We've said that the +1 oxidation state is uncommon for indium but is the most stable state for thallium. Verify this statement by calculating E ° and ΔG ° (in kilojoules) for the disproportionation reaction

3 M+1aq2S M3+1aq2 + 2 M1s2 M = In or Tl

Is disproportionation a spontaneous reaction for In+ and/orTl+? Standard reduction potentials for the relevant halfreactions are

In3+1aq2 + 2 e- S In+1aq2 E° = -0.44 V

In+1aq2 + e- S In1s2 E° = -0.14 V

Tl3+1aq2 + 2 e- S Tl+1aq2 E° = +1.25 V

Tl+1aq2 + e- S Tl1s2 E° = -0.34 V

Video transcript

Hi, everyone. Welcome back. Here's our next problem. The plus one oxidation state is the most stable state for TL but is not as common for G A, calculate the standard potential. And standard Gipps free energy in kilojoules for the disproportion reaction below to explain this phenomenon. And our reaction is where M equals either G A or TL three M plus aqueous goes to M three plus aqueous plus two M solid is the reaction spontaneous for either G A plus or TL plus. The relevant standard reduction potentials are listed below and we have reduction reactions of TL three plus, going to TL plus TL plus, going to TL G A three plus, going to G A plus and G A plus going to G A. So we're given those values, then we have our four answer choices which show for TL plus and G A plus. The standard production, standard potential, the standard gift free free energy. And whether it's non spontaneous or spontaneous, I'm not going to read those all out. We'll do our calculations and then match some to our answer choices. So we have these half reactions, these redox reactions which might be a little confusing at first because we only have one element. But we should pay attention to the fact that in our original reaction, it's being converted into two different forms, two different oxidation states. So we have oxidation and reduction going on, we can write them as two half reactions. From that. Given that we have these standard reduction potentials, we can calculate our E standard for the equation given seeing whether it's spontaneous for the M plus form to be converted to the M three plus form. And we can use the equation. Delta G standard equals negative N fe standard to relate our calculated E standard two delta G standard for a little background of the problem. Let's think about the fact that both gallium and thallium are group three A elements, they have three valence electrons, two S electrons and one P. So we're thinking about whether it's more favorable for them just to lose the one P electron and be a one plus ion or lose all three and B plus three. So let's start with our reaction. We're going to start with TL plus and look at the two half reactions there. So we have TL plus being converted to the TL three plus form. So that would be TL plus aqueous, it has to lose two electrons to become TL three plus. So it's going to go to TL three plus aqueous less to electrons. Then we know that RT L plus will also be converted to just elemental thallium. Then it has to go from a TL with a single positive charge to neutral elemental thallium. So it's going to pick up an electron. So plus an electron goes to tl in the solid form. Well, to add our two equations together, to get our original equation, we'll need to multiply our second equation by two to balance out our number of electrons. So each of our items in that second reaction will get a two coefficient. Now, let's look at our standard potentials for our first reaction. One thing we have to be careful about, we have TL plus as a reactant. Tl three plus is our product. But our standard potential is given to us for the opposite reaction with TL three plus as a reactant. So what does that mean? We need to switch the sign of the E standard? So instead of plus 1.25 our E standard will be negative 1.25 volts. The second equation is written in the same direction as the one we're given with TL plus being converted to TL. So we can use the same sign as we're given a standard is negative 0.34 volts note that although we multiplied the equation by two, we don't need to multiply our E standard. It's an intrinsic property does not matter, depend on how much of our reactants or products we have just like temperature. So we'll look at our final equation, we cancel out the electrons. And we see that we have the equation given to us at the beginning of the problem three TF plus aqueous, going to TL three plus aqueous plus two TL solid. Then we add together our E standards. And for that overall reaction, our calculated E standard is going to be negative 1.59 volts. So we have our first answer here negative 1.59 volts for a calculated E standard for TL plus. So we let's go ahead and look at our answer choices to see if we can rule anything out with that first value we've calculated and choice A for TL plus E standard is negative 1.59. So that's correct. In choice B it's also negative 1.59. But in choice C that E standard is positive 2.59. So choice C cannot be our answer. It's the wrong value of E standard. Choice D has E standard for TL plus as positive 2.99 also incorrect. So we just crossed that out. So we've already ruled out two of our answer choices. Well, now let's