1
00:00:01,090 --> 00:00:03,510
我们上集遇到了弱酸

2
00:00:03,560 --> 00:00:05,820
今天我们来试个弱碱的例子

3
00:00:05,860 --> 00:00:09,020
我们以氨为例吧

4
00:00:09,070 --> 00:00:10,750
氨(NH3)

5
00:00:10,790 --> 00:00:12,960
就是1个氮(N) 和3个氢(H)

6
00:00:12,990 --> 00:00:14,310
它是个弱碱

7
00:00:14,350 --> 00:00:17,670
因为它喜欢从水那儿获得氢

8
00:00:17,700 --> 00:00:19,430
让水只剩下一个氢氧根

9
00:00:19,450 --> 00:00:21,900
所以它增加了氢氧根的浓度

10
00:00:21,940 --> 00:00:25,130
所以如果溶液里有些氨分子

11
00:00:25,170 --> 00:00:26,620
加上水分子

12
00:00:26,660 --> 00:00:29,600
我准备倒点水进去

13
00:00:29,650 --> 00:00:35,350
往溶液里加水

14
00:00:35,390 --> 00:00:37,510
因为这是个弱碱

15
00:00:37,550 --> 00:00:40,920
所以反应不会只往一个方向进行

16
00:00:40,970 --> 00:00:46,250
这反应是个可逆平衡反应

17
00:00:46,290 --> 00:00:48,160
又因为这是个弱碱 它…

18
00:00:48,200 --> 00:00:52,050
这个时候布伦斯特定义

19
00:00:52,090 --> 00:00:53,620
就派上用场了

20
00:00:53,660 --> 00:00:56,600
它是个质子的受体而不是供体

21
00:00:56,650 --> 00:01:00,710
所以它变成了铵根

22
00:01:00,750 --> 00:01:04,510
或者铵阳离子

23
00:01:04,550 --> 00:01:07,010
因为铵根比氨多了一个氢

24
00:01:07,060 --> 00:01:09,560
所以现在它多了一个质子

25
00:01:09,610 --> 00:01:11,390
所以是正电

26
00:01:11,410 --> 00:01:12,870
同时它在溶液里

27
00:01:12,910 --> 00:01:14,670
又因为它从水里拿走了氢

28
00:01:14,710 --> 00:01:20,390
所以再加上溶液中的OH-

29
00:01:20,430 --> 00:01:21,220
记住

30
00:01:21,260 --> 00:01:22,960
根据质子酸碱理论

31
00:01:23,000 --> 00:01:25,000
因为它是个质子的受体

32
00:01:25,040 --> 00:01:26,890
所以它被看成碱

33
00:01:26,930 --> 00:01:28,400
或者如果根据阿伦尼乌斯的定义

34
00:01:28,440 --> 00:01:32,180
因为溶液中OH-的浓度增加了

35
00:01:32,220 --> 00:01:34,050
所以它也是阿仑尼乌斯碱

36
00:01:34,090 --> 00:01:35,940
好 已知…

37
00:01:35,980 --> 00:01:38,260
随机取个数吧

38
00:01:38,300 --> 00:01:48,150
假设是0.2mol/L的NH3

39
00:01:48,200 --> 00:01:52,580
那么它pH会是多少呢？

40
00:01:52,620 --> 00:01:55,750
那么pH是多少咧

41
00:01:55,790 --> 00:01:58,460
0.2mol/L的氨的pH

42
00:01:58,500 --> 00:01:59,560
那么第一步就是

43
00:01:59,610 --> 00:02:00,760
要找出

44
00:02:00,800 --> 00:02:03,640
这个碱反应的平衡常数

45
00:02:03,680 --> 00:02:09,270
我刚刚去维基百科了一下

46
00:02:09,310 --> 00:02:11,100
我差点说成液体百科

47
00:02:11,150 --> 00:02:12,850
因为我老在讲液体

48
00:02:12,890 --> 00:02:15,120
还有平衡 平衡百科

49
00:02:15,160 --> 00:02:17,780
不过我去的是维基百科啦

50
00:02:17,820 --> 00:02:19,230
那里有一个小图表

51
00:02:19,270 --> 00:02:20,920
几乎包含所有你要查的化合物

52
00:02:20,950 --> 00:02:23,180
还有它们的pKb

53
00:02:23,230 --> 00:02:26,670
pKb

54
00:02:26,710 --> 00:02:28,280
你看 这有个p

55
00:02:28,310 --> 00:02:29,010
那就说明

56
00:02:29,070 --> 00:02:39,190
它是平衡常数的负常用对数

57
00:02:39,230 --> 00:02:43,320
查表可知 它的pKb是4.75

58
00:02:43,360 --> 00:02:44,950
我们现在做一点小运算

59
00:02:44,980 --> 00:02:47,400
来解平衡常数

60
00:02:47,440 --> 00:02:48,150
我们来看看吧

61
00:02:48,190 --> 00:02:50,420
如果我们两边加个负号

62
00:02:50,460 --> 00:02:53,940
就得到以弱碱水解的

63
00:02:53,980 --> 00:02:57,800
平衡常数的常用对数

64
00:02:57,840 --> 00:02:58,960
这里的b就表示碱

65
00:02:59,000 --> 00:03:02,250
等于-4.75

66
00:03:02,290 --> 00:03:06,370
或者说10的-4.75次方就是Kb

67
00:03:06,410 --> 00:03:11,710
Kb=10^(-4.75)

68
00:03:11,750 --> 00:03:14,410
这个指数不是口算就能算出来的

69
00:03:14,450 --> 00:03:16,170
所以我要拿出计算器来算

70
00:03:16,210 --> 00:03:26,220
所以如果是10的-4.75次方 等于

71
00:03:26,260 --> 00:03:31,030
近似取1.8×10^(-5)

72
00:03:31,070 --> 00:03:37,740
这个平衡常数就等于1.8×10^(-5)

