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To calculate the equilibrium constant \(K_c\) for the given reaction:

\[
4 \text{HBr}(g) + \text{O}_2(g) \rightleftharpoons 2 \text{Br}_2(g) + 2 \text{H}_2\text{O}(g)
\]

we use the following general formula for the equilibrium constant:

\[
K_c = \frac{[\text{Products}]^{\text{coefficients}}}{[\text{Reactants}]^{\text{coefficients}}}
\]

From the balanced equation, we can write the expression for \(K_c\) as:

\[
K_c = \frac{[\text{Br}_2]^2 [\text{H}_2O]^2}{[\text{HBr}]^4 [\text{O}_2]}
\]

Given equilibrium concentrations from the table:
- \([\text{HBr}] = 1.5 \, \text{M}\)
- \([\text{O}_2] = 0.77 \, \text{M}\)
- \([\text{Br}_2] = 0.14 \, \text{M}\)
- \([\text{H}_2O] = 0.48 \, \text{M}\)

Substitute these values into the equilibrium expression:

\[
K_c = \frac{(0.14)^2 \times (0.48)^2}{(1.5)^4 \times (0.77)}
\]

Now, let's calculate it step by step:

1. \((0.14)^2 = 0.0196\)
2. \((0.48)^2 = 0.2304\)
3. \((1.5)^4 = 5.0625\)
4. Now, calculate the numerator: \(0.0196 \times 0.2304 = 0.00451824\)
5. Calculate the denominator: \(5.0625 \times 0.77 = 3.897125\)

Finally, calculate \(K_c\):

\[
K_c = \frac{0.00451824}{3.897125} \approx 0.00116
\]

Rounded to two significant digits, the equilibrium constant \(K_c\) is:

\[
K_c \approx 0.0012
\]

Let me know if you want further details or have any questions!

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**Relative questions:**
1. How is the equilibrium constant affected by changes in temperature?
2. What would happen to the equilibrium concentrations if you added more \(\text{HBr}\)?
3. How does the value of \(K_c\) indicate whether the reaction favors the reactants or products?
4. What are the units of \(K_c\) in this particular reaction?
5. How does this reaction follow Le Chatelier’s principle?

**Tip:** Always ensure you correctly balance chemical equations before using them in equilibrium calculations.

Calculate the value of the equilibrium constant Kc for the reaction: 4 HBr(g) + O2(g) → 2 Br2(g) + 2 H2O(g) with the given concentrations: [HBr] = 1.5 M, [O2] = 0.77 M, [Br2] = 0.14 M, [H2O] = 0.48 M. Round your answer to 2 significant digits.

Learn how to calculate the equilibrium constant (Kc) for the reaction between hydrogen bromide and oxygen to form bromine and water. Given equilibrium concentrations of [HBr] = 1.5 M, [O2] = 0.77 M, [Br2] = 0.14 M, [H2O] = 0.48 M, this step-by-step solution is suitable for high school chemistry students.

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