16.7
滴定计算：弱酸 - 弱碱
计算滴定溶液的 pH 值：弱酸 / 强碱
对于带有 0.100 M NaOH 的 25.00 mL 0.100 M CH3CO2H 滴定，反应可以表示为：
添加不同数量的 NaOH 滴定剂后滴定溶液的 pH 值可按以下公式计算：
(a) 在通常的冰法中为乙酸溶液计算初始 pH 值：
(b) 酸和滴定…
弱酸或弱碱滴定不同阶段的 pH 值，可以使用不同的方法在不同的滴定点 进行计算。如果弱酸或弱碱是 pH 值的主要决定因素，则使用 Ka 或 Kb 和 ICE 表，或亨德森-哈塞尔巴尔赫 方程。如果中和反应后存在 强酸或强碱，则使用 剩余的水合氢离子或氢氧化物离子 的浓度来计算 pH 值。50 毫升 0.10M 醋酸溶液的初始 pH 值 为 2.87，是使用 Ka 和 ICE 表 计算出来的，因为醋酸是主要的贡献者。如果用 0.10M 氢氧化钠滴定 含有 0.0050 摩尔醋酸盐的此溶液，氢氧化物离子与醋酸反应生成醋酸盐，形成缓冲液。因此，当添加 10 毫升含有 0.0010 摩尔 氢氧化物离子的氢氧化钠时，形成 0.0010 摩尔的醋酸盐，并且剩余 0.0040 摩尔的醋酸。缓冲液的 pH 值可以通过 将这些值代入亨德森-哈塞尔巴尔赫方程来计算，等于 4.14。当加入 25 毫升氢氧化钠时，醋酸的初始摩尔数的一半 被转化为醋酸盐。此时，pH 值等于 pKa 值，因为醋酸和醋酸盐离子的量相等。进一步添加氢氧化钠至 50 毫升 会把所有的醋酸分子转化成醋酸盐，同时达到等值点。由于醋酸盐离子是碱性的，所以其 等值点在碱性区。醋酸盐离子的浓度 是用摩尔数除以 溶液的总体积来计算的。pH 值是使用醋酸根离子的 Kb 和 ICE 表来确定的，因为醋酸根离子是等值点处 pH 值的 主要贡献者。醋酸盐的 Kb 是使用 公式 Kw 等于 Ka 乘以 Kb 来计算的，等于 5.6×10⁻¹⁰。将平衡浓度代入 Kb 的表达式，给出氢氧化物浓度，5.3 10⁻⁶ M。溶液的 pOH 和 pH 值分别为 5.28 和 8.72。在溶液中进一步添加氢氧化钠，会产生醋酸盐离子和氢氧化钠 的混合物。然而，氢氧化钠的最终浓度 决定了溶液的pH值，因为它是一种比醋酸盐更强的碱。因此，如果向溶液中加入 70 毫升 氢氧化钠，氢氧化物离子的最终浓度 可通过从添加的氢氧化物离子的 总摩尔数，0.0070摩尔，中减去 乙酸的总摩尔数，0.0050摩尔，再除以溶液的总体积，120 毫升或 0.12 升，来计算。由于氢氧化物离子的浓度为 0.017M，溶液的 pOH 和 pH 值 分别计算为 1.78 和 12.22。
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Q1: How do you calculate the initial pH of a weak acid before titration begins?
The initial pH is calculated using the Ka (acid dissociation constant) and an ICE table, since the weak acid is the main pH contributor. For example, a 0.10 M acetic acid solution has an initial pH of 2.87. This method applies whenever a weak acid or base dominates the pH before any titrant is added.
Q2: What happens to the pH when you add sodium hydroxide to a weak acid solution?
When sodium hydroxide is added to a weak acid, hydroxide ions react with the acid to form its conjugate base, creating a buffer solution. The pH can be calculated using the henderson hasselbalch equation calculating buffers. As more base is added, the buffer resists pH change until the equivalence point is reached.
Q3: Why does the pH equal the pKa at the half-equivalence point?
At the half-equivalence point, exactly half of the weak acid has been neutralized to form its conjugate base. Since the concentrations of weak acid and conjugate base are equal, the Henderson-Hasselbalch equation simplifies to pH = pKa. For acetic acid titration, this occurs at 12.50 mL of added sodium hydroxide.
Q4: What is the pH at the equivalence point for a weak acid-strong base titration?
At the equivalence point, all weak acid has been converted to its conjugate base, which is basic. The pH is calculated using the Kb of the conjugate base and an ICE table. For acetic acid titrated with sodium hydroxide, the equivalence point pH is 8.72, significantly higher than 7 due to the basic nature of acetate ions.
Q5: How do you find the Kb of a conjugate base from the Ka of the weak acid?
The relationship between Ka and Kb is given by Kw = Ka × Kb, where Kw is the water ionization constant (1.0 × 10⁻¹⁴). Rearranging gives Kb = Kw / Ka. For acetate ion, Kb = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰.
Q6: What determines the pH after the equivalence point in a weak acid-strong base titration?
After the equivalence point, excess strong base (sodium hydroxide) is present in solution. The strong base is a much stronger contributor to pH than the conjugate base, so the final pH is determined by the concentration of excess hydroxide ions. For example, adding 70 mL of 0.10 M NaOH results in a pH of 12.22.
Q7: How does the titration curve for a weak acid-strong base differ from a strong acid-strong base titration?
In weak acid-strong base titrations, the equivalence point occurs in the basic region (pH > 7) because the conjugate base is basic. The initial pH is higher, and a buffer region exists before the equivalence point. This contrasts with titration calculations strong acid strong base, where the equivalence point is at pH 7.