/ News & Press / Video / 18.5 Gibbs Free Energy and the Equilibrium Constant

18.5 Gibbs Free Energy and the Equilibrium Constant

WEBVTT
Kind: captions
Language: en

00:00:00.030
so if you guys are called from the whole
00:00:02.240 00:00:02.250 gas chapter PV equals NRT and all that
00:00:04.220 00:00:04.230 jazz what was STP what does it stand for
00:00:07.720 00:00:07.730 standard temperature pressure what were
00:00:09.589 00:00:09.599 the standard temperature and pressure
00:00:11.950 00:00:11.960 one atmosphere it was zero degrees
00:00:16.099 00:00:16.109 Celsius
00:00:16.609 00:00:16.619 273 Kelvin that was STP from the gas
00:00:19.640 00:00:19.650 chapter but in thermodynamics we usually
00:00:21.980 00:00:21.990 define something different called
00:00:23.570 00:00:23.580 standard conditions standard conditions
00:00:26.420 00:00:26.430 and standard conditions is a little bit
00:00:28.700 00:00:28.710 different so we still talk about a
00:00:32.450 00:00:32.460 pressure of one atmosphere so however
00:00:42.190 00:00:42.200 the concentration of all reactants and
00:00:46.580 00:00:46.590 products equals one so aqueous species
00:00:49.639 00:00:49.649 the concentration equals one molar for
00:00:53.330 00:00:53.340 gases their partial pressure is one
00:00:56.240 00:00:56.250 atmosphere but either way all
00:00:58.540 00:00:58.550 concentrations for aqueous and gaseous
00:01:00.920 00:01:00.930 species equals one reactant side and
00:01:03.500 00:01:03.510 product side so standard conditions kind
00:01:05.810 00:01:05.820 of a funky set of conditions you already
00:01:07.789 00:01:07.799 have equal amounts of reactants and
00:01:09.950 00:01:09.960 equal amounts of products one molar or
00:01:12.289 00:01:12.299 one atmosphere concentrations for
00:01:13.850 00:01:13.860 everything that's standard condition and
00:01:16.810 00:01:16.820 technically we don't actually define a
00:01:20.870 00:01:20.880 temperature any temperature can be at
00:01:23.600 00:01:23.610 standard conditions and I say that and
00:01:26.179 00:01:26.189 unfortunately some textbooks and just in
00:01:28.280 00:01:28.290 general and Gen chem not P chem but Gen
00:01:30.710 00:01:30.720 chem we often talk about one temperature
00:01:33.350 00:01:33.360 more than the other and sometimes it
00:01:36.289 00:01:36.299 kind of gets grouped into standard
00:01:37.370 00:01:37.380 conditions it's technically not again
00:01:40.179 00:01:40.189 but you'll see it so commonly that I'm
00:01:43.130 00:01:43.140 going to throw it up there 298 Kelvin 25
00:01:46.819 00:01:46.829 degrees Celsius is approximately room
00:01:49.819 00:01:49.829 temperature and that's what we use so
00:01:52.219 00:01:52.229 this is different temperature than STP
00:01:54.350 00:01:54.360 and again it's really not technically
00:01:56.149 00:01:56.159 part of standard conditions but in Gen
00:01:58.100 00:01:58.110 chem it usually gets grouped in with it
00:01:59.510 00:01:59.520 so I'm going to throw it up there cool
00:02:02.539 00:02:02.549 these are your standard conditions and
00:02:04.039 00:02:04.049 so when you see
00:02:07.920 00:02:07.930 delta g standard that's the conditions
00:02:14.290 00:02:14.300 that corresponds to you have one molar
00:02:17.590 00:02:17.600 or atmosphere concentrations of all
00:02:19.330 00:02:19.340 reactants and all products equal amounts
00:02:21.190 00:02:21.200 of both
00:02:28.070 00:02:28.080 so what if we're not doing a reaction
00:02:30.290 00:02:30.300 under standard conditions how often do
00:02:32.450 00:02:32.460 you think you might do a chemistry
00:02:33.560 00:02:33.570 reaction in a chem lab and start out
00:02:36.080 00:02:36.090 with both reactants and products at
00:02:38.120 00:02:38.130 exactly that concentration of one almost
00:02:41.210 00:02:41.220 never almost never but unfortunately
00:02:43.940 00:02:43.950 this is the only set of conditions for
00:02:45.260 00:02:45.270 which you typically find a bunch of
00:02:46.460 00:02:46.470 published values you can look up a whole
00:02:48.500 00:02:48.510 bunch of reaction thousands and
