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Write structural formulas and give the IUPAC names for the nine alkanes that have the molecular formula C_{7}H_{16} .

Hey guys, so this problem is our job to draw a name the nine isomers that have the molecular formula C7H16, okay? So there are actually nine different alkanes, right? So let's draw the nine alkanes that represent this molecular formula, so notice that we can start out by having a regular heptane, so it would look something like this, we have 1, 2, 3, 4, 5, 6, 7 and this is just heptane, so that you just want to do is to keep going down, we can have heptane then go to hexane pentane and butane, okay? So this is our heptane. Now, the next one we're going to do hexane one hexane derivative, so let's say we have 1, 2, 3, 4, 5, 6 carbons now and we need to add in a methyl group, so where are we going to add that methyl group? Well, it's not going to be the ends, right? because that would make heptane, but we could add it right here and that would now be 2 methyl hexane, where else could we add it? Well, let's just copy this compound paste it in? Well, would you agree that, that would be equivalent to adding it right here, right? And let's erase this, it would also be 2 methyl hexane, so that one way to add it would just be to one of these two spots in the middle and we have to add it the only one that gets it would be equivalent as well, so let's just say, we added it now here, this will now give us a 3 methyl hexane, okay? So now let's move on to our pentanes, so now it's going to be a 5 carbon chain, so we have 1, 2, 3, 4 and 5, let's draw it a little bit better, these are going to be now our pentanes, but now we have to add on two carbons, so we can do this different ways, right? We can either add them on to say in the same position right here and now what would this be? this would be 2, 2-dimethyl, right? Because we have two methyl groups and then pentane but now let's say we try to draw another one because there's definitely going to be more derivatives for this one. Now, let's see what we get. Well, would you agree that this would be equivalent to adding our 2 methyl groups right here and erase these? yep, so the only place now to add these two methyl on the same carbon would be right here, right? Now, this would give us 3,3-dimethyl pentane, okay? But we can also add those two carbons separated, so what I mean by that is say now we paste it in that structure again, we need a little bigger, we're going to paste in another one, make it a little bit bigger, how we're going to add these two carbons? Well, we can add them coming off of here and here, right? Well, we could also add them coming off of here and here, right? So what would be the name of these two? Well, the first one would be kind of like this 2, 3, 4 2, 3 this would be a 2,4-dimethyl pentane, right? The next one would be a 2,3-dimethyl pentane as well and now what are we missing? we have 1, 2, 3, 4, 5, 6, 7, we're missing two more, okay? So, let me just jump out of the page and we're going to draw in those last two, right? Because we know we need to have nine in total. So, for the next one what we're going to do is we can actually have an ethyl ethyl substituent, what I mean by that is again we have five carbons and now we're going to add an ethyl group, so we're going to add an ethyl group off this chain right here, okay? So, now we have seven carbons again, the name we would name this is this would be our position three, this would be 3, not methyl anyone, right? 3-ethyl, so this two carbons still pentane, okay? Now, there's actually one more that we can draw. Now, that last one would be an isomer that has 3 methyl substituents and a 4 carbon chain, so there's going to be our four carbon chain 2, 3, 4 and what we can do is we can add a methyl here, a methyl there and one methyl coming up right here. Now, what do you think the name would be for this one? what's going to be butane, right? So let's write at the end butane, the only substituents we're adding on our methyl groups and there's three of them, so we can expect it to be trimethyl and now we need to indicate the positions by numbers of where our constituents are, so it's going to be 2, 2, right? because this is the position 2 and 3, 3, that's tri methyl butane, okay? So I'm going to jump back into the image now. Alright guys, so these are the nine different isomers that correspond to the molecular formula C7H16. Alright, so I hope that makes sense, the best way to do this was by doing it systematically, what I mean by that is we did heptane first, we then moved on to our hexanes, what we did next is we did our pentanes, right? Then we had quite a few of those, actually the one behind me right here and then the last one that we did if I move out a little bit more you'll see it our butane one, okay? So I hope this made sense, let me know if you guys have any questions.