Consider a solution containing 0.100 M fluoride ions and 0.126 M hydrogen fluoride. The concentration of fluoride ions after the addition of 5.00 mL of 0.0100 M HCl to 25.0 mL of this solution is __ M.
A) 0.00167
B) 0.00253
C) 0.0817
D) 0.0980
E) 0.0850

Question

Quizplus · Accepted Answer

The correct answer is C.The addition of HCl will protonate some of the fluoride ions, reducing their concentration. The equilibrium constant for the reaction is:$$HF + H^+ ightleftharpoons F^- + H_2O$$$$K_a = \frac{[F^-][H_2O]}{[HF][H^+]} = 3.55 	imes 10^{-4}$$We can use the ICE table to determine the equilibrium concentrations of the species:$$\begin{array}{ccc} 	ext{Reaction}&HF & F^- & H^+ \\ 	ext{Initial}&0.126 & 0.100 & 0.00500 \\ 	ext{Change}&-x & +x & +x \\ 	ext{Equilibrium}&0.126-x & 0.100+x & 0.00500+x \end{array}$$Substituting the equilibrium concentrations into the equilibrium constant expression, we get:$$3.55 	imes 10^{-4} = \frac{(0.100+x)(0.00500+x)}{(0.126-x)x}$$Solving for x, we get:$$x = 1.67 	imes 10^{-3}$$Therefore, the equilibrium concentration of fluoride ions is:$$[F^-] = 0.100 + x = 0.10167 	ext{ M}$$

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