### Video Transcript

In the equation shown, what will the coefficient for O₂ be if the equation is balanced and all the coefficients are in their simplest integer ratio? Blank ZnS solid plus blank O₂ gas react to form blank ZnO solid plus blank SO₂ gas. A) one, B) two, C) three, D) four, or E) six.

A coefficient in a chemical equation is simply a number that indicates how many we have of something. When we have a complete equation, these numbers can show us the ratio between individual components, like one ZnS per one ZnO. An integer is simply a whole number, like one, two, or three. But a fraction like a half is not a whole number.

So when we simplify the equation, we need to make sure that all the coefficients are integers. And they’re in their simplest ratio, which means we’ve divided through by any common factors. For instance, in this example, two, four, and two can all be divided by two and still generate integers. But if we do it again, we end up with nonintegers. So we just need to stop here, one to two to one.

Now that we know where we’re going, let’s have a crack at balancing this equation. If we assume we’re starting with one of everything, we have one zinc on the left and one zinc on the right. We have one sulfur on the left and one sulfur on the right. But we have two oxygens on the left from our molecule of oxygen and three on the right, one in the zinc oxide and one in the sulfur dioxide. So our zinc and sulfur are balanced, but the oxygen is not.

The easiest way to balance this is to take a step back and look at the whole equation. Zinc is contained in one reactant and one product. If we increase either of these coefficients, we have to increase the other so that we can maintain balancing of the zinc. Sulfur is also contained in only one reactant and one product. So these two coefficients are also tied together. If we increase the amount of zinc sulfide, we need to increase the amount of sulfur dioxide to keep the sulfurs balanced. But zinc sulfide is part of both of these pairs. So all three of these coefficients are actually tied together. If we increase one, we have to increase the others.

We get three oxygens on the right and two on the left. The lowest common multiple of these two numbers is six. So if we double up the zinc sulfide, the zinc oxide, and the sulfur dioxide, we’re still balanced in zinc and sulfur. But we have six oxygens on the right. And if we triple up the amount of oxygen, we’ll have six oxygens on the left to balance out the six on the right. And we’re balanced in oxygen, sulfur, and zinc.

The final ratio we get, two to three to two to two, is the simplest integer ratio. Two and three don’t share any common factors besides one. So this is our final answer. All we need to do is isolate the coefficient for oxygen, O₂, which is three.