1
00:00:00,000 --> 00:00:05,010
我们知道如果把水留在容器里不管

2
00:00:05,050 --> 00:00:06,670
假设有些水

3
00:00:06,710 --> 00:00:07,900
那么它会到达

4
00:00:07,950 --> 00:00:10,730
自身解离的平衡

5
00:00:10,770 --> 00:00:14,290
所以一部分水会变成一些氢离子

6
00:00:14,330 --> 00:00:19,110
这些会粘上其它的水分子

7
00:00:19,180 --> 00:00:20,860
变成H3O+

8
00:00:20,910 --> 00:00:23,730
不过只要写成氢离子就行

9
00:00:23,780 --> 00:00:26,160
氢离子其实是个游离的质子

10
00:00:26,200 --> 00:00:29,430
加上氢氧根离子

11
00:00:29,480 --> 00:00:31,230
同时我们也知道

12
00:00:31,270 --> 00:00:36,930
在25°C的平衡状态下

13
00:00:36,970 --> 00:00:38,020
记住啦

14
00:00:38,060 --> 00:00:40,310
平衡常数和平衡反应

15
00:00:40,350 --> 00:00:42,380
只由温度确定

16
00:00:42,420 --> 00:00:43,490
没别的了

17
00:00:43,530 --> 00:00:46,900
假设一个分子 当然啦

18
00:00:46,940 --> 00:00:49,730
也是在25°C下

19
00:00:49,770 --> 00:00:51,760
我们上上集讲过这个

20
00:00:51,800 --> 00:00:53,040
平衡常数

21
00:00:53,060 --> 00:00:54,500
我们来复习一下

22
00:00:54,550 --> 00:00:58,260
就是产物的浓度

23
00:00:58,300 --> 00:01:03,600
除以反应物的浓度

24
00:01:03,650 --> 00:01:05,710
但在这里反应物只有水

25
00:01:05,760 --> 00:01:06,920
而它是溶剂

26
00:01:06,970 --> 00:01:10,050
如果反应物无处不在

27
00:01:10,100 --> 00:01:11,870
你回想一下那个直观的例子

28
00:01:11,910 --> 00:01:13,620
就知道它存在的概率是1

29
00:01:13,670 --> 00:01:16,070
它就是无处不在

30
00:01:16,110 --> 00:01:17,670
所以不用考虑它

31
00:01:17,710 --> 00:01:19,330
或者你可以看成除以1之类的

32
00:01:19,350 --> 00:01:23,900
这等于水的平衡常数

33
00:01:23,940 --> 00:01:27,150
我们已知这个常数是10的-14次方

34
00:01:27,190 --> 00:01:30,150
因为水单独存在时

35
00:01:30,190 --> 00:01:35,090
氢离子浓度是10的-7次方

36
00:01:35,130 --> 00:01:39,150
氢氧根的浓度也是10的-7次方

37
00:01:39,200 --> 00:01:41,410
同时对它们取对数

38
00:01:41,430 --> 00:01:46,160
如果你对Kw…

39
00:01:46,200 --> 00:01:47,630
这是什么意思呢？

40
00:01:47,670 --> 00:01:49,350
如果把p放在某个东西前面

41
00:01:49,400 --> 00:01:51,470
就表示 对这个东西取负常用对数

42
00:01:51,510 --> 00:01:54,020
取10^(-14)的负对数

43
00:01:54,060 --> 00:01:57,450
10^(-14)的对数就是-14

44
00:01:57,500 --> 00:01:59,950
所以它的负对数就是14

45
00:02:00,000 --> 00:02:06,620
结果pKw就是14 就等于…

46
00:02:06,660 --> 00:02:10,270
如果我把另一边也取负对数

47
00:02:10,320 --> 00:02:11,490
我来算算

48
00:02:11,540 --> 00:02:13,180
这就是对数的性质了

49
00:02:13,220 --> 00:02:16,510
这就属于数学而不是化学的范畴了

50
00:02:16,550 --> 00:02:22,180
所以是H+的对数乘以OH-

51
00:02:22,220 --> 00:02:24,100
乘以咱们的氢氧根

52
00:02:24,150 --> 00:02:26,150
这是等价的 只是对数运算

53
00:02:26,200 --> 00:02:32,340
这等于 氢的负对数减去

54
00:02:32,390 --> 00:02:40,340
或者你可以说是加上 OH-的负对数

55
00:02:40,370 --> 00:02:42,210
来看看这是啥？

56
00:02:42,220 --> 00:02:47,230
这就是pH嘛

57
00:02:47,280 --> 00:02:50,350
它就是一个负对数

58
00:02:50,390 --> 00:02:53,240
这是10的-7次方 对吧？

59
00:02:54,480 --> 00:02:56,110
它的常用对数是-7

60
00:02:56,150 --> 00:02:57,590
把负号提前

61
00:02:57,630 --> 00:03:00,080
pH就等于7了

62
00:03:00,120 --> 00:03:01,720
那这是啥呢？

63
00:03:01,760 --> 00:03:02,810
看这儿

64
00:03:02,840 --> 00:03:06,380
这就是咱们的pOH嘛

65
00:03:06,430 --> 00:03:09,190
就是氢氧根浓度的负对数

66
00:03:09,220 --> 00:03:12,880
当然喇 它的浓度也是10^(-7)

