Which of the formulas above represent substances that are isomers of one another? A) None, B) I and II only, C) I and III only, D) II and III only, or E) I, II, and III.
So what we’ve been given are three formulas. And we have to work out whether they can be grouped together at all to form a set of isomers. Isomers are groups of chemicals with the same molecular formula, but different structures. For instance, this is propan-1-ol. There are three carbon atoms per molecule. So the molecular formula starts with C3. And there are eight hydrogens per molecule and one oxygen. But we can take those three carbon atoms in the same configuration, put them together with the oxygen and the eight hydrogens, and make propan-2-ol. In propan-1-ol, the alcohol group is attached to the first carbon at the end, whereas in propan-2-ol it’s connected in the middle.
We can say that propan-1-ol and propan-2-ol are isomers of each other because they have the same molecular formula but different structures. So for this question, our first step will be to find the molecular formulas for I, II, and III. If we find two or more of them have the same molecular formula, we’ll compare the structures. If they’re different, they’re isomers.
There are two carbon atoms in the first structure, two hydrogen atoms and two bromine atoms. So the molecular formula for I is C₂H₂Br₂. Likewise, there are two carbon atoms in the second structure, but only one hydrogen and three bromines. So I and II cannot be isomers because they don’t have the same molecular formula. Lastly, structure III has two carbon atoms, just like structure I and II, and two hydrogen atoms and two bromines. Structure II does not have the same molecular formula as either I or III. So it can’t be an isomer of either of them.
Now, we can move on to comparing the structures of I and III. There’s still the possibility that they actually describe the same chemical. So we don’t know for sure that they are isomers. In structure I, we have a single bromine atom attached to the left-hand carbon and a single bromine attached to the right-hand carbon. Both carbons also have a hydrogen attached. However, in structure III, there are two bromines attached to the left-hand carbon and two hydrogens attached to the right. I and III have the same molecular formula. But they have different structures.
We can be extra sure of this because they have different names. Structure I is 1,2-dibromoethene, while structure II is the formula for 1,1-dibromoethene. If we were being even more precise, we’d say that structure I is trans-1,2-dibromoethene because the two bromine atoms are on opposite sides of the carbon carbon double bond. However, this information isn’t necessary to answer the question. Simply by inspection, we’ve seen that the connectivity of the atoms in structures I and III is very different. So they have the same molecular formula, but different structures.
So our answer for “which of the formulas above represents substances that are isomers of one another” is I and III only.