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Question 17.9: Calculating the Common-Ion Effect on Acid Ionization (Effect...

Calculating the Common-Ion Effect on Acid Ionization (Effect of a Strong Acid)

The degree of ionization of acetic acid, \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, in a 0.10  \mathrm{M} aqueous solution at 25^{\circ} \mathrm{C} is 0.013. K_{a} at this temperature is 1.7 \times 10^{-5}. Calculate the degree of ionization of \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} in a 0.10  \mathrm{M} solution at 25^{\circ} \mathrm{C} to which sufficient \mathrm{HCl} is added to make it 0.010  \mathrm{M}  \mathrm{HCl}. How is the degree of ionization affected?


This is an acid-ionization problem, but it differs from the simple ionization illustrated by Example 17.2. Here you have a starting concentration of \mathrm{H}_{3} \mathrm{O}^{+} (=0.010  M) from the addition of a strong acid (\mathrm{HCl}). This gives a different type of equation in Step 2, but you solve it in Step 3 by using a similar approximation method. You assume that x is small compared with starting concentrations of acid and \mathrm{H}_{3} \mathrm{O}^{+}, so that the resulting equation is linear, rather than quadratic. The calculation of degree of ionization follows that in Example 17.2.

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