73
00:03:37,780 --> 00:03:39,480
那现在我们就可以利用这些数

74
00:03:39,520 --> 00:03:41,870
来做一个运算

75
00:03:41,910 --> 00:03:43,990
和上集的那个非常相似

76
00:03:44,020 --> 00:03:46,480
在这儿很难直接算出

77
00:03:46,520 --> 00:03:48,220
氢离子浓度 对吗？

78
00:03:48,250 --> 00:03:50,320
因为我们的平衡反应只有氢氧根

79
00:03:50,360 --> 00:03:53,360
但如果知道了氢氧根的浓度

80
00:03:53,400 --> 00:03:55,760
然后我就能倒回去算氢浓度

81
00:03:55,800 --> 00:03:58,850
因为氢氧根浓度 乘氢离子浓度

82
00:03:58,900 --> 00:04:02,750
一定得等于10的负14次

83
00:04:02,800 --> 00:04:07,170
或者算出pOH以后 再加上pH就是14

84
00:04:07,210 --> 00:04:09,340
我们在好几个视频之前就讲过这个了

85
00:04:09,380 --> 00:04:13,290
所以这个平衡常数

86
00:04:13,320 --> 00:04:15,390
或者它的表达式就会是这个

87
00:04:15,430 --> 00:04:24,070
1.8×10^(-5)等于

88
00:04:24,110 --> 00:04:26,060
分母是

89
00:04:26,100 --> 00:04:28,930
反应物的浓度

90
00:04:28,960 --> 00:04:30,730
记住啊 不用管溶剂

91
00:04:30,780 --> 00:04:32,550
所以只要写NH3就行

92
00:04:32,590 --> 00:04:35,060
我们放了0.2mol/L进去

93
00:04:35,100 --> 00:04:36,740
不过一部分 设为x吧

94
00:04:36,780 --> 00:04:37,940
会变成

95
00:04:37,980 --> 00:04:40,290
右边这些离子

96
00:04:40,330 --> 00:04:43,720
那么分母中 我们要用0.2减去

97
00:04:43,760 --> 00:04:46,220
x 就是转化成右边的量

98
00:04:46,260 --> 00:04:47,450
所以在右边

99
00:04:47,490 --> 00:04:52,970
会有浓度为x的NH4+ 和OH-

100
00:04:53,020 --> 00:04:57,980
这是氨的浓度

101
00:04:58,030 --> 00:05:00,910
然后是x乘以x

102
00:05:00,950 --> 00:05:07,980
这是NH4+的浓度 这是4

103
00:05:08,020 --> 00:05:10,690
然后这个浓度

104
00:05:10,730 --> 00:05:16,150
这儿就是OH-的浓度 对吧？

105
00:05:16,190 --> 00:05:17,770
我们只要解出x

106
00:05:17,810 --> 00:05:21,290
我们来算一下吧 解x

107
00:05:21,330 --> 00:05:23,830
一旦有了x的值 就得到了OH-的浓度

108
00:05:23,870 --> 00:05:25,300
我们就可以算出pOH

109
00:05:25,350 --> 00:05:28,050
接着就能算出pH

110
00:05:28,090 --> 00:05:32,010
好了 等式两边同时乘以(2-x)

111
