Worked example: writing empirical formulas for ionic compounds

0:00- [Instructor] Let's try to figure out the empirical formula for some more complex ionic compounds. Let's say we're thinking about iron oxide, and this is actually a picture of iron oxide. This isn't just any iron oxide, this is iron III oxide. We know that this is going to be an ionic compound because it's formed between a metal, iron, and a non-metal, oxygen.

0:22Now, when we're talking about ionic compounds formed with what's often known as transition metals, and these are these metals right over here, and you can see that iron is right over there, different numbers of electrons can be taken from them. This is sometimes referred to as their oxidation state.

0:43So when you have these Roman numerals right over here, that essentially tells you how many electrons have been taken away from it. Another way to think about it, you can think about this is its charge. If three electrons are taken from a neutral iron, then it's going to have a positive three charge.

1:02Now, this tells us this is an oxide, so it's an ionic compound that is formed with an ion version of oxygen. Now, if we look at oxygen, let me do this in another color, if we look at oxygen right over here, it has eight total electrons, but in that second shell it has six electrons, six valence electrons.

1:22It wants to get to eight, so typically oxygen will take two electrons from someone else. So when we're dealing with oxides, we're typically dealing with taking two electrons from someone else or having a negative two charge. Now, we know that these two things need to combine in some way so that the entire compound, the entire ionic compound, has a neutral charge.

1:47So how could that happen? Well, think about it this way. If you had two irons and three oxygens, then the charges cancel out. Let me write that down. So if we had two irons and we had three oxygens, then the total charge on the irons is going to be two times three, positive three, which is positive six, and the total charge of the oxygens is going to be three times negative two, which is negative six.

2:16So positive six, negative six, they end up being neutral, to zero. Now, you might say, Sal, how did you figure that out? Well, I encourage you to say, there's an intuition there, but there's also something known as the crossover technique, which is really just saying, okay, if you have this type of situation where you know that iron III is going to have a positive three charge, and oxygen typically is going to have a negative two charge, or two minus charge, well then you can swap the charges for how many of the other one you have.

2:44So oxygen has a negative two charge, so then you're gonna have two irons. And iron has a positive three or three plus charge, so you're going to have three oxygens. So that's often called the crossover trick, but I want you to get the intuition for why that works.

2:59Just one iron and one oxygen isn't going to cancel out. So if you have two irons, then that's a positive six charge, so you need three oxygens to counteract that, to get to a neutral iron III oxide. Let's do another example. Let's say that we're looking at calcium oxide.

3:19So once again, what type of ion is calcium likely to form? Well, we see calcium right over here, and all of the elements in this second column, it's easiest for them to get to a full outer shell by losing two electrons, so calcium will typically have, by losing two electrons, the calcium ion will have a two plus charge.

3:42And then we've already talked about oxides will typically have a two minus charge. Now, if you just blindly did this crossover technique, you'd say, all right, two minus charge for the oxygen, so I would put two calciums there. And then two plus charge for the calcium, so I would put two oxygens there.

4:06You'd say, well maybe this is the empirical formula, but you want to make the empirical formula as simple as possible, and you notice that both of these twos are divisible by two, so you can, in some ways the way you learned to reduce fractions in middle school, you could reduce this here and say, all right, well if I divide both of these by two, I get to a calcium oxide like this, which is the true empirical formula for calcium oxide.

4:36Now, my brain tends to not like to do the crossover trick because it's a trick and you're not really thinking about what's going on. What I like to say, is well, look, calcium, oxide, two plus, two minus, they will just automatically cancel out each other, so I would go straight to the calcium oxide.

4:52Now, the last thing I'll emphasize is things that are in the same column in the periodic table oftentimes can be swapped out in these ionic compounds. For example, calcium oxide exists, but calcium sulfide is also another ionic compound, and sulfur, because it's in the same column of the periodic table, it also tends to form a negative ion with a two minus charge.

5:20So the empirical formula for calcium sulfide, very similar to that for calcium oxide. It is just going to be Ca, let me do that in a lighter color. It is just going to be calcium, for every one calcium, you have one sulfur. Positive two charge, or a two plus charge, and a two minus charge right over here.

5:41Likewise, you have sodium chloride, sodium chloride. We can also have sodium fluoride, or you could also have lithium fluoride or lithium chloride, and you can go on and on and on.