Niobium oxide crystallizes in the following cubic unit cell:

What is the formula of niobium oxide, and what is the oxidation state of niobium? (LO 12.5) (a) NbO, Nb = +2 (b) Nb2O, Nb = +2 (c) NbO2, Nb = +4 (d) Nb2O3, Nb = +3

Video transcript

Hey everyone, we're told that an iron oxide follows the crystal lattice shown below, determine the formula for the iron oxide and the oxidation state of iron first. We need to recognize that we have a face centered cubic. Now let's go ahead and determine our value for our iron. Looking at our crystal city so we can see that we have one internal for our iron And we have 12 edges And this is going to be 1/4 of an atom. So when we determine our value for iron, We're going to take that one internal and we're going at 12 times 1/4. This will get us to a value of four of iron. Now let's go ahead and determine our value for oxygen. Looking at our oxygen, we can see that we have and six, we have six face And this is going to be 1/2 of an atom. We also have eight corners And this is going to be 1/8 of an atom. Now let's go ahead and determine our value for oxygen. So we're going to take that six and we're going to multiply it by one half next we're going to add eight times 18. And when we calculate this out, we get four of oxygen. So it looks like our formula is going to come up to f. E. 404 for our iron oxide. And since we can simplify this, it's going to become F. E. O. And to determine our oxidation state, we know that oxygen has an oxidation state of -2. And since this is at its neutral state, this will be equal to zero. And if we label iron as X, we get X plus negative two equals zero, solving for X, we get X equals positive two. So our oxidation state for iron is going to be plus two, and our formula for iron oxide is going to be f E. O. Now I hope that made sense and let us know if you have any questions.