67
00:03:12,920 --> 00:03:16,920
所以咱们的pOH等于负的浓度的对数-7

68
00:03:16,970 --> 00:03:18,190
把负号提前

69
00:03:18,230 --> 00:03:19,420
pOH等于7

70
00:03:19,460 --> 00:03:24,480
于是你就得到这个pKw的小式子了

71
00:03:24,510 --> 00:03:28,440
或者叫水解离的平衡常数的负对数

72
00:03:28,490 --> 00:03:32,540
pKw等于

73
00:03:32,580 --> 00:03:41,630
水的pH 加上水的pOH

74
00:03:41,680 --> 00:03:43,560
而这个 在25°C

75
00:03:43,610 --> 00:03:45,280
这得是个不变的常数

76
00:03:45,320 --> 00:03:46,920
因为我们要开始捣乱

77
00:03:46,970 --> 00:03:49,270
通过倒点酸或碱到水里头

78
00:03:49,310 --> 00:03:55,930
所以25°C下 pKw为14

79
00:03:55,970 --> 00:03:57,940
记住 只要温度不变

80
00:03:57,990 --> 00:04:00,460
而你又没有对分子做太过分的事

81
00:04:00,510 --> 00:04:03,500
平衡常数就不会变

82
00:04:03,550 --> 00:04:05,100
所以我们才叫它常数嘛

83
00:04:05,150 --> 00:04:07,330
铺垫了半天了

84
00:04:07,370 --> 00:04:09,960
我们快想想如果我倒点酸进去

85
00:04:10,010 --> 00:04:13,650
会发生什么…

86
00:04:13,690 --> 00:04:16,940
假设我放的是盐酸

87
00:04:16,980 --> 00:04:21,690
我换个创意点的颜色写吧

88
00:04:21,730 --> 00:04:23,660
这儿有盐酸

89
00:04:23,700 --> 00:04:27,230
它是个水溶液

90
00:04:27,270 --> 00:04:31,230
我们都知道它是完全电离的

91
00:04:31,270 --> 00:04:39,240
就是说 这儿只剩下氢离子

92
00:04:39,280 --> 00:04:40,350
在这种情况下

93
00:04:40,400 --> 00:04:43,270
它当然是和水分子黏在一块

94
00:04:43,280 --> 00:04:45,240
形成水合氢离子

95
00:04:45,280 --> 00:04:52,090
加上氯离子阴离子 或者叫负离子

96
00:04:52,130 --> 00:04:54,490
就在那儿

97
00:04:54,530 --> 00:05:09,030
假设我放1mol/L的…

98
00:05:09,070 --> 00:05:10,090
或者

99
00:05:10,140 --> 00:05:12,560
有时也可以写成1大写M的\N【译者注：1M=1molar=1mol/L】

100
00:05:12,600 --> 00:05:14,290
盐酸

101
00:05:14,340 --> 00:05:16,480
那么本质上我在干嘛呢？

102
00:05:16,520 --> 00:05:18,520
取1mol/L的盐酸

103
00:05:18,540 --> 00:05:19,760
理论上就是

104
00:05:19,810 --> 00:05:26,480
每升溶液里

105
00:05:26,520 --> 00:05:28,550
有1mol的HCl

106
00:05:28,570 --> 00:05:29,590
主要还是水啦

107
00:05:29,640 --> 00:05:31,250
它是个水溶液嘛

108
00:05:31,290 --> 00:05:33,560
每升水 对吧？

109
00:05:33,590 --> 00:05:36,260
在这儿这些东西的浓度

110
00:05:36,300 --> 00:05:37,860
会变成多少呢？

111
00:05:37,900 --> 00:05:38,700
特别是

112
00:05:38,740 --> 00:05:41,960
氢的浓度 会变成多少？

113
00:05:42,000 --> 00:05:46,730
嗯… 它完全电离 对吧？

114
00:05:46,750 --> 00:05:47,890
所以这个全部…

115
