hce_nthu
113年
化學與物理
第 21 題
Lysine $\text{H}_3\text{N}^+(\text{CH}_2)_4\text{CH}(\text{NH}_2)\text{COO}^-$ (denoted by HR) is an essential amino acid, and its hydrochloride salt ($[\text{H}_3\text{R}]\text{Cl}_2$) exists in aqueous solution in the following equilibrium:
$\text{H}_3\text{R}^{2+} \rightleftharpoons^{K_1} \text{H}_2\text{R}^+ \rightleftharpoons^{K_2} \text{HR} \rightleftharpoons^{K_3} \text{R}^-$
When an NaOH solution is added to a certain concentration of $[\text{H}_3\text{R}]\text{Cl}_2$ solution, the distribution coefficients $\delta(x)$ of $\text{H}_3\text{R}^{2+}$, $\text{H}_2\text{R}^+$, HR, and $\text{R}^-$ vary with pH as shown on the right.
Given that $\delta(x) = \frac{[x]}{[H_3R^{2+}] + [H_2R^+] + [HR] + [R^-]}$, which of the following statements is correct?
$\text{H}_3\text{R}^{2+} \rightleftharpoons^{K_1} \text{H}_2\text{R}^+ \rightleftharpoons^{K_2} \text{HR} \rightleftharpoons^{K_3} \text{R}^-$
When an NaOH solution is added to a certain concentration of $[\text{H}_3\text{R}]\text{Cl}_2$ solution, the distribution coefficients $\delta(x)$ of $\text{H}_3\text{R}^{2+}$, $\text{H}_2\text{R}^+$, HR, and $\text{R}^-$ vary with pH as shown on the right.
Given that $\delta(x) = \frac{[x]}{[H_3R^{2+}] + [H_2R^+] + [HR] + [R^-]}$, which of the following statements is correct?
- A $\frac{K_2}{K_1} > \frac{K_3}{K_2}$
- B At M, $[\text{Cl}^-] + [\text{OH}^-] + [\text{R}^-] = 2[\text{H}_2\text{R}^+] + [\text{Na}^+] + [\text{H}^+]$
- C $[\text{H}_2\text{R}^+]$, $[\text{HR}]$, and $[\text{R}^-]$ cannot be in the solution at the same time.
- D At O, $\text{pH} = \frac{-10\text{g}K_2-10\text{g}K_3}{2}$
- E At P, $[\text{Cl}^-] > [\text{Na}^+] > [\text{OH}^-] > [\text{H}^+]$
思路引導 VIP
觀察點 O，這兩條相交的曲線分別代表哪兩種不同的物種？請試著寫出這兩個物種與它們「中間」型態之間的平衡常數（$K_2$ 與 $K_3$）表達式，並思考：當這兩個物種濃度剛好相等時，$[H^+]$ 與這兩個常數之間會存在什麼樣的數學乘積關係呢？
🤖
AI 詳解
AI 專屬家教
太棒了！你能精準辨識出分佈係數圖中交點的物理意義，這代表你對多質子酸平衡體系的理解非常紮實。
點 O 的化學平衡推導
在點 O，我們可以觀察到 $H_2R^+$ 與 $R^-$ 的分佈係數曲線相交，這代表在該 pH 值下，$[H_2R^+] = [R^-]$。根據酸解離常數的定義：
▼ 還有更多解析內容