1 00:00:00,000 --> 00:00:01,090 2 00:00:01,090 --> 00:00:04,299 We've dealt with the weak acid, so let's try an example 3 00:00:04,299 --> 00:00:05,339 with the weak base. 4 00:00:05,339 --> 00:00:06,589 Let's say we had ammonia. 5 00:00:06,589 --> 00:00:09,730 6 00:00:09,730 --> 00:00:12,350 That's nitrogen with three hydrogens. 7 00:00:12,349 --> 00:00:16,369 And it's a weak base because it likes to accept hydrogen 8 00:00:16,370 --> 00:00:18,750 from water, leaving the water with just a hydroxide. 9 00:00:18,750 --> 00:00:21,190 So it increases the hydroxide concentration. 10 00:00:21,190 --> 00:00:23,940 So if you have some ammonia in an aqueous 11 00:00:23,940 --> 00:00:28,150 solution, plus water. 12 00:00:28,149 --> 00:00:29,429 I'll throw the water in there. 13 00:00:29,429 --> 00:00:35,469 Plus water in an aqueous solution. 14 00:00:35,469 --> 00:00:36,939 It's a weak base. 15 00:00:36,939 --> 00:00:40,530 So this reaction doesn't go in just one direction. 16 00:00:40,530 --> 00:00:41,890 It's an equilibrium reaction. 17 00:00:41,890 --> 00:00:45,670 18 00:00:45,670 --> 00:00:49,980 And since this is a weak base, it-- and this is where the 19 00:00:49,979 --> 00:00:53,140 Bronsted-Lowry definition really kind of pops out. 20 00:00:53,140 --> 00:00:57,039 Is that it's a proton acceptor instead of a donor. 21 00:00:57,039 --> 00:01:03,960 So it turns into ammonium, or an ammonia cation. 22 00:01:03,960 --> 00:01:06,969 Ammonium has another hydrogen on it, so now 23 00:01:06,969 --> 00:01:08,914 it has another proton. 24 00:01:08,915 --> 00:01:11,195 So it's the plus charge. 25 00:01:11,194 --> 00:01:12,449 An it's an aqueous. 26 00:01:12,450 --> 00:01:15,250 And it took that hydrogen from the water. 27 00:01:15,250 --> 00:01:20,049 So plus OH minus aqueous. 28 00:01:20,049 --> 00:01:22,429 And remember, if you look at it from the Bronsted-Lowry 29 00:01:22,430 --> 00:01:25,110 definition , it was a proton acceptor. 30 00:01:25,109 --> 00:01:26,599 So that made it a base. 31 00:01:26,599 --> 00:01:28,209 Or if you look at the Arrhenius definition, it 32 00:01:28,209 --> 00:01:32,009 increased the concentration of OH in the solution, so that 33 00:01:32,010 --> 00:01:33,859 makes it an Arrhenius base. 34 00:01:33,859 --> 00:01:37,060 But anyway, given that we have-- let me 35 00:01:37,060 --> 00:01:37,969 pick a random number. 36 00:01:37,969 --> 00:01:48,890 Let's say we have 0.2 molar of NH3. 37 00:01:48,890 --> 00:01:51,950 What is going to be the pH? 38 00:01:51,950 --> 00:01:55,710 So what's going to be our pH of the solution, considering 39 00:01:55,709 --> 00:01:58,259 that it's 0.2 molar of NH3. 40 00:01:58,260 --> 00:01:59,350 So the first thing we need to do. 41 00:01:59,349 --> 00:02:01,929 We need to figure out the equilibrium constant for this 42 00:02:01,930 --> 00:02:03,220 base reaction. 43 00:02:03,219 --> 00:02:10,819 And I just went to Wikipedia-- I wanted to say liquidpedia, 44 00:02:10,819 --> 00:02:13,370 I'm talking about liquids so much. 45 00:02:13,370 --> 00:02:14,129 And equilibrium. 46 00:02:14,129 --> 00:02:15,169 Equipedia. 47 00:02:15,169 --> 00:02:19,069 But I went to Wikipedia, and they have a little chart for 48 00:02:19,069 --> 00:02:20,629 almost any compound you look for. 49 00:02:20,629 --> 00:02:21,879 And they give you pKb. 50 00:02:21,879 --> 00:02:26,120 51 00:02:26,120 --> 00:02:27,759 Which is, you see that p there. 