00:05:47,930 --> 00:05:49,630
这不是可逆平衡反应

116
00:05:49,680 --> 00:05:52,620
注意 我只画了单向的箭头指着右边

117
00:05:52,660 --> 00:05:54,690
连个很小的左箭头都没有

118
00:05:54,740 --> 00:05:57,660
盐酸是个强酸

119
00:05:57,700 --> 00:06:00,520
那么如果溶液中有

120
00:06:00,550 --> 00:06:02,780
1mol/L的HCl

121
00:06:02,820 --> 00:06:04,110
你不会找到任何这个

122
00:06:04,150 --> 00:06:05,220
你只能看到这些

123
00:06:05,270 --> 00:06:11,010
所以溶液中氢离子的浓度

124
00:06:11,050 --> 00:06:16,640
就等于1mol/L

125
00:06:16,680 --> 00:06:20,080
当然溶液里面还有1mol/L的氯离子

126
00:06:20,130 --> 00:06:21,210
不过不用管它

127
00:06:21,240 --> 00:06:23,840
如果我之前没提水会电离

128
00:06:23,870 --> 00:06:25,370
那么很容易就能算出来

129
00:06:25,390 --> 00:06:27,750
这个溶液的pH

130
00:06:27,800 --> 00:06:30,070
现在盐酸已经倒进去了

131
00:06:30,120 --> 00:06:35,980
而pH就表示氢离子的浓度

132
00:06:36,030 --> 00:06:39,120
又已知氢离子的浓度了

133
00:06:39,160 --> 00:06:42,510
就是1molar 或者说1mol/L

134
00:06:42,550 --> 00:06:49,040
那么pH就会等于

135
00:06:49,080 --> 00:06:55,160
氢离子浓度的以10为底的负对数

136
00:06:55,210 --> 00:06:56,360
浓度是1

137
00:06:56,410 --> 00:06:59,380
10的几次方等于1呢？

138
00:06:59,420 --> 00:07:02,530
嗯 任何数的0次方都等于1

139
00:07:02,570 --> 00:07:03,470
10也是

140
00:07:03,510 --> 00:07:06,000
因为0的负数就是0

141
00:07:06,040 --> 00:07:07,830
所以你的pH就是0

142
00:07:07,850 --> 00:07:15,020
如果这儿有1mol/L的盐酸

143
00:07:15,060 --> 00:07:19,450
你把它都倒进水溶液里

144
00:07:19,490 --> 00:07:20,920
啊 我意思是说

145
00:07:20,960 --> 00:07:22,790
当我说1mol/L时

146
00:07:22,830 --> 00:07:23,930
就表示已经放进去了

147
00:07:23,980 --> 00:07:28,190
那么如果溶液的浓度是1mol/L

148
00:07:28,230 --> 00:07:30,970
溶剂是水

149
00:07:31,010 --> 00:07:33,450
它的pH就是0

150
00:07:33,500 --> 00:07:35,340
这pH是0

151
00:07:35,360 --> 00:07:45,120
没有任何酸在里面的水 pH等于7

152
00:07:45,160 --> 00:07:49,870
我们把这个pH值称为中性

153
00:07:49,910 --> 00:07:54,420
现在我们就假设有

154
00:07:54,470 --> 00:07:59,180
1mol/L的盐酸 我们可以说…

155
00:07:59,230 --> 00:08:01,040
我用红色吧 因为…

156
00:08:01,080 --> 00:08:08,450
可以说水中的HCl的pH等于0

157
00:08:08,490 --> 00:08:12,000
所以很明显pH越低酸性越强

158
00:08:12,040 --> 00:08:15,120
我们已经在前面的视频里讲过了

159
00:08:15,160 --> 00:08:18,540
现在我们算一下盐酸的pOH是多少

160
00:08:18,590 --> 00:08:25,390
水溶液中的盐酸的pOH

161
00:08:25,440 --> 00:08:28,970