00:02:50.120 00:02:50.130 thousands and thousands upon thousands
00:02:51.530 00:02:51.540 of them and they'll give you values only
00:02:54.020 00:02:54.030 for this standard condition so what if
00:02:56.420 00:02:56.430 you want to find out what Delta G under
00:02:58.160 00:02:58.170 some other non-standard set of
00:02:59.600 00:02:59.610 conditions well you still look up that
00:03:01.460 00:03:01.470 value in a book and then they tell you
00:03:05.420 00:03:05.430 to add this fudge factor to account for
00:03:09.950 00:03:09.960 any conditions that are not standard you
00:03:12.800 00:03:12.810 can put in a different temperature and
00:03:15.130 00:03:15.140 then Q the reaction quotient products
00:03:18.020 00:03:18.030 over reactants you can put in all the
00:03:20.150 00:03:20.160 concentrations and so if they're not one
00:03:22.340 00:03:22.350 that'll get factored in notice what if
00:03:25.070 00:03:25.080 you were under standard conditions and
00:03:26.510 00:03:26.520 all reactants and products had
00:03:27.980 00:03:27.990 concentrations of one what would Q be
00:03:30.620 00:03:30.630 into that case if all reactants and
00:03:34.250 00:03:34.260 products were one then Q would be also
00:03:37.610 00:03:37.620 equal to well be 1 over 1 which is 1 and
00:03:40.670 00:03:40.680 what's the natural log of 1 0 and under
00:03:44.390 00:03:44.400 those conditions this second term would
00:03:45.830 00:03:45.840 go away and your Delta G would equal the
00:03:48.530 00:03:48.540 standard value so this kind of makes
00:03:50.030 00:03:50.040 sense cool so this is how you calculate
00:03:54.350 00:03:54.360 Delta G when you're not under standard
00:03:56.930 00:03:56.940 conditions
00:03:57.470 00:03:57.480 you still got to use the standard value
00:03:59.479 00:03:59.489 and look it up and whatever but now
00:04:01.790 00:04:01.800 you've got the rest of this as well so
00:04:06.710 00:04:06.720 we'll talk about Delta G standard for
00:04:08.240 00:04:08.250 another minute here we can make some
00:04:12.229 00:04:12.239 generalizations about Delta G standard
00:04:14.060 00:04:14.070 so again standard conditions you have
00:04:16.190 00:04:16.200 more reactants or more products at that
00:04:17.659 00:04:17.669 point strict question neither you got
00:04:22.400 00:04:22.410 equal amounts of both right because
00:04:23.600 00:04:23.610 everything's one molar one atmosphere
00:04:25.100 00:04:25.110 two equal amounts equal concentrations
00:04:27.230 00:04:27.240 of reactants and products at standard
00:04:28.760 00:04:28.770 conditions so if I told you that Delta G
00:04:30.800 00:04:30.810 standard was negative what does that
00:04:33.230 00:04:33.240 mean it means that spontaneous as
00:04:36.140 00:04:36.150 standard conditions is it spontaneous
00:04:38.659 00:04:38.669 under non-standard conditions I don't
00:04:40.190 00:04:40.200 know it might be but
00:04:41.480 00:04:41.490 doesn't tell me about non-standard
00:04:42.620 00:04:42.630 conditions this little circle only tells
00:04:45.020 00:04:45.030 me that about standard conditions so
00:04:47.360 00:04:47.370 under standard equal amounts of both
00:04:48.770 00:04:48.780 it's spontaneous
00:04:49.580 00:04:49.590 Delta G standard is negative okay so if
00:04:53.360 00:04:53.370 I start out with equal amounts of
00:04:54.499 00:04:54.509 reactants and products at standard
00:04:58.070 00:04:58.080 conditions and the reaction is
00:04:59.270 00:04:59.280 spontaneous as it's written left to
00:05:00.950 00:05:00.960 right then I'm going to end up with more
00:05:03.020 00:05:03.030 what by the time I reach equilibrium
00:05:04.960 00:05:04.970 more products under those conditions and
00:05:08.360 00:05:08.370 if once I reach equilibrium or products
00:05:10.249 00:05:10.259 then what should I expect for the value
00:05:11.900 00:05:11.910 of the equilibrium constant
00:05:16.300 00:05:16.310 don't say zero because products over
00:05:19.999 00:05:20.009 reactants and you got more products than
00:05:21.409 00:05:21.419 reactants more numerator than
