1 00:00:00,030 --> 00:00:02,400 The following content is provided under a creative 2 00:00:02,400 --> 00:00:03,860 commons license. 3 00:00:03,860 --> 00:00:06,840 Your support will help MIT OpenCourseWare continue to 4 00:00:06,840 --> 00:00:10,570 offer high quality educational resources for free. 5 00:00:10,570 --> 00:00:13,410 To make a donation or view additional materials from 6 00:00:13,410 --> 00:00:17,440 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,440 --> 00:00:18,690 ocw.mit.edu. 8 00:00:21,612 --> 00:00:22,590 JOCELYN: Hi. 9 00:00:22,590 --> 00:00:25,960 Jocelyn here and we're going to go over fall 2009 exam 10 00:00:25,960 --> 00:00:28,060 three problem number three. 11 00:00:28,060 --> 00:00:31,280 As always, let's read the question first. Calcium 12 00:00:31,280 --> 00:00:35,110 ammonium phosphate dissolves in water according to the 13 00:00:35,110 --> 00:00:38,070 dissolution equation, for which the value of the 14 00:00:38,070 --> 00:00:42,630 solubility product, ksp, has been determined to be 4.4 15 00:00:42,630 --> 00:00:45,050 times 10 to the -14. 16 00:00:45,050 --> 00:00:47,880 Calculate the solubility of the compound in water. 17 00:00:47,880 --> 00:00:51,730 Express your answers in units of molartiy, ie moles of the 18 00:00:51,730 --> 00:00:53,910 compound per liter of solution. 19 00:00:56,620 --> 00:01:00,080 So the first thing we want to do is write down what the 20 00:01:00,080 --> 00:01:02,610 question's asking. 21 00:01:02,610 --> 00:01:05,150 Part A-- 22 00:01:05,150 --> 00:01:17,760 how much calcium ammonium phosphate 23 00:01:17,760 --> 00:01:21,790 can dissolve in water? 24 00:01:33,570 --> 00:01:38,930 And we're going to call this cs-- 25 00:01:38,930 --> 00:01:44,020 or the saturation concentration. 26 00:01:44,020 --> 00:01:48,330 Next we need to figure out how to find this out, right? 27 00:01:48,330 --> 00:01:50,720 So it gives us that the ksp-- 28 00:01:53,730 --> 00:01:58,630 4.4 times 10 to the -14. 29 00:01:58,630 --> 00:02:02,580 So we need to know something about the ksp and although 30 00:02:02,580 --> 00:02:06,410 it's called the solubility product, it's the same as 31 00:02:06,410 --> 00:02:09,270 other equilibrium constants. 32 00:02:09,270 --> 00:02:14,590 So equilibrium constants tells us about the concentrations at 33 00:02:14,590 --> 00:02:19,210 equilibrium and therefore the maximum solubility. 34 00:02:19,210 --> 00:02:28,080 Looking at the equation, we have calcium ammonium 35 00:02:28,080 --> 00:02:30,760 phosphate dissolving-- 36 00:02:30,760 --> 00:02:33,680 which is a solid-- 37 00:02:33,680 --> 00:02:45,490 dissolving into calcium ions, ammonium ions 38 00:02:45,490 --> 00:02:49,190 and phosphate ions. 39 00:02:49,190 --> 00:02:52,290 As with every equilibrium constant, we can write down an 40 00:02:52,290 --> 00:02:55,725 equation relating to the concentration of the species. 41 00:02:58,230 --> 00:03:11,983 So our ksp is the product of the concentration. 42 00:03:17,960 --> 00:03:20,240 And a common mistake made on this problem 43 00:03:20,240 --> 00:03:22,250 was that people included-- 44 00:03:22,250 --> 00:03:25,870 students included the calcium ammonium phosphate solid on 45 00:03:25,870 --> 00:03:28,400 the bottom as you normally would-- 46 00:03:28,400 --> 00:03:30,170 where you would normally put the reactant. 47 00:03:30,170 --> 00:03:33,030 However, remember that for equilibrium constants, we 48 00:03:33,030 --> 00:03:37,130 don't put solids in there because the 49 00:03:37,130 --> 00:03:41,440 activities don't change-- 50 00:03:41,440 --> 00:03:42,900 or the concentration doesn't change. 51 00:03:42,900 --> 00:03:45,680 It doesn't really make sense to add it in. 52 00:03:45,680 --> 00:03:51,810 So here we just look at the solvated ions and we see that 53 00:03:51,810 --> 00:03:55,510 we have a 1:1:1 molar ratio here. 54 00:03:55,510 --> 00:03:57,590 That's going to make our life a little bit easier. 55 00:04:00,160 --> 00:04:03,170 So now we need to figure out what the solubility of the 56 00:04:03,170 --> 00:04:06,380 compound is and to do that, we want to look at 57 00:04:06,380 --> 00:04:08,010 this chemical equation. 