嗯 这得回到勒夏特列原理 对吧？

162
00:08:29,010 --> 00:08:30,630
回想一下之前提到的

163
00:08:30,680 --> 00:08:34,730
这里只有纯水

164
00:08:34,770 --> 00:08:37,920
如果把1mol/L的盐酸放进来

165
00:08:37,970 --> 00:08:43,930
本质上我们就是把一堆

166
00:08:43,980 --> 00:08:47,370
质子放进来了

167
00:08:47,420 --> 00:08:50,680
我们大大地增大了氢离子的浓度

168
00:08:50,730 --> 00:08:52,820
那勒夏特列原理就会说 噢

169
00:08:52,860 --> 00:08:55,300
这不就是得要消耗很多氢氧根

170
00:08:55,340 --> 00:08:57,430
反应就得往这个方向移动

171
00:08:57,480 --> 00:08:59,510
这个平衡就会往这个方向移动

172
00:08:59,540 --> 00:09:00,680
不过要记住

173
00:09:00,720 --> 00:09:03,730
水自身电离的浓度只有10的-7次方

174
00:09:03,770 --> 00:09:07,390
我们可是倒了一百万倍…

175
00:09:07,430 --> 00:09:13,850
就是说这只占在千万分之一mol/L

176
00:09:13,890 --> 00:09:15,950
现在我们要倒进去了 多少来着？

177
00:09:15,990 --> 00:09:18,600
10的7次

178
00:09:18,640 --> 00:09:22,780
我们把比那多一千万倍的氢离子

179
00:09:22,830 --> 00:09:23,960
倒进水里

180
00:09:24,010 --> 00:09:25,840
所以氢氧根都被耗光了

181
00:09:25,880 --> 00:09:26,790
可能变成水了

182
00:09:26,810 --> 00:09:31,500
所以氢氧根的浓度降低太多太多

183
00:09:31,540 --> 00:09:32,800
因为我们真的倒了太多了

184
00:09:32,840 --> 00:09:34,750
而这个的浓度会上升

185
00:09:34,790 --> 00:09:37,310
因为它只能消耗一部分氢氧根

186
00:09:37,350 --> 00:09:38,820
这儿并没那么多

187
00:09:38,860 --> 00:09:41,280
这儿只有10^(-7)mol/L

188
00:09:41,320 --> 00:09:43,510
而氢最后还是1mol/L

189
00:09:43,560 --> 00:09:45,270
而如果它最后还是1mol/L

190
00:09:45,310 --> 00:09:47,520
因为10^(-7)mol/L

191
00:09:47,570 --> 00:09:49,280
本质上 你可以看成是

192
00:09:49,330 --> 00:09:51,080
它全都被这东西耗光了

193
00:09:51,120 --> 00:09:54,200
结果OH-的浓度会是多少呢？

194
00:09:54,240 --> 00:09:55,190
嗯… 已知

195
00:09:55,230 --> 00:10:00,040
25°C下水的pKw是14

196
00:10:00,090 --> 00:10:02,390
且水的pKw是等于

197
00:10:02,430 --> 00:10:05,760
溶液的pH 加pOH

198
00:10:05,800 --> 00:10:12,760
而且盐酸pH是0 对吧？

199
00:10:12,810 --> 00:10:14,900
我们有1mol/L的盐酸

200
00:10:14,950 --> 00:10:18,740
那么1mol/L盐酸的pOH就是14

201
00:10:18,790 --> 00:10:24,310
所以咱们这儿的pOH就等于14了

202
00:10:24,350 --> 00:10:26,070
现在我们同样倒点碱进水里

203
00:10:26,110 --> 00:10:27,770
再算一下它的pH是多少

204
00:10:27,810 --> 00:10:29,030
倒一种强碱

205
00:10:29,080 --> 00:10:31,020
我想你会发现它只是反过来

206
00:10:31,060 --> 00:10:36,210
假设有氢氧化钾(KOH)

