题目

13.常温下,一元酸HA的 _(a)(HA)=1.0times (10)^-3 在某体系中, ^+ 与 ^- 离子不能穿过-|||-隔膜,未电离的HA可自由穿过该膜(如图所示),-|||-溶液I 膜溶液II-|||-=7.0 =1.0-|||-H^++A^-=HA HA=H^++A^--|||-设溶液中 _(a)(HA)=c(HA)+c((A)^-), 当达到平衡时,下列叙述正确的是 ()-|||-A.溶液I中 ((H)^+)=c((OH)^-)+c((A)^-)-|||-B.溶液Ⅱ中的HA的电离度 (dfrac (c({A)^-)}({c)_(A)(HA)}) 为dfrac (1)(101)-|||-C.溶液I和Ⅱ中的c(H A)不相等-|||-D.溶液I和Ⅱ中的c.(HA)之比为 -4

题目解答

答案

【答案】

【解析】

A．常温下溶液I的pH=7.0，则溶液I中 $%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%3D%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BO%7D%5Cmathrm%7BH%7D%7D%5E%7B-%7D%5Cright%29%3D1%5Ctimes%20%7B10%7D%5E%7B-7%7D%5Cmathrm%7Bm%7D%5Cmathrm%7Bo%7D%5Cmathrm%7Bl%7D%2F%5Cmathrm%7BL%7D%EF%BC%8C%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%5Clt%20%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BO%7D%5Cmathrm%7BH%7D%7D%5E%7B-%7D%5Cright%29%2B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29$ ，A错误；

B．常温下溶液II的pH=1.0，溶液中 $%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%3D0.1%5Cmathrm%7Bmol%7D%2F%5Cmathrm%7BL%7D$ ， $%7B%5Cmathrm%7BK%7D%7D_%7B%5Cmathrm%7Ba%7D%7D%3D%5Cdfrac%7B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%5Ccdot%20%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29%7D%7B%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ， $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%3D%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%2B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29$ ，则 $%5Cdfrac%7B0.1%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29%7D%7B%7Bc%7D_%7B%E6%80%BB%7D%5Cleft%28HA%5Cright%29-c%5Cleft%28HA%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ，解得 $%5Cdfrac%7B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29%7D%7B%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29%7D%3D%5Cdfrac%7B1%7D%7B101%7D$ ，B正确；

C．根据题意，未电离的HA可自由穿过隔膜，故溶液I和II中的c(HA)相等，C错误；

D．常温下溶液I的pH=7.0，溶液I中 $%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%3D1%5Ctimes%20%7B10%7D%5E%7B-7%7D%5Cmathrm%7Bmol%7D%2F%5Cmathrm%7BL%7D$ ， $%7B%5Cmathrm%7BK%7D%7D_%7B%5Cmathrm%7Ba%7D%7D%3D%5Cdfrac%7B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%5Ccdot%20%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29%7D%7B%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ， $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%3D%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%2B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29$ ， $%5Cdfrac%7B%7B10%7D%5E%7B-7%7D%5Cleft%5B%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29-%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29%5Cright%5D%7D%7B%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ，溶液I中 $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%3D%28%7B10%7D%5E%7B4%7D%2B1%29%5Ccdot%20%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29$ ，溶液II的pH=1.0，溶液II中 $%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%3D0.1%5Cmathrm%7Bmol%7D%2F%5Cmathrm%7BL%7D$ ， $%7B%5Cmathrm%7BK%7D%7D_%7B%5Cmathrm%7Ba%7D%7D%3D%5Cdfrac%7B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BH%7D%7D%5E%7B%2B%7D%5Cright%29%5Ccdot%20%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29%7D%7B%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ， $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%3D%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%2B%5Cmathrm%7Bc%7D%5Cleft%28%7B%5Cmathrm%7BA%7D%7D%5E%7B-%7D%5Cright%29$ ， $%5Cdfrac%7B%7B10%7D%5E%7B-1%7D%5Cleft%5B%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29-%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29%5Cright%5D%7D%7B%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BH%7D%5Cmathrm%7BA%7D%5Cright%29%7D%3D1.0%5Ctimes%20%7B10%7D%5E%7B-3%7D$ ，溶液II中 $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29%3D1.01%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29$ ，未电离的HA可自由穿过隔膜，故溶液I和II中的 $%5Cmathrm%7Bc%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29$ 相等，溶液I和II中 $%7B%5Cmathrm%7Bc%7D%7D_%7B%E6%80%BB%7D%5Cleft%28%5Cmathrm%7BHA%7D%5Cright%29$ 之比为 $%5Cleft%5B%5Cright%28%7B10%7D%5E%7B4%7D%2B1%29%5Ccdot%20%5Cmathrm%7Bc%7D%28%5Cmathrm%7BHA%7D%5Cleft%29%5Cright%5D%EF%BC%9A%5B1.01%5Cmathrm%7Bc%7D%28%5Cmathrm%7BHA%7D%5Cleft%29%5Cright%5D%3D%28%7B10%7D%5E%7B4%7D%2B1%29%EF%BC%9A1.01%5Capprox%20%7B10%7D%5E%7B4%7D$ ，D错误；

答案选B。

解析

步骤 1：分析溶液I的pH值
常温下溶液I的pH=7.0，说明溶液I中$c({H}^{+})=c({OH}^{-})=1\times {10}^{-7}mol/L$。由于${H}^{+}$与${A}^{-}$离子不能穿过隔膜，所以溶液I中$c({H}^{+})\lt c({OH}^{-})+c({A}^{-})$，因此A选项错误。

步骤 2：分析溶液II的pH值
常温下溶液II的pH=1.0，说明溶液II中$c({H}^{+})=0.1mol/L$。根据${K}_{a}(HA)=1.0\times {10}^{-3}$，可以计算出溶液II中HA的电离度为$\dfrac {c({A}^{-})}{{c}_{A}(HA)}=\dfrac {1}{101}$，因此B选项正确。

步骤 3：分析溶液I和II中的c(HA)
由于未电离的HA可自由穿过隔膜，所以溶液I和II中的c(HA)相等，因此C选项错误。根据步骤2的计算，溶液I和II中的c(HA)之比为$10^{-4}$，因此D选项错误。