00:05:23.749 00:05:23.759 denominator all about one not zero so in
00:05:31.670 00:05:31.680 this case if Delta G standard is
00:05:33.740 00:05:33.750 negative K your equilibrant will be pot
00:05:37.100 00:05:37.110 will be any value will be greater than
00:05:38.689 00:05:38.699 one you'll have more products than
00:05:40.850 00:05:40.860 reactants that's a reaction that favors
00:05:42.230 00:05:42.240 products and this kind of makes sense in
00:05:45.260 00:05:45.270 kind of a somewhat of an intuitive sense
00:05:47.209 00:05:47.219 I see Delta G standard being negative
00:05:49.219 00:05:49.229 and I should think I action spontaneous
00:05:50.930 00:05:50.940 well it's really spontaneous under
00:05:52.820 00:05:52.830 standard conditions but even if it's
00:05:54.409 00:05:54.419 spontaneous understand occasions you
00:05:55.700 00:05:55.710 should end up when the reaction is done
00:05:57.589 00:05:57.599 at equilibrium with more products and so
00:06:00.050 00:06:00.060 K is the given one and you can say the
00:06:02.060 00:06:02.070 exact converse as well if Delta G
00:06:04.010 00:06:04.020 standard is positive well again standard
00:06:08.060 00:06:08.070 condition to get equal amounts but if
00:06:09.499 00:06:09.509 Delta G standard is positive then as the
00:06:11.809 00:06:11.819 reaction is written left to right is it
00:06:13.219 00:06:13.229 spontaneous no under those standards
00:06:16.430 00:06:16.440 actually be spontaneous going the other
00:06:17.600 00:06:17.610 way and so you'd end up with more
00:06:20.050 00:06:20.060 reactants than products by the time you
00:06:23.209 00:06:23.219 reach equilibrium and in that case you'd
00:06:25.249 00:06:25.259 therefore expect keq to be smaller than
00:06:29.029 00:06:29.039 one so we connect this back to the
00:06:33.649 00:06:33.659 equilibrium chapter the whole
00:06:35.420 00:06:35.430 equilibrium chapter is really a part of
00:06:37.370 00:06:37.380 thermodynamics technically
00:06:43.240 00:06:43.250 okay so now that we've established that
00:06:45.830 00:06:45.840 I want to come back to this equation
00:06:47.300 00:06:47.310 real quick so where do you get this
00:06:50.870 00:06:50.880 value again typically for a chemical
00:06:52.880 00:06:52.890 reaction in a book you look it up in a
00:06:55.220 00:06:55.230 book so let's say I just happen to have
00:06:59.510 00:06:59.520 a chemical reaction going on and I
00:07:01.850 00:07:01.860 decided I want to start out at perfectly
00:07:03.830 00:07:03.840 standard conditions okay
00:07:05.720 00:07:05.730 and so the Delta G value for my reaction
00:07:08.060 00:07:08.070 right when I started was exactly the
00:07:10.160 00:07:10.170 number in the book and then I let the
00:07:12.020 00:07:12.030 reaction go it turns out it was
00:07:13.490 00:07:13.500 spontaneous and so it goes forming more
00:07:16.010 00:07:16.020 products and using up reactants as that
00:07:18.710 00:07:18.720 reaction proceeds am i under standard
00:07:20.240 00:07:20.250 conditions anymore
00:07:21.080 00:07:21.090 no but if I look that value back up in
00:07:24.350 00:07:24.360 the book is it going to be a different
00:07:25.940 00:07:25.950 number that I looked up the first time
00:07:26.960 00:07:26.970 no it's the same number I'm not under
00:07:29.600 00:07:29.610 standard condition so the value doesn't
00:07:31.250 00:07:31.260 apply anymore but it's the number of the
00:07:33.470 00:07:33.480 book this is a constant value for a
00:07:35.450 00:07:35.460 given temperature it's this value though
00:07:38.240 00:07:38.250 that ever changes as the reaction goes
00:07:40.430 00:07:40.440 on this number is either going to get
00:07:42.230 00:07:42.240 bigger or smaller depending on if you
00:07:43.670 00:07:43.680 know which direction of reaction to go
00:07:44.930 00:07:44.940 in and stuff like that this is the one
00:07:46.550 00:07:46.560 that changes so when the reaction
00:07:48.470 00:07:48.480 reaches equilibrium will this number
00:07:51.230 00:07:51.240 that you looked up in a book still be
