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1- The value of \( K \) foe the following reaction is 0.25 : \( \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{NO}_{2(\mathrm{~g})} \rightleftarrows \mathrm{SO}_{3(\mathrm{~g})}+\mathrm{NO}(\mathrm{g}) \), The value of K at the same temperature for this reaction below is \( \qquad \) \[ \begin{aligned} 2 \mathrm{SO}_{2(\mathrm{~g})}+2 \mathrm{NO}_{2(\mathrm{~g})} & \rightleftarrows 2 \mathrm{SO}_{3(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \\ \text { a-16 } & \text { b- } 0.5 \end{aligned} \text { c- } 0.2 \quad \mathrm{~d}-0.0625 . \]

Ask by Tucker Clark. in Iraq
Jan 24,2025

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Answer

The new equilibrium constant \( K' \) is 0.0625.

Solution

To determine the new equilibrium constant \( K' \) for the doubled reaction, we'll use the relationship between the equilibrium constants of reactions that are scaled by a factor. **Given:** \[ \mathrm{SO}_{2(\mathrm{g})} + \mathrm{NO}_{2(\mathrm{g})} \rightleftarrows \mathrm{SO}_{3(\mathrm{g})} + \mathrm{NO}(\mathrm{g}), \quad K = 0.25 \] **Doubled Reaction:** \[ 2 \mathrm{SO}_{2(\mathrm{g})} + 2 \mathrm{NO}_{2(\mathrm{g})} \rightleftarrows 2 \mathrm{SO}_{3(\mathrm{g})} + 2 \mathrm{NO}(\mathrm{g}) \] **Relationship Between \( K \) and \( K' \):** When a balanced chemical equation is multiplied by a factor of \( n \), the new equilibrium constant \( K' \) is related to the original \( K \) by: \[ K' = K^n \] In this case, the equation is multiplied by \( n = 2 \): \[ K' = (0.25)^2 = 0.0625 \] **Answer:** **d-0.0625**

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To find the value of \( K \) for the scaled reaction \( 2 \mathrm{SO}_{2(\mathrm{~g})}+2 \mathrm{NO}_{2(\mathrm{~g})} \rightleftarrows 2 \mathrm{SO}_{3(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \), we recall that when a balanced equation is multiplied by a coefficient, the equilibrium constant is raised to the power of that coefficient. Since we multiplied the entire reaction by 2, we need to take \( K \) to the power of 2. Thus, \( K' = K^2 = (0.25)^2 = 0.0625 \). So, the correct answer is (d) 0.0625. Remember, equilibrium constants can indeed be a little puzzling, but they follow predictable rules! Always check what you're multiplying by or changing - that way, you're less likely to slip up on the exponent game!

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