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

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**