207
00:10:36,250 --> 00:10:37,910
这是个强碱

208
00:10:37,950 --> 00:10:44,100
所以它会在水里完全电离成钾离子

209
00:10:44,140 --> 00:10:46,590
带正电

210
00:10:46,620 --> 00:10:50,590
加上氢氧根离子

211
00:10:50,630 --> 00:10:51,930
它会完全电离

212
00:10:51,960 --> 00:10:53,860
如果这些全都在水溶液里

213
00:10:53,900 --> 00:10:55,440
我写下来吧

214
00:10:55,490 --> 00:11:02,980
水溶液 顾名思义就是在水里头 这不用说~

215
00:11:03,000 --> 00:11:05,950
然后假设放1mol/L

216
00:11:06,000 --> 00:11:07,520
记住 浓度很重要

217
00:11:07,560 --> 00:11:09,730
你不能光说 哦 盐酸的pH就是0

218
00:11:09,780 --> 00:11:10,600
不行

219
00:11:10,640 --> 00:11:14,140
你得说1mol/L盐酸 pH是0

220
00:11:14,180 --> 00:11:15,750
实际上我刚才也没写出来

221
00:11:15,790 --> 00:11:19,780
我在这写一下吧 1mol/L

222
00:11:19,820 --> 00:11:20,850
留给你们自己算算

223
00:11:20,900 --> 00:11:24,790
2mol/L的盐酸的pH和pOH是多少

224
00:11:24,840 --> 00:11:27,290
或者取10mol/L的盐酸

225
00:11:27,340 --> 00:11:30,270
给你们算算它的pH

226
00:11:30,320 --> 00:11:39,880
回过头来 我们有1mol/L氢氧化钾

227
00:11:39,920 --> 00:11:41,270
1mol/L这个

228
00:11:41,310 --> 00:11:43,380
它在水里完全电离

229
00:11:43,420 --> 00:11:46,550
啥都不剩

230
00:11:46,590 --> 00:11:50,910
那么OH-的的浓度是多少呢？

231
00:11:50,930 --> 00:11:55,080
OH-的浓度是1mol/L

232
00:11:55,130 --> 00:11:56,520
对吧？

233
00:11:56,560 --> 00:11:58,110
如果你有1mol/L这个

234
00:11:58,150 --> 00:11:59,440
就有1mol/L这个

235
00:11:59,480 --> 00:12:01,700
因为这个在水里全都没了

236
00:12:01,740 --> 00:12:04,710
那么pOH是多少？

237
00:12:04,750 --> 00:12:08,620
pOH就是这个的负对数

238
00:12:08,670 --> 00:12:10,930
1的对数是0

239
00:12:10,960 --> 00:12:13,230
0的负数还是0

240
00:12:13,270 --> 00:12:18,440
然后在这种情况下你的pH

241
00:12:18,480 --> 00:12:19,790
嗯… 你可能会说

242
00:12:19,830 --> 00:12:21,030
哦 它不就是氢的浓度嘛

243
00:12:21,070 --> 00:12:22,830
虽然你并不知道氢离子的浓度是多少

244
00:12:22,870 --> 00:12:24,860
但你知道当你倒了一堆这个后

245
00:12:24,910 --> 00:12:26,260
它就会消耗一堆氢离子

246
00:12:26,290 --> 00:12:27,600
所以氢离子就会减少很多

247
00:12:27,640 --> 00:12:28,690
于是你可能会问 嗯… 那要怎么算？

248
00:12:28,720 --> 00:12:30,000
好吧 你记得吧

249
00:12:30,030 --> 00:12:33,310
25°C

250
00:12:33,350 --> 00:12:34,950
水的平衡常数

251
00:12:34,990 --> 00:12:37,590
等于pH加pOH

252
00:12:37,630 --> 00:12:39,330