52 00:02:27,759 --> 00:02:32,090 That just means it's the minus log base 10 of 53 00:02:32,090 --> 00:02:33,564 the equilibrium constant. 54 00:02:33,564 --> 00:02:38,870 55 00:02:38,870 --> 00:02:42,700 And they give that as being 4.75. 56 00:02:42,699 --> 00:02:45,329 So we can just do a little bit of math here to solve for the 57 00:02:45,330 --> 00:02:47,000 equilibrium constant. 58 00:02:47,000 --> 00:02:47,620 So let's see. 59 00:02:47,620 --> 00:02:53,219 If we multiply both sides by negative, you get log base 10 60 00:02:53,219 --> 00:02:57,460 of our equilibrium constant for this base reaction. 61 00:02:57,460 --> 00:02:58,570 That's why the b is there. 62 00:02:58,569 --> 00:03:03,030 Is equal to minus 4.75, or 10 to the minus 63 00:03:03,030 --> 00:03:05,400 4.75 should be Kb. 64 00:03:05,400 --> 00:03:11,539 So Kb is equal to 10 to the minus 4.75. 65 00:03:11,539 --> 00:03:14,039 That's not an easy exponent to figure out in your head, so 66 00:03:14,039 --> 00:03:16,530 I'll bring out the calculator for that. 67 00:03:16,530 --> 00:03:27,849 So if we take 10 to the 4.75 minus, it equals, let's just 68 00:03:27,849 --> 00:03:31,460 say 1.8 times 10 to the negative 5. 69 00:03:31,460 --> 00:03:37,320 This is equal to 1.8 times 10 to the minus 5. 70 00:03:37,319 --> 00:03:40,090 So now we can use this information and we can do a 71 00:03:40,090 --> 00:03:42,259 mathematical thing very similar to we 72 00:03:42,259 --> 00:03:45,009 did in the last video. 73 00:03:45,009 --> 00:03:46,479 It's going to be hard to figure out the hydrogen 74 00:03:46,479 --> 00:03:47,759 concentration directly, right? 75 00:03:47,759 --> 00:03:50,519 Because our equilibrium reaction only has hydroxide. 76 00:03:50,520 --> 00:03:53,500 But if we know the hydroxide concentration, then we can 77 00:03:53,500 --> 00:03:55,770 back into the hydrogen concentration, knowing that 78 00:03:55,770 --> 00:04:01,510 this plus the hydrogen concentration has to equal 10 79 00:04:01,509 --> 00:04:02,439 to the minus 14. 80 00:04:02,439 --> 00:04:06,620 Or if you figure out the pOH, that plus the pH has to be 14. 81 00:04:06,620 --> 00:04:09,000 And we did that a couple of videos ago. 82 00:04:09,000 --> 00:04:14,060 So this equilibrium constant or this formula 83 00:04:14,060 --> 00:04:14,879 would look like this. 84 00:04:14,879 --> 00:04:24,939 1.8 times 10 to the minus 5 will be equal to-- in the 85 00:04:24,939 --> 00:04:27,879 denominator, we have our concentration of reactants. 86 00:04:27,879 --> 00:04:30,060 And remember, you don't include the solvent. 87 00:04:30,060 --> 00:04:31,980 So you only include the NH3. 88 00:04:31,980 --> 00:04:35,480 We have 0.2 molars is what we put in, but some of it, let's 89 00:04:35,480 --> 00:04:37,980 say X of it, is going to be converted into this stuff on 90 00:04:37,980 --> 00:04:39,670 the right-hand side. 91 00:04:39,670 --> 00:04:43,379 So in the denominator, we're going to have 0.2 minus 92 00:04:43,379 --> 00:04:45,870 whatever gets converted into the right-hand side. 93 00:04:45,870 --> 00:04:49,509 And so then in the right-hand side, we're going to have x of 94 00:04:49,509 --> 00:04:51,469 NH4 and x of OH. 95 00:04:51,470 --> 00:04:54,300 96 00:04:54,300 --> 00:04:58,139 This is the concentration of ammonia. 