58 00:04:08,010 --> 00:04:11,380 We see that for one mole-- 59 00:04:11,380 --> 00:04:22,590 so one mole of calcium ammonium phosphate dissolved 60 00:04:22,590 --> 00:04:38,790 gives you one mole of the calcium ion, the sodium ion 61 00:04:38,790 --> 00:04:40,490 and the phosphate ion. 62 00:04:43,070 --> 00:04:47,900 Thus, we can say the amount of calcium ammonium phosphate 63 00:04:47,900 --> 00:04:52,910 dissolved, which we called Cs, is going to be equivalent to 64 00:04:52,910 --> 00:04:54,330 each of these concentrations. 65 00:05:05,120 --> 00:05:09,900 Because we're asked for how much of the compound is 66 00:05:09,900 --> 00:05:14,410 dissolved, but we're given the ksp, which is in terms of the 67 00:05:14,410 --> 00:05:17,600 concentrations of these solvated ions. 68 00:05:17,600 --> 00:05:18,000 I'm sorry. 69 00:05:18,000 --> 00:05:20,270 This doesn't equal the product. 70 00:05:20,270 --> 00:05:21,520 These are all equal. 71 00:05:24,320 --> 00:05:30,010 Now we can plug the Cs into our ksp 72 00:05:30,010 --> 00:05:33,380 equation that we had before. 73 00:05:33,380 --> 00:05:35,880 So instead of the concentration of 74 00:05:35,880 --> 00:05:39,650 calcium ions, we have-- 75 00:05:39,650 --> 00:05:41,550 it's equal to the concentration of 76 00:05:41,550 --> 00:05:43,840 the compound dissolved. 77 00:05:43,840 --> 00:05:49,470 The same goes for the ammonium and the phosphate, because 78 00:05:49,470 --> 00:05:56,050 again, we have 1:1:1:1 stoichiometric coefficients. 79 00:05:56,050 --> 00:06:02,790 And we can be a little more concise. 80 00:06:02,790 --> 00:06:07,030 Now it's just a matter of solving for the saturated 81 00:06:07,030 --> 00:06:08,560 concentration. 82 00:06:08,560 --> 00:06:18,650 So doing some algebra here. 83 00:06:18,650 --> 00:06:19,970 Then we plug in the numbers. 84 00:06:26,510 --> 00:06:36,330 And we get that the solubility of calcium ammonium phosphate 85 00:06:36,330 --> 00:06:42,210 is 3.53 times 10 to the -5 moles-- 86 00:06:42,210 --> 00:06:43,290 molar, sorry. 87 00:06:43,290 --> 00:06:49,440 So that means 3.53 times -5 moles per liter of water. 88 00:06:49,440 --> 00:06:50,450 That's not very much. 89 00:06:50,450 --> 00:06:56,030 So we can say generally or relatively this calcium 90 00:06:56,030 --> 00:07:00,120 ammonium phosphate is not that soluble in water. 91 00:07:00,120 --> 00:07:01,490 So let's move on to part B. 92 00:07:08,590 --> 00:07:11,890 Part B says, calculate the solubility of calcium ammonium 93 00:07:11,890 --> 00:07:16,060 phosphate in 2.2 molar calcium bromide. 94 00:07:16,060 --> 00:07:18,890 Express your answer in units molarity. 95 00:07:18,890 --> 00:07:21,310 Assume that in water, calcium bromide completely 96 00:07:21,310 --> 00:07:23,440 disassociates into calcium 2 plus 97 00:07:23,440 --> 00:07:24,740 cations and bromide anions. 98 00:07:29,510 --> 00:07:33,790 This is basically asking us for the same value. 99 00:07:33,790 --> 00:07:36,280 It's asking us for the solubility of calcium ammonium 100 00:07:36,280 --> 00:07:39,240 phosphate, but under slightly different conditions. 101 00:07:39,240 --> 00:07:40,920 So we want to write those conditions down. 102 00:07:51,920 --> 00:07:55,050 Now we have to ask ourselves why would the fact that we 103 00:07:55,050 --> 00:07:58,920 have a concentration of calcium bromide affect the 104 00:07:58,920 --> 00:08:01,440 solubility of calcium ammonium phosphate? 105 00:08:01,440 --> 00:08:03,640 And the thing to remember here is the 106 00:08:03,640 --> 00:08:06,330 common ion effect, right? 107 00:08:06,330 --> 00:08:10,590 2 molar calcium bromide will-- 108 00:08:10,590 --> 00:08:21,130 when dissolved in water, the concentration of calcium from 109 00:08:21,130 --> 00:08:26,870 just the calcium bromide will be 2.2 molar, right? 110 00:08:26,870 --> 00:08:29,610 Because we're told that it completely disassociates. 111 00:08:29,610 --> 00:08:36,140 So if we look at the disassociation reaction, we 112 00:08:36,140 --> 00:08:40,190 see that for every mole of calcium bromide, we get one 113 00:08:40,190 --> 00:08:44,480 mole of calcium and two moles of bromide. 114 00:08:53,370 --> 00:08:58,330 So having calcium bromide will alter our answer from the 115 00:08:58,330 --> 00:09:04,300 previous problem because the ksp will always be the same. 116 00:09:04,300 --> 00:09:07,200 It's an equilibrium constant, right? 