2 S(s) + 2 O2(g) ⇄ 2 SO2(g) K1 = 2 × 10^105 2 SO2(g) + O2(g) ⇄ 2 SO3(g) K2 = 7 × 10^24 Given the val — Equilibrium Chemistry Question

STEPS:

1. Analyze the relationship between the reactions: Compare the two given intermediate reactions to the target reaction:
* Reaction 1: $2\text{ S}(s) + 2\text{ O}_2(g) \rightleftharpoons 2\text{ SO}_2(g) \quad K_1 = 2 \times 10^{105}$
* Reaction 2: $2\text{ SO}_2(g) + \text{ O}_2(g) \rightleftharpoons 2\text{ SO}_3(g) \quad K_2 = 7 \times 10^{24}$
* Target Reaction: $2\text{ S}(s) + 3\text{ O}_2(g) \rightleftharpoons 2\text{ SO}_3(g) \quad K_3 = ?$
2. Determine how to combine the equations: Notice that adding Reaction 1 and Reaction 2 together yields the exact stoichiometry of the Target Reaction:
$$(2\text{ S}(s) + 2\text{ O}_2(g)) + (2\text{ SO}_2(g) + \text{ O}_2(g)) \rightleftharpoons 2\text{ SO}_2(g) + 2\text{ SO}_3(g)$$
The intermediate product $2\text{ SO}_2(g)$ appears on both the reactant and product sides and cancels out, leaving:
$$2\text{ S}(s) + 3\text{ O}_2(g) \rightleftharpoons 2\text{ SO}_3(g)$$
3. Apply the rule for combining equilibrium constants: When two or more individual chemical equations are added to produce a net overall reaction, the equilibrium constant for the net reaction ($K_3$) is the product of the equilibrium constants of the individual steps:
$$K_3 = K_1 \times K_2$$
*(Note: This is a key contrast to Hess's Law for enthalpy changes, where individual $\Delta H$ values are added rather than multiplied).*
4. Substitute the values and solve:
$$K_3 = (2 \times 10^{105}) \times (7 \times 10^{24})$$
5. Perform the scientific notation math: Multiply the coefficients and add the exponents:
* Coefficients: $2 \times 7 = 14$
* Exponents: $10^{105} \times 10^{24} = 10^{105 + 24} = 10^{129}$
$$K_3 = 14 \times 10^{129} = \mathbf{1.4 \times 10^{130}} \approx \mathbf{1 \times 10^{130}}$$
This matches Option A.

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WHY_OTHERS_WRONG:

• B is incorrect: $3 \times 10^{80}$ represents a math error where a student divided the exponents ($105 - 24 \approx 81$) or divided the constants instead of multiplying them.
• C is incorrect: $1 \times 10^{65}$ represents a substantial mathematical error, likely due to an incorrect manipulation of exponents (such as subtracting a rounded value) or a misunderstanding of how the $K$ values relate.
• D is incorrect: $2 \times 10^{40}$ is a math mismatch that does not align with any correct algebraic combination of the given equilibrium constants.
• E is incorrect: $7 \times 10^{24}$ is simply the equilibrium constant for the second step ($K_2$). This option fails to incorporate the first step's equilibrium constant ($K_1$) into the overall reaction.