我们在视频一开始就铺垫了

253
00:12:39,370 --> 00:12:43,740
所以14就等于pH加上0

254
00:12:43,760 --> 00:12:45,860
0就是这里的pOH

255
00:12:45,910 --> 00:12:49,620
所以pH就是14

256
00:12:49,660 --> 00:12:51,200
那如果你有1mol/L…

257
00:12:51,240 --> 00:12:53,540
这里我用了氢氧化钾

258
00:12:53,580 --> 00:12:56,150
不过如果你有1mol/L的强碱

259
00:12:56,190 --> 00:12:57,840
我写一下这个

260
00:12:57,880 --> 00:13:05,930
1mol/L的强碱

261
00:13:05,970 --> 00:13:08,600
记住 强在化学里是个正式的术语

262
00:13:08,640 --> 00:13:11,350
表示完全电离

263
00:13:11,390 --> 00:13:18,510
这儿pH为14 pOH为0

264
00:13:18,560 --> 00:13:22,970
如果是1mol/L的强酸

265
00:13:23,010 --> 00:13:25,860
如果某人声称自己有pH是0的东西

266
00:13:25,900 --> 00:13:29,130
而且他们打算丢给你

267
00:13:29,170 --> 00:13:32,100
你就应该谢绝或逃离

268
00:13:32,140 --> 00:13:35,840
因为这很可能会伤害你的…

269
00:13:35,890 --> 00:13:37,820
呃 跑题了

270
00:13:37,870 --> 00:13:39,850
假设有1mol/L强酸

271
00:13:39,890 --> 00:13:47,940
其pH为0 pOH为14

272
00:13:47,980 --> 00:13:50,220
反正在下集我就会好好演示

273
00:13:50,240 --> 00:13:52,580
可能会让你有一个印象

274
00:13:52,630 --> 00:13:54,280
知道这是个绝对标度

275
00:13:54,320 --> 00:13:56,590
这儿0就是你得到的酸度

276
00:13:56,630 --> 00:13:59,070
14是通过pH计算得来的碱度

277
00:13:59,110 --> 00:14:00,450
不过这不是重点

278
00:14:00,490 --> 00:14:01,790
实际上可能比这高

279
00:14:01,830 --> 00:14:02,940
也可能比这低

280
00:14:02,990 --> 00:14:07,620
刚才那个例子是1mol/L强酸

281
00:14:07,660 --> 00:14:09,760
假设现在是2mol/L的强酸

282
00:14:09,800 --> 00:14:11,950
或者其实是10mol/L

283
00:14:11,990 --> 00:14:12,840
可以吧？

284
00:14:12,880 --> 00:14:18,600
假设氢的浓度是10mol/L

285
00:14:18,640 --> 00:14:21,990
如果把10mol/L的强酸

286
00:14:22,040 --> 00:14:24,360
加进水溶液里

287
00:14:24,410 --> 00:14:27,210
我用mol/L 说明加了以后浓度是10

288
00:14:27,250 --> 00:14:29,270
那pH是多少？

289
00:14:29,320 --> 00:14:32,780
就等于10的以10为底的负对数

290
00:14:32,820 --> 00:14:34,910
10的常用对数 就是1

291
00:14:34,950 --> 00:14:36,770
10的1次方

292
00:14:36,810 --> 00:14:38,320
所以这个对数等于-1

293
00:14:38,360 --> 00:14:39,980
所以pH等于1

294
00:14:39,990 --> 00:14:41,670
如果有10mol/L的

295
00:14:41,710 --> 00:14:45,530
盐酸或硝酸 或类似的东西

296
00:14:45,570 --> 00:14:47,490
好了 这集到此为止

297
00:14:47,530 --> 00:14:49,070
下集见