97 00:04:58,139 --> 00:05:00,300 And then we have x times x. 98 00:05:00,300 --> 00:05:07,829 This is the concentration of NH4 plus-- that's a 4. 99 00:05:07,829 --> 00:05:10,319 And then this is the concentration, 100 00:05:10,319 --> 00:05:15,329 right here, of OH minus. 101 00:05:15,329 --> 00:05:15,870 Right? 102 00:05:15,870 --> 00:05:17,860 And we just solve for x. 103 00:05:17,860 --> 00:05:19,850 Let's do that. 104 00:05:19,850 --> 00:05:21,080 Solve for x. 105 00:05:21,079 --> 00:05:23,389 And once we have x, we know the concentration of OH. 106 00:05:23,389 --> 00:05:25,310 We'll be able to figure out the pOH, and then we'll be 107 00:05:25,310 --> 00:05:27,899 able to figure out the pH. 108 00:05:27,899 --> 00:05:28,750 OK. 109 00:05:28,750 --> 00:05:32,300 Multiply this times both sides of this equation. 110 00:05:32,300 --> 00:05:35,060 And just so you know, that same simplification step that 111 00:05:35,060 --> 00:05:36,379 we did in the previous thing. 112 00:05:36,379 --> 00:05:44,259 When this is several orders of magnitude smaller than this 113 00:05:44,259 --> 00:05:49,829 number right here-- I want to give you-- heuristics are just 114 00:05:49,829 --> 00:05:51,289 kind of rules of thumb that sometimes work. 115 00:05:51,290 --> 00:05:53,170 Let's just do the quadratic equation. 116 00:05:53,170 --> 00:05:56,150 But you can kind of think about sometimes when you can 117 00:05:56,149 --> 00:05:57,000 get rid of that middle term. 118 00:05:57,000 --> 00:05:57,759 But let's just multiply it. 119 00:05:57,759 --> 00:06:03,449 0.2 two times 1.8 is 0.36. 120 00:06:03,449 --> 00:06:07,979 0.36 times 10 to the minus 5, right? 121 00:06:07,980 --> 00:06:11,650 2 times 1.8 would be 3.6, this is 0.36. 122 00:06:11,649 --> 00:06:20,659 Minus 1.8 times 10 to the minus 5 x, right? 123 00:06:20,660 --> 00:06:22,942 Is equal to that. 124 00:06:22,942 --> 00:06:24,900 x squared. 125 00:06:24,899 --> 00:06:29,259 Let's put everything on the same side of the equation. 126 00:06:29,259 --> 00:06:31,219 I'm going to move all of these the right-hand side, so you 127 00:06:31,220 --> 00:06:35,090 get 0 is equal to x squared. 128 00:06:35,089 --> 00:06:37,989 Add this to both sides of the equation. 129 00:06:37,990 --> 00:06:44,519 Plus 1.8 times 10 to the minus 5 x. 130 00:06:44,519 --> 00:06:48,870 1.8 times 10 to the minus 5. 131 00:06:48,870 --> 00:06:50,939 Just so you can see the coefficients separate from the 132 00:06:50,939 --> 00:06:53,009 x terms. 133 00:06:53,009 --> 00:06:59,860 Minus 0.36 times 10 to the minus 5. 134 00:06:59,860 --> 00:07:00,990 So let's solve this. 135 00:07:00,990 --> 00:07:04,610 And once again, if you wanted to kind of do it, you could 136 00:07:04,610 --> 00:07:06,720 eliminate this term and then just figure out the straight 137 00:07:06,720 --> 00:07:07,540 up square root. 138 00:07:07,540 --> 00:07:08,360 But we won't do that. 139 00:07:08,360 --> 00:07:09,889 We'll actually use a quadratic equation. 140 00:07:09,889 --> 00:07:12,610 So a is 1. 141 00:07:12,610 --> 00:07:13,949 b is this. 142 00:07:13,949 --> 00:07:14,529 That's b. 143 00:07:14,529 --> 00:07:15,199 And this is c. 144 00:07:15,199 --> 00:07:17,339 And you just supply than in the quadratic equation. 145 00:07:17,339 --> 00:07:20,500 So you get minus b. 146 00:07:20,500 --> 00:07:26,230 So you minus 1.8 times 10 to the minus 5 power. 