00:05:32,070 --> 00:05:35,320
接下来你懂的 这步近似化简

112
00:05:35,360 --> 00:05:36,720
和上集那个是一样的

113
00:05:36,760 --> 00:05:39,700
当它比这里这个数

114
00:05:39,750 --> 00:05:42,410
小几个数量级

115
00:05:42,450 --> 00:05:49,430
我想说…

116
00:05:49,470 --> 00:05:50,640
提示就是

117
00:05:50,680 --> 00:05:52,130
经验法则有时还是挺好用的

118
00:05:52,150 --> 00:05:53,780
我们来解这个二次方程吧

119
00:05:53,810 --> 00:05:54,880
不过你可以稍微想想

120
00:05:54,920 --> 00:05:57,540
有时可以忽略中间这项

121
00:05:57,580 --> 00:05:58,890
不过我们先乘上它吧

122
00:05:58,930 --> 00:06:02,960
0.2乘以1.8等于0.36

123
00:06:03,010 --> 00:06:08,350
0.36×10^(-5) 对吧？

124
00:06:08,390 --> 00:06:11,660
2乘1.8是3.6 这个就是0.36

125
00:06:11,690 --> 00:06:20,650
-1.8乘10^(-5)乘x 对吧？

126
00:06:20,690 --> 00:06:25,100
等于x2

127
00:06:25,140 --> 00:06:27,870
咱们把东西全部搬到同一侧

128
00:06:27,920 --> 00:06:31,450
我要把它们都放到右边

129
00:06:31,490 --> 00:06:35,170
就得到0等于x2…

130
00:06:35,220 --> 00:06:38,480
方程两边同时加上这个

131
00:06:38,520 --> 00:06:43,460
加上1.8×10^(-5)x

132
00:06:43,500 --> 00:06:49,330
1.8×10^(-5)

133
00:06:49,370 --> 00:06:50,090
这样你就可以

134
00:06:50,130 --> 00:06:52,980
把系数和x清楚分开

135
00:06:53,020 --> 00:07:00,350
减去0.36×10^(-5)

136
00:07:00,390 --> 00:07:01,510
解这个方程

137
00:07:01,550 --> 00:07:03,450
再说一次 如果想简单点

138
00:07:03,480 --> 00:07:05,710
你可以忽略这一项

139
00:07:05,750 --> 00:07:08,020
然后直接用平方根算

140
00:07:08,070 --> 00:07:08,790
不过我们不用这样

141
00:07:08,840 --> 00:07:10,320
我们用一般的二次方程的解法

142
00:07:10,350 --> 00:07:12,300
那么a是1

143
00:07:12,340 --> 00:07:13,850
b在这

144
00:07:13,880 --> 00:07:14,970
那就是b

145
00:07:14,990 --> 00:07:15,970
而这个是c

146
00:07:16,010 --> 00:07:17,870
你只要把它们放进解的公式里面
【译者注：一元二次方程的一般形式为ax2+bx+c=0】

147
00:07:17,890 --> 00:07:20,660
先写-b

148
00:07:20,700 --> 00:07:26,700
也就是 -1.8×10^(-5)