use the same process to calculate the standard for our gallium. So I went ahead and filled out both reactions and how they get added together and cancel each other out because it's exactly the same as the format for TL plus. So again, we have that final reaction of three G A plus aqueous, going to G A three plus aqueous plus two G A solid. And when we look at our standard potentials for our first reaction of G A plus to J A three plus, once again, we need to reverse the sign since it's written in the opposite direction of what we're given. So our E standard will be positive 0.35 volts for reaction of GA A plus going to G A, it's in the same order. So we can use the same sign E standard is negative 0.20 volts note there are opposite signs, but we add them together to get our final value of positive 0.15 volts. That's again one of our answers. So let's highlight that and we can look at our answer choices to see if we can rule out anything further. For choice, A for G A plus E standard is listed as negative 0.15 correct number, wrong sign. So cross that out and we can eliminate choice A. So by process of elimination, we've gotten to choice B, it has the correct value of E standard for G A plus as well as TL plus. If I were on a test, I don't have to go any further. And it's important to note that often when we have these really long problems with lots of steps, always check your multiple choice options because you may not have to do the whole darn thing, you may be able to eliminate three out of four choices early on in the process like we could hear. So let's scroll down. We're gonna go ahead and calculate are delta G standard. We have to scroll down because we've run out of room. We can still see our E standard values. And we're going to use our equation that relates these two things. Delta G standard equals negative N fe standard where N is the number of moles of electrons transferred and F is the ferity constant. We need to remember that we want our final answer to be in Kaos. We're going to have to going to have to do some conversion here because our E standard is in volts. So we'll start with TL plus. So we would say that delta G standard equals, well, we'll start with negative N, we have two moles of electrons get that that get transferred in our reaction. So negative two moles of electrons and then we'll multiply by f the Faraday constant. We're going to round that just a little bit and use the value 20 96,000, excuse me, 96,500 cool arms per moles of electron. Then we will multiply that by re standard value which for TL plus was negative 1.59 volts. But we have these pesky coulombs and volts in here. We want to end up with kilojoules. So we're going to use a conversion factor that says that one jewel is equivalent to one Kam vault. So we have jules in the numerator and Kulon volts in the denominator of our conversion factor. And the last step we're going to need to go to kilojoules. So I'll make another conversion factor saying that one kilojoule on the numerator is equivalent to 1000 jewels in a denominator. So we have a whole long equation here. Let's look at how our units will cancel, moles of electron are going to cancel Coombs will cancel, vaults will cancel out jewels will cancel out. And last unit standing is Koules, which is indeed what we want to end up with. And we get our final answer here of delta G standard four TL plus is positive 307 kilojoules. That's another value we're looking for in our answer. So we're going to highlight that. Last of all we need to say, is this reaction spontaneous or non spontaneous? Why positive delta G means that the reaction is non spontaneous. It needs an input of energy from outside to take place. So there's our final answer. And how does that explain our phenomenon? Well, if the reaction changing TL plus to TL three plus is non spontaneous, it's not going to happen on its own, then TL plus will be the favored form or the more stable form. So we'll write more stable over by TL plus and we can double check on our answer. Choice B plus 3 +07 kilojoules, non spontaneous. Last step four G A plus. What is our delta G standard? Once again, we have negative two moles of electrons Faraday constant. Of course, is the same 96,500 coulombs over moles of electrons multiplied by our E standard, which in this case is positive 0.15 volts multiplied by that conversion factor one jewel over one Coulon bolt multiplied by the conversion factor of one kilojoule over 1000 jules. Once again, all of our units cancel out except for killer Jews. And we have our final answer here that our delta G standard will be negative 28 0.9 kilojoules. Delta G is negative less than zero, which means that this reaction is spontaneous energy will be released. And since the conversion of G A plus to G A three plus is spontaneous J three plus will be less stable. So that does indeed explain our phenomenon. And we have our correct answer as choice B for T I plus G standard is negative 1.59 volts. Delta G standard is positive 307 kilojoules, non spontaneous. Wow four G A plus E standard is positive 0.15 volts. Delta G standard is negative 28.9 kilojoules. And the reaction is spontaneous. See you in the next video.