117 00:09:07,200 --> 00:09:10,960 So even though it has to do with calcium ammonium 118 00:09:10,960 --> 00:09:13,570 phosphate, we have to take into account that we already 119 00:09:13,570 --> 00:09:17,340 have calcium in the system. 120 00:09:17,340 --> 00:09:20,590 So before we start plugging in any numbers, we should think 121 00:09:20,590 --> 00:09:22,190 about this problem. 122 00:09:22,190 --> 00:09:24,780 Do we think that already having calcium in the system 123 00:09:24,780 --> 00:09:28,350 will increase or decrease the solubility of the calcium 124 00:09:28,350 --> 00:09:29,600 ammonium phosphate? 125 00:09:32,430 --> 00:09:36,560 Hopefully we can agree that it would probably decrease the 126 00:09:36,560 --> 00:09:39,690 solubility because you already have those calcium ions. 127 00:09:39,690 --> 00:09:43,800 So putting more calcium ions into the water is going to be 128 00:09:43,800 --> 00:09:46,820 harder and therefore less calcium ammonium phosphate 129 00:09:46,820 --> 00:09:48,180 will dissolve. 130 00:09:48,180 --> 00:09:51,420 Now that we know what kind of number we're looking for, we 131 00:09:51,420 --> 00:09:56,080 can start doing the actual calculation. 132 00:09:56,080 --> 00:09:59,520 So again, we'll start with our equation for the ksp, which 133 00:09:59,520 --> 00:10:03,010 for calcium ammonium phosphate has not changed. 134 00:10:03,010 --> 00:10:05,240 I'm just going to rewrite it on this board here. 135 00:10:18,560 --> 00:10:22,650 But now instead of having each of these be equal 136 00:10:22,650 --> 00:10:24,920 concentrations, we already have some 137 00:10:24,920 --> 00:10:26,000 calcium in the system. 138 00:10:26,000 --> 00:10:27,450 So we need to take that into account. 139 00:10:37,310 --> 00:10:41,900 And I'm going to call the saturation concentration Cs 140 00:10:41,900 --> 00:10:44,280 star because we're under different conditions, right? 141 00:10:49,220 --> 00:10:55,400 The calcium bromide does not contribute any ammonium or 142 00:10:55,400 --> 00:11:00,420 phosphate ions so those concentrations will just be 143 00:11:00,420 --> 00:11:02,470 determined by how much of the calcium 144 00:11:02,470 --> 00:11:05,710 ammonium phosphate dissolves. 145 00:11:05,710 --> 00:11:12,600 From before, we can use what we found in part A to simplify 146 00:11:12,600 --> 00:11:14,630 this a little bit. 147 00:11:14,630 --> 00:11:18,600 So in part A, we know that without anything else, without 148 00:11:18,600 --> 00:11:21,620 a common ion effect, that we have decided will decrease the 149 00:11:21,620 --> 00:11:22,940 solubility. 150 00:11:22,940 --> 00:11:31,240 We have 3.35 times 10 to the -5th molar solubility. 151 00:11:31,240 --> 00:11:41,650 Therefore, we can say with good certainty that our 152 00:11:41,650 --> 00:11:45,710 saturation concentration with the common ion effect will be 153 00:11:45,710 --> 00:11:52,090 much, much less than 2.2 molar because 2.2 molar is much 154 00:11:52,090 --> 00:11:54,610 greater than our pure solubility. 155 00:11:57,260 --> 00:12:00,070 Going back to our equation over here, that 156 00:12:00,070 --> 00:12:09,308 means we can have-- 157 00:12:15,720 --> 00:12:20,360 and now we have a fairly simple algebraic problem. 158 00:12:23,650 --> 00:12:29,300 Dividing by 2.2 and then taking the square root, we get 159 00:12:29,300 --> 00:12:34,460 that the saturation concentration under these 160 00:12:34,460 --> 00:12:35,030 conditions-- 161 00:12:35,030 --> 00:12:37,320 2.2 molar calcium bromide-- 162 00:12:37,320 --> 00:12:45,360 will be 1.41 times 10 to the -7 molar. 163 00:12:45,360 --> 00:12:49,750 And going back to our answer from part A, we see that this 164 00:12:49,750 --> 00:12:52,600 is indeed a lower solubility. 165 00:12:52,600 --> 00:12:59,720 There's less calcium ammonium phosphate that can be 166 00:12:59,720 --> 00:13:03,170 dissolved and that makes sense from our previous thought 167 00:13:03,170 --> 00:13:05,360 about this problem. 168 00:13:05,360 --> 00:13:09,888 And so now that you've found the answer, box 169 00:13:09,888 --> 00:13:12,530 it and we're done.