A chemist prepares a solution containing a weak acid, HA, and its conjugate base, A-. The initial concentration of HA is 0.20 M, and the initial concentration of A- is 0.10 M. If the pH of this solution is measured to be 4.0, and the acid dissociation constant (Ka) for HA is 1.0 × 10⁻⁵, what is the reaction quotient (Q) for the dissociation of HA at this moment, and how does it compare to Ka?
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The answer
Correct answer: A. The reaction quotient Q is 5.0 × 10⁻⁵, indicating that Q > Ka, so the reaction will shift to the left.
Tested concept: Reaction quotient (Q)
Explanation
The dissociation reaction for the weak acid HA is: HA(aq) <=> H+(aq) + A-(aq). The reaction quotient Q is defined as Q = [H+][A-]/[HA]. First, we need to find the concentration of H+ from the given pH: pH = -log[H+] 4.0 = -log[H+] [H+] = 10⁻⁴ M Now, substitute the given initial concentrations and the calculated [H+] into the Q expression: [HA] = 0.20 M [A-] = 0.10 M [H+] = 1.0 × 10⁻⁴ M Q = (1.0 × 10⁻⁴)(0.10) / (0.20) Q = (1.0 × 10⁻⁵) / (0.20) Q = 5.0 × 10⁻⁵ Next, compare Q to the given Ka: Ka = 1.0 × 10⁻⁵ Q = 5.0 × 10⁻⁵ Since Q (5.0 × 10⁻⁵) > Ka (1.0 × 10⁻⁵), the reaction quotient is greater than the equilibrium constant. This means the system has a higher product-to-reactant ratio than it would at equilibrium, and thus the reaction will shift to the left (towards the reactants) to reach equilibrium.
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