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To calculate the equilibrium constant \( K_p \) for the reaction:

\[
2 \text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2 \text{SO}_3(g)
\]

We use the following formula for \( K_p \):

\[
K_p = \frac{P_{\text{SO}_3}^2}{P_{\text{SO}_2}^2 \cdot P_{\text{O}_2}}
\]

where:
- \( P_{\text{SO}_2} = 90.1 \, \text{atm} \)
- \( P_{\text{O}_2} = 30.8 \, \text{atm} \)
- \( P_{\text{SO}_3} = 16.7 \, \text{atm} \)

Substituting these values:

\[
K_p = \frac{(16.7)^2}{(90.1)^2 \cdot (30.8)}
\]

Now, let's calculate the value:

1. \( (16.7)^2 = 278.89 \)
2. \( (90.1)^2 = 8118.01 \)
3. Multiply \( 8118.01 \times 30.8 = 249234.71 \)

Now, divide:

\[
K_p = \frac{278.89}{249234.71} = 0.001118
\]

Rounding to 2 significant digits:

\[
K_p \approx 0.0011
\]

Would you like any further clarification on the process?

Here are 5 related questions to extend this understanding:
1. What is the difference between \( K_p \) and \( K_c \)?
2. How does temperature affect the value of \( K_p \)?
3. What would happen to \( K_p \) if the pressure of \( SO_2 \) were increased?
4. Can \( K_p \) be used to predict the direction of the reaction?
5. How does the stoichiometry of the reaction influence the equilibrium expression?

**Tip**: Ensure you always check the units of pressure when calculating \( K_p \), as it must be consistent across all gases.

Calculate the value of the equilibrium constant Kp for the reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), given that at equilibrium the pressures are 90.1 atm for SO2, 30.8 atm for O2, and 16.7 atm for SO3. Round the answer to 2 significant digits.

Learn how to calculate the equilibrium constant Kp for the reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), using partial pressures of 90.1 atm for SO2, 30.8 atm for O2, and 16.7 atm for SO3. This detailed solution uses the equilibrium constant formula and is ideal for undergraduate chemistry students.

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