149
00:07:26,750 --> 00:07:27,490
加减

150
00:07:27,530 --> 00:07:29,520
我们只要加的 因为如果用了减

151
00:07:29,560 --> 00:07:30,790
就会得到一个负的浓度

152
00:07:30,840 --> 00:07:33,220
所以加上 这个平方根

153
00:07:33,270 --> 00:07:35,490
这里好难算

154
00:07:35,530 --> 00:07:37,460
先是b2

155
00:07:37,500 --> 00:07:39,710
b等于1.8×10^(-5)

156
00:07:39,750 --> 00:07:42,160
这是1.8

157
00:07:42,200 --> 00:07:45,760
它的平方是3.24

158
00:07:45,800 --> 00:07:48,880
所以是3.24乘以

159
00:07:48,920 --> 00:07:50,360
10^(-5)的平方就是

160
00:07:50,400 --> 00:07:53,860
10^(-10)

161
00:07:53,900 --> 00:07:58,100
减去4乘a a是1

162
00:07:58,140 --> 00:07:59,900
乘以c c是负的

163
00:07:59,950 --> 00:08:02,500
所以就是4乘… 负负得正

164
00:08:02,540 --> 00:08:08,740
乘以0.36×10^(-5)

165
00:08:08,780 --> 00:08:20,620
4乘以0.36等于1.44

166
00:08:20,660 --> 00:08:22,270
我应该可以口算的

167
00:08:22,310 --> 00:08:26,050
结果就是1.44e(-5)

168
00:08:26,080 --> 00:08:28,800
就是乘10^(-5) 我写下来吧

169
00:08:28,830 --> 00:08:32,770
这是1.44

170
00:08:32,820 --> 00:08:36,750
当然 这些还得除以2a 也就是2

171
00:08:36,800 --> 00:08:37,710
嗯…

172
00:08:37,720 --> 00:08:39,320
这就是x的值

173
00:08:39,370 --> 00:08:41,200
我的OH-的浓度

174
00:08:41,250 --> 00:08:42,930
我算算

175
00:08:42,970 --> 00:08:51,650
3.24×10^(-10)

176
00:08:51,690 --> 00:08:52,830
就是这个

177
00:08:52,880 --> 00:09:04,420
加上1.44×10^(-5)等于这个数

178
00:09:04,460 --> 00:09:06,060
那么根号下就等于这个

179
00:09:06,100 --> 00:09:07,710
然后取它的平方根

180
00:09:07,780 --> 00:09:13,280
也就是0.5次方

181
00:09:13,320 --> 00:09:16,180
就是0.00379

182
00:09:16,250 --> 00:09:19,020
我再个颜色

183
00:09:19,070 --> 00:09:26,000
算出来x就等于-1.8×10^(-5)

