 \text{ L}} = 0.20 \text{ M}$ $[\text{CH}_4] = \frac{0.40 \text{ mol}}{3.00 \text{ L}} = 0.1333 \text{ M}$ $[\text{H}_2\text{O}] = \frac{0.20 \text{ mol}}{3.00 \text{ L}} = 0.0667 \text{ M}$

Now, substitute these concentrations into the equilibrium constant expression:

$K_c = \frac{(0.60)^3 (0.20)}{(0.1333)(0.0667)}$

Calculate the numerator:

$(0.60)^3 = 0.216$ $0.216 \times 0.20 = 0.0432$

Calculate the denominator:

$0.1333 \times 0.0667 = 0.008888$

Finally, compute $K_c$:

$K_c = \frac{0.0432}{0.008888} \approx 4.86$

Therefore, the equilibrium constant $K_c$ for the reaction is approximately 4.86.

Do you want details or have any questions?

Here are five questions you can ask:

1. How do you determine equilibrium concentrations in a chemical reaction?
2. What are the units of the equilibrium constant $K_c$?
3. How does the equilibrium constant change with temperature?
4. Can you explain the significance of the equilibrium constant value?
5. What happens to the equilibrium position if the concentration of a reactant is increased?

Tip: Always ensure to convert moles to molarity (concentration) when calculating the equilibrium constant for reactions occurring in a solution.