00:07:52.490 00:07:52.500 any different no but when the reaction
00:07:55.490 00:07:55.500 reaches equilibrium this number is now
00:07:58.670 00:07:58.680 what zero so in this case it's when
00:08:05.660 00:08:05.670 Delta G naught standard value it's when
00:08:14.960 00:08:14.970 the non standard value is going to hit
00:08:16.670 00:08:16.680 zero that's when you're at equilibrium
00:08:17.720 00:08:17.730 the standard value is what it is you
00:08:20.000 00:08:20.010 look it up in a book it doesn't change
00:08:22.490 00:08:22.500 for a given temperature it's the non
00:08:24.200 00:08:24.210 standard value that's going to
00:08:25.160 00:08:25.170 eventually reach zero once you've
00:08:27.380 00:08:27.390 reached equilibrium so if we look at
00:08:31.730 00:08:31.740 this then if it's this value that goes
00:08:33.530 00:08:33.540 to zero then this equation a special
00:08:37.130 00:08:37.140 case when you reach equilibrium
00:08:38.839 00:08:38.849 you'd get zero equals Delta G standard
00:08:44.200 00:08:44.210 plus rtln and in this case if you're at
00:08:48.110 00:08:48.120 equilibrium we can just say q is equal
00:08:49.970 00:08:49.980 to what at equilibrium
00:08:53.619 00:08:53.629 okay and if you rearrange this you now
00:08:58.280 00:08:58.290 find that delta g standard is equal to
00:09:01.610 00:09:01.620 negative RT natural log of K and so here
00:09:11.389 00:09:11.399 is a mathematical relationship between
00:09:13.040 00:09:13.050 Delta G standard and K EQ it's the same
00:09:16.639 00:09:16.649 relationship we just established here
00:09:21.019 00:09:21.029 you can actually mathematically
00:09:22.309 00:09:22.319 calculate things if I give you K EQ and
00:09:24.379 00:09:24.389 a temperature you can calculate delta T
00:09:26.780 00:09:26.790 standard if I give you Delta G standard
00:09:28.819 00:09:28.829 and a temperature you can calculate K EQ
00:09:33.879 00:09:33.889 questions on that one thing to note are
00:09:39.829 00:09:39.839 here what is our call that you remember
00:09:43.689 00:09:43.699 not a rate constant but gas constant so
00:09:47.480 00:09:47.490 universal gas constant in this case the
00:09:54.650 00:09:54.660 most common value you're going to have
00:09:55.939 00:09:55.949 provided for you
00:09:56.929 00:09:56.939 that's relevant to this chapter is 8.314
00:10:01.040 00:10:01.050 joules per mole Kelvin unfortunately
00:10:03.410 00:10:03.420 this is not the only value they're going
00:10:04.759 00:10:04.769 to give you right where else did you see
00:10:06.860 00:10:06.870 our originally yeah PV equals NRT same R
00:10:12.069 00:10:12.079 but for PV equals NRT instead of joules
00:10:15.319 00:10:15.329 per mole Kelvin we're usually going to
00:10:17.329 00:10:17.339 give it to you in liter atmospheres per
00:10:19.970 00:10:19.980 mole Kelvin and Express in those units
00:10:21.920 00:10:21.930 it's a totally different number it's
00:10:23.090 00:10:23.100 0.08206 so you got to be careful we're
00:10:26.540 00:10:26.550 dealing with energy right now then you
00:10:28.040 00:10:28.050 better use the R value that gives you
00:10:29.749 00:10:29.759 units that you recognize as being energy
00:10:31.850 00:10:31.860 joules not the liters and atmospheres
00:10:34.220 00:10:34.230 that you'd recognize common stuff for
00:10:35.960 00:10:35.970 gases so use the right units but here
00:10:38.809 00:10:38.819 you got to be careful let's say I give
00:10:41.720 00:10:41.730 you Delta G standard and a temperature n
00:10:44.299 00:10:44.309 R and I say what's ke q well what is r
00:10:48.829 00:10:48.839 have units of joules per mole Kelvin
00:10:51.939 00:10:51.949 what is Delta G standard usually have
00:10:54.679 00:10:54.689 units of kilojoules so when you go to
00:10:58.759 00:10:58.769 divide R through you better make sure
00:11:00.530 00:11:00.540 Delta G standard and r have the same
00:11:02.299 00:11:02.309 units because this is usually given R in
00:11:04.699 00:11:04.709 joules but
00:11:05.630 00:11:05.640 standard in kilojoules you better make a
00:11:07.640 00:11:07.650 match

Sales phone