A metal forms the salt MCl 3 . Electrolysis of the molten salt with a current of 0.700 A for 6.63 h produced 3.00 g of the metal. What is the molar mass of the metal?

Here it states, A metal forms the salt Mcl3. Electrolysis of the molten salt with a current of 0.700 amperes for 6.63 hours produced 3 grams of the metal. What is the molar mass of the metal? All right. Let's unpackage everything that's being said here. First of all, we're being asked to figure out what our molar mass of the metal will be. Remember, molar mass is in units of grams per mole. Technically, we already know what half of our molar mass or at least half of the information needed to get our molar mass. We know what grams we have. That goes on top. All we really have to determine now is how many moles of the metal m do we possess in order to totally figure out what our molar mass will be. From there, we can then identify it from the periodic table. Now when we talk about electrolysis, electrolysis is just breaking apart an ionic compound through the use of electricity. We're using a current of 0.700 amperes to break up an ionic compound into its elements. Here, we have our metal and remember, metals form cations by losing their electrons. Non metals become anions by gaining electrons. That's the natural process, right? Here, to become a cation, you have to undergo oxidation and to become an anion, you have to gain electrons so that's reduction. But here's the thing, electrolysis is for a non spontaneous process. We have to supply outside energy for it to occur. The outside energy is the current here. What's happening is instead of the metal undergoing oxidation, the metal undergo reduction. And the non metal, instead of undergoing reduction, is going to undergo oxidation. The opposite is happening because electrolysis is a non spontaneous process. It's doing what is the opposite of what we normally would expect to happen. Here for reduction, we have our metal being reduced. Here, this 3 came from the metal itself. The metal has its ion form is 3 plus. It's going to gain 3 electrons to become neutral metal. Okay. And then here, the nonmetal chlorine which normally would undergo reduction is going under oxidation. Here, we'd have our chloride ion as a liquid. Here, its oxidation number is negative one. But now it's gonna become 0. It's gonna become more positive because it gets changed into its natural form. And in this process, we have 2 electrons involved. So these represent the 2 half reactions in this process. Now the number of electrons are not the same. They have to be the same. So we would multiply this here by 2 so that we have 6 electrons, and multiply this by 3 so that we have 6 electrons. So that gives us a new set of equations. So that's 2m3+aqueous, plus 6 electrons, gives me 2 m solid. And then 3 and then 6 or actually Yeah. 6cl minus liquid gives us 3cl2gas plus 6 electrons. So my overall equation here, when we combine everything together would give me 2 mcl3, gives me 2 m solid plus 3 cl2gas. This here represents electrolysis where our ionic compound is broken through the use of a current which is 0.700 amperes in order to form its elemental states. That's the whole process that we're talking about here. Now, from this information, what we can say is we need to determine what the molar mass is. We need to determine our moles so that we can plug it into here. We're gonna say we're gonna start with 6.63 hours. We're gonna change those hours into seconds. Remember, why are we doing this? Because amps, which is another, unit for current, is in units of coulombs per second. And because seconds are present, that means I need to deal with time in terms of seconds. We're going to sit here for every 1 hour, we have 36 100 seconds. And with those seconds, I can now bring in the current. So we have 0.700 coulombs per one second. Now that I have coulombs, I can bring in Faraday's constant. So we have 9.647 times 104 coulombs for every 1 mole of electrons. And now this part here is important because we're gonna figure out the number of moles of electrons involved and the moles of my metal m involved. Alright. So we can look at it 2 different ways. We can either use these original equations or we can use these new equations after we've determined the number of electrons as being the same. So you could say here for every one mole of metal m, there are 3 moles of electrons involved. Or you could say for every 2 moles of metal m, there are 6 electrons involved. Proportionally, nothing's changing. So it doesn't matter which one I use. Here, I'll just say for every, 2 moles of m, there are 6 electrons involved. So at this point, that gives me moles as 0.05 773 moles of m. Take those moles and plug them in here. Now we take 3 grams and we divide it by the moles that we just found. That's going to give me a molar mass of my metal of 51.9662 grams per mole. If you look this mass up on the periodic table, you'll see that the metal that has this mass is chromium. Our unknown metal M is chromium which would mean that MCl3 is really CrCl3. It represents chromium chloride. Those are the steps involved in determining the molar mass of the metal. Remember, when it comes to electrolysis, all we're doing is we're running a current, so some electricity in order to change an ionic compound back into its elemental forms. This is a non spontaneous process which is why outside energy in the form of the current is needed. Normally, the metal would and the metal will gain electrons to undergo reduction, but electrolysis is a non spontaneous process. The opposite is occurring which is why outside energy is needed. The metal now is undergoing reduction while the non metal is undergoing oxidation. Remember these key terms and key concepts in terms of electrolysis and then just remember the steps that we needed to take in order to find our moles of our unknown metal, m.