Equilibrium constants for some reactions are given. In which of the following case does the reaction — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Step 1 - Define the Equilibrium Constant (\(K\)) For any general reversible reaction: \[\ce{aA + bB <=> cC + dD}\] The equilibrium constant in terms of concentration (\(K_c\)) is defined by the law of chemical equilibrium as the ratio of the product of equilibrium concentrations of the products to that of the reactants, with each concentration term raised to a power equal to its stoichiometric coefficient: \[K = \frac{[\ce{C}]^c [\ce{D}]^d}{[\ce{A}]^a [\ce{B}]^b}\] Step 2 - Understand the Relation Between \(K\) and Extent of Completion The magnitude of the equilibrium constant \(K\) provides direct quantitative information about the extent of a reaction before equilibrium is established: * A very large value of \(K\) (\(K \gg 1\)) implies that the numerator (concentrations of products) is much larger than the denominator (concentrations of reactants). This means the reaction proceeds heavily in the forward direction and goes nearly to completion. * A very small value of \(K\) (\(K \ll 1\)) indicates that the concentrations of reactants at equilibrium are much greater than those of products. Hence, the reaction barely proceeds in the forward direction. * When \(K \approx 1\), both reactants and products are present in comparable concentrations at equilibrium. Thus, the reaction that goes **farthest to completion** is the one with the **largest equilibrium constant** value of \(K\). Step 3 - Compare the Given Values of \(K\) Let us systematically evaluate the values of \(K\) given in the options: 1. For Option (A): \(K = 10^2 = 100\) 2. For Option (B): \(K = 10^{-2} = 0.01\) 3. For Option (C): \(K = 10\) 4. For Option (D): \(K = 1\) Comparing these numerical values: \[10^2 > 10 > 1 > 10^{-2}\] \[100 > 10 > 1 > 0.01\] The largest value among the given options is \(K = 10^2\). Therefore, the reaction with \(K = 10^2\) will have the highest ratio of product concentration to reactant concentration at equilibrium, meaning it goes farthest to completion. Step 4 - Evaluate the Options * **Option (A) \(K = 10^2\)**: Correct. Since \(10^2\) is the largest equilibrium constant value among all options, this reaction goes farthest to completion. * **Option (B) \(K = 10^{-2}\)**: Incorrect. This is the smallest value of \(K\) among the options, meaning the reaction proceeds the least in the forward direction. * **Option (C) \(K = 10\)**: Incorrect. Although this reaction proceeds significantly in the forward direction, its extent of completion is less than that of the reaction with \(K = 10^2\). * **Option (D) \(K = 1\)**: Incorrect. At equilibrium, reactants and products are present in comparable concentrations, which is less complete than the reaction with \(K = 10^2\). \[\boxed{\text{A}}\]