147 00:07:26,230 --> 00:07:27,060 Plus or minus. 148 00:07:27,060 --> 00:07:28,790 We'll only have to do the plus because if we do the minus, 149 00:07:28,790 --> 00:07:30,250 we'll end up with a negative concentration. 150 00:07:30,250 --> 00:07:34,439 So plus, the square root-- we have to do a lot of math 151 00:07:34,439 --> 00:07:36,969 here-- b squared. 152 00:07:36,970 --> 00:07:39,220 So it's 1.8 times 10 to the negative 5. 153 00:07:39,220 --> 00:07:41,550 So it's 1.8. 154 00:07:41,550 --> 00:07:45,210 If you square it, it's 3.24. 155 00:07:45,209 --> 00:07:51,149 So it's 3.24 times-- if you square 10 to the minus 5-- 10 156 00:07:51,149 --> 00:07:57,629 to the minus 10 minus 4 times a, which is 1, 157 00:07:57,629 --> 00:07:59,379 times c, which is minus. 158 00:07:59,379 --> 00:08:04,860 So it's 4 times-- the minuses cancel out-- times 0.36 times 159 00:08:04,860 --> 00:08:08,220 10 to the minus 5. 160 00:08:08,220 --> 00:08:20,140 Which is 4 times 0.36 is equal to 1.44. 161 00:08:20,139 --> 00:08:21,435 I should have been able to do that in my head. 162 00:08:21,435 --> 00:08:25,439 Now you have 1.44 e minus 5. 163 00:08:25,439 --> 00:08:30,120 Times 10 to-- let me write that. 164 00:08:30,120 --> 00:08:32,548 So this is 1.44. 165 00:08:32,548 --> 00:08:36,259 And of course all of this is over 2a. 166 00:08:36,259 --> 00:08:37,389 So let's see. 167 00:08:37,389 --> 00:08:38,788 This is my x value. 168 00:08:38,788 --> 00:08:41,860 My concentration of OH. 169 00:08:41,860 --> 00:08:42,350 So let's see. 170 00:08:42,350 --> 00:08:51,379 I have 3.24 times 10 to the minus 10. 171 00:08:51,379 --> 00:08:53,019 That's that. 172 00:08:53,019 --> 00:09:03,870 Plus 1.44 times 10 to the minus 5 is equal to that. 173 00:09:03,870 --> 00:09:05,529 So that's this whole thing under the radical. 174 00:09:05,529 --> 00:09:08,179 And I want to take the square root of that. 175 00:09:08,179 --> 00:09:12,519 And so that is to the 0.5 power. 176 00:09:12,519 --> 00:09:16,679 So I get 0.00379. 177 00:09:16,679 --> 00:09:19,589 So I'll switch colors. 178 00:09:19,590 --> 00:09:25,820 So I get x is equal to a minus 1.8 times 10 to the minus 5 179 00:09:25,820 --> 00:09:33,320 plus 0.003794. 180 00:09:33,320 --> 00:09:35,660 All of that over 2. 181 00:09:35,659 --> 00:09:36,329 Do the math. 182 00:09:36,330 --> 00:09:42,660 So to that I'm going to subtract minus this point 183 00:09:42,659 --> 00:09:43,059 right here. 184 00:09:43,059 --> 00:09:43,750 I have this value. 185 00:09:43,750 --> 00:09:44,990 I'm just subtracting this. 186 00:09:44,990 --> 00:09:53,769 Minus 1.8 e 5 negative is equal to that. 187 00:09:53,769 --> 00:09:54,750 This is the whole numerator. 188 00:09:54,750 --> 00:09:57,470 And now I need to just divide it by 2. 189 00:09:57,470 --> 00:10:03,680 Divided by 2 is equal to 0.001. 190 00:10:03,679 --> 00:10:04,429 Let me write that. 191 00:10:04,429 --> 00:10:05,909 So x. 192 00:10:05,909 --> 00:10:08,139 So I'll switch colors arbitrarily again. 193 00:10:08,139 --> 00:10:18,480 x is equal to 0.001888-- I mean, then there's a 3 and so 194 00:10:18,480 --> 00:10:19,690 forth and so on. 195 00:10:19,690 --> 00:10:21,740 But if you remember from our original equation. 