184
00:09:26,040 --> 00:09:33,830
加上0.003794

185
00:09:33,880 --> 00:09:35,690
再除以2

186
00:09:35,730 --> 00:09:36,950
算一下

187
00:09:36,990 --> 00:09:43,300
我要减去这儿负的这项

188
00:09:43,330 --> 00:09:44,180
我得到这个值

189
00:09:44,220 --> 00:09:45,460
我只要减去这个

190
00:09:45,480 --> 00:09:53,870
减去1.8e(-5) 等于这个

191
00:09:53,910 --> 00:09:55,230
这是分子的值

192
00:09:55,240 --> 00:09:57,360
现在我只要把它除以2就行

193
00:09:57,410 --> 00:10:04,250
除以2以后 就等于0.001……

194
00:10:04,270 --> 00:10:05,170
我来写一下

195
00:10:05,210 --> 00:10:06,460
x就出来了

196
00:10:06,470 --> 00:10:08,430
我再随便换个颜色

197
00:10:08,470 --> 00:10:17,780
x等于0.001888

198
00:10:17,820 --> 00:10:20,140
呐 后面还有3等等

199
00:10:20,180 --> 00:10:21,980
不过如果你还记得一开始那个等式

200
00:10:22,020 --> 00:10:23,030
x是什么呢？

201
00:10:23,070 --> 00:10:26,630
它既是铵根的浓度

202
00:10:26,670 --> 00:10:28,670
也是氢氧根的浓度

203
00:10:28,710 --> 00:10:31,120
但我们只关心氢氧根的浓度

204
00:10:31,160 --> 00:10:35,390
所以x就等于氢氧根浓度

205
00:10:35,430 --> 00:10:38,530
现在如果我想算出pOH

206
00:10:38,570 --> 00:10:42,360
我只要对这个数取负对数

207
00:10:42,380 --> 00:10:44,630
就是等于

208
00:10:44,670 --> 00:10:46,460
我们先取个对数吧

209
00:10:46,500 --> 00:10:49,610
它的对数就是这个 然后加个负号

210
00:10:49,630 --> 00:10:54,930
结果就是2.72

211
00:10:54,970 --> 00:10:57,780
现在如果我们想算出pH

212
00:10:57,830 --> 00:11:01,990
氢离子的浓度

213
00:11:02,040 --> 00:11:04,750
要记住 一个25°C下的

214
00:11:04,770 --> 00:11:07,390
水溶液里

215
00:11:07,430 --> 00:11:15,080
水的pK等于pOH+pH

216
00:11:15,120 --> 00:11:19,080
25°C下的pK是14

217
00:11:19,120 --> 00:11:23,680
因为浓度是10^(-14)mol/L

218
00:11:23,720 --> 00:11:25,080
嗯… 不再深入了

219
00:11:25,130 --> 00:11:26,910
只要知道它们分别是10^(-7)就行

220
00:11:26,950 --> 00:11:28,670
总之 这就是水解离的

221
00:11:28,710 --> 00:11:30,520
平衡常数

222
00:11:30,570 --> 00:11:34,770
而pOH 水是中性时 它就是7

223
00:11:34,810 --> 00:11:38,710
也就是说 OH-的浓度是10^(-7)

224
00:11:38,760 --> 00:11:40,150
取负对数以后就是7

225
00:11:40,190 --> 00:11:44,420
不过现在呢 咱们知道OH-的浓度高了很多

226
00:11:44,460 --> 00:11:45,640
pOH是2.72

227
00:11:45,690 --> 00:11:47,630
记住 负对数很容易看错的

228
00:11:47,670 --> 00:11:52,620
应该是pOH越低 OH-浓度就越高

229
00:11:52,660 --> 00:11:53,650
对吧？

230
00:11:53,700 --> 00:11:57,610
pOH越低呢 就是这个数低了 嗯？

231
00:11:57,640 --> 00:11:59,070
pOH越低

232
00:11:59,120 --> 00:12:01,100
pH就越高

233
00:12:01,140 --> 00:12:03,970
我不想把你弄太糊涂

234
00:12:04,010 --> 00:12:05,180
究竟pH是多少呢？

235
00:12:05,220 --> 00:12:14,910
这儿pH就等于 14减去2.72

236
00:12:14,950 --> 00:12:20,530
我算算 这个减去14就等于…

237
00:12:20,570 --> 00:12:24,050
就取11.3吧

238
00:12:24,070 --> 00:12:26,780
pH等于11.3

239
00:12:26,820 --> 00:12:28,150
这个数很合理

240
00:12:28,190 --> 00:12:30,840
因为咱们说过它是弱碱嘛

241
00:12:30,890 --> 00:12:33,790
氨 是一个弱碱

242
00:12:33,830 --> 00:12:35,400
所以它是碱性的

243
00:12:35,440 --> 00:12:39,480
所以它会使pH大于中性的7

244
00:12:39,530 --> 00:12:41,930
所以pH就应该大于7

245
00:12:41,970 --> 00:12:44,550
不过你可以和强碱比较一下

246
00:12:44,590 --> 00:12:47,530
它们浓度为1mol/L时 pH就是14

247
00:12:47,560 --> 00:12:49,250
这让我们的pH…

248
00:12:49,290 --> 00:12:54,070
虽然我们的浓度只有0.2mol/L

249
00:12:54,110 --> 00:12:57,010
总之 比起化学 这更像数学题

250
00:12:57,050 --> 00:12:59,800
最后希望这集讲明白了一些东西