Question 13.7: Nicotinic acid, HC6H4O2N (Ka = 1.4 ×10^-5), is another name ...

Nicotinic acid, HC_6H_4O_2N (K_a = 1.4 \times 10^{-5}), is another name for niacin, an important member of the vitamin B group. Determine [H^+] in a solution prepared by dissolving 3.0 g of nicotinic acid (MM = 123.11 g/mol), HNic, in enough water to form 245 mL of solution.

ANALYSIS

Information given:                      molar mass for nicotinic acid, HNic (123.11 g/mol); mass of HNic (3.0 g)                                                                                                  volume of solution (245 mL)                                                                                                                K_a = 1.4 \times 10^{-5})
Information implied:                            [HNic]_o
Asked for:                                                        [H^+]_{eq}

STRATEGY

1. Determine the original concentration,  [\quad ]_o, of HNic.
2. Let x = Δ[H^+].
Since all the coefficients in the reaction are one, Δ[HNic] and Δ[Nic^-] also equal x.
3. Draw a table as illustrated in Example 13.5.
4. Write the K expression for the ionization and subsitute the equilibrium concentrations for HNic, Nic^- , and H^+ obtained from the table.
5. To avoid the quadratic equation, assume x << [HNic]_o. Thus [HNic]_{eq} = 0.10. Then, substitute into the K_a expression and solve for x.