196 00:10:21,740 --> 00:10:22,490 What was x? 197 00:10:22,490 --> 00:10:26,759 It was what's both the ammonium concentration and the 198 00:10:26,759 --> 00:10:27,855 hydroxide concentration. 199 00:10:27,855 --> 00:10:30,529 We care about the hydroxide concentration. 200 00:10:30,529 --> 00:10:36,059 So this is equal to my concentration of hydroxide. 201 00:10:36,059 --> 00:10:40,579 Now if I want to figure out my pOH, I just take the minus log 202 00:10:40,580 --> 00:10:44,610 of this number, which is equal to-- 203 00:10:44,610 --> 00:10:46,830 So let's just take the log of it. 204 00:10:46,830 --> 00:10:49,180 The log is that, and then I take the minus of that. 205 00:10:49,179 --> 00:10:55,179 So it's 2.72. 206 00:10:55,179 --> 00:11:00,419 And now if we want to figure out the pH, my concentration 207 00:11:00,419 --> 00:11:03,370 of hydrogen ions-- just remember, when you're in an 208 00:11:03,370 --> 00:11:10,740 aqueous solution at 25 degrees Celsius, your pK of water is 209 00:11:10,740 --> 00:11:15,870 equal to your pOH plus your pH. 210 00:11:15,870 --> 00:11:19,730 This at 25 degrees is 14. 211 00:11:19,730 --> 00:11:22,815 Because you have 10 to the minus 14 molar concentration-- 212 00:11:22,815 --> 00:11:24,580 well no, actually, I don't want to go into that. 213 00:11:24,580 --> 00:11:26,720 You have 10 to the minus 7 of each of these. 214 00:11:26,720 --> 00:11:28,509 But anyway, this is equilibrium constant for the 215 00:11:28,509 --> 00:11:30,309 disassociation of water. 216 00:11:30,309 --> 00:11:37,169 This, when water's neutral is 7 or a concentration of OH of 217 00:11:37,169 --> 00:11:38,279 10 to the minus 7. 218 00:11:38,279 --> 00:11:39,759 We can take the minus log, this becomes 7. 219 00:11:39,759 --> 00:11:44,069 But now we know we have a much higher concentration of OH. 220 00:11:44,070 --> 00:11:45,080 2.72. 221 00:11:45,080 --> 00:11:47,550 Remember, that minus log kind of flips it. 222 00:11:47,549 --> 00:11:52,669 So a lower pOH means a higher concentration of pOH. 223 00:11:52,669 --> 00:11:53,229 Right? 224 00:11:53,230 --> 00:11:57,200 And a lower pOH, if this is lower, right? 225 00:11:57,200 --> 00:11:58,480 This is a lower pOH. 226 00:11:58,480 --> 00:12:00,289 That means your pH is higher. 227 00:12:00,289 --> 00:12:03,569 228 00:12:03,570 --> 00:12:04,870 So what is your pH going to be? 229 00:12:04,870 --> 00:12:15,024 So your pH is going to be equal to 14 minus 2.72. 230 00:12:15,024 --> 00:12:21,710 So let me do the minus plus 14 is equal to-- 231 00:12:21,710 --> 00:12:23,570 let's just say 11.3. 232 00:12:23,570 --> 00:12:26,650 So your pH is equal to 11.3. 233 00:12:26,649 --> 00:12:30,850 Which makes sense, because we said this was a weak base. 234 00:12:30,850 --> 00:12:33,680 Ammonia is a weak base. 235 00:12:33,679 --> 00:12:35,069 So it's basic. 236 00:12:35,070 --> 00:12:39,120 So it should increase your pH above the neutral 7. 237 00:12:39,120 --> 00:12:42,804 So the pH should be greater than 7, but as you compare it 238 00:12:42,804 --> 00:12:45,279 to some of the strong bases before that took our pH when 239 00:12:45,279 --> 00:12:49,409 you added a molar to 14, this took our pH-- although we only 240 00:12:49,409 --> 00:12:54,009 did add 0.2 molar of it to 11.3. 241 00:12:54,009 --> 00:12:56,970 Anyway, this is more of a math problem than chemistry, but 242 00:12:56,970 --> 00:12:59,800 hopefully it clarified a few things as well.