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 \( \qquad \) \[ \begin{aligned} 2 \mathrm{SO}_{2(\mathrm{~g})}+2 \mathrm{NO}_{2(\mathrm{~g})} & \rightleftarrows 2 \mathrm{SO}_{3(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \\ \text { a-16 } & \text { b- } 0.5 \end{aligned} \text { c- } 0.2 \quad \mathrm{~d}-0.0625 . \]
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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!