We're now going to calculate the empirical formula for a given compound. The empirical formula itself can be calculated from the masses or percentages of elements within a compound. We're going to say in this example question, it says, determine the empirical formula of a compound that is 68.40 percent chromium and 31.60% oxygen. So step 1, you're going to write down the symbols for each element in the question. We're dealing with chromium and its symbol as Cr and oxygen with its symbol as O. Now step 2, we're going to write down the masses in grams of each element given. Notice here in this question that they're not giving us masses. What they're giving us are percentages. So, we're going to convert all the percentages into grams by assuming there are 100 grams of the compound. And also, if you look at the percentages and you add them up, so 68.40 percent plus 31.60 percent, you'll see that you get a 100% of your total compound. This makes sense because if our compound is made up of chromium and only oxygen, together they should add up to the complete compound. So we're going to convert 68.40% to 68.40 grams of Cr, and 31.60 grams of O.

Step 3, convert all the masses into moles. Now, this requires some mole concept theory on your part. So remember, this is just a simple conversion. So we have 68.40 grams of Cr, we want to get rid of grams of Cr, so we put grams of Cr on the bottom, We put moles on top. We're gonna say 1 mole of Cr. If you look at your periodic table, you'll see that 1 mole of Cr weighs 51.996 grams. So grams here will cancel out, And here's the thing, we're gonna say, to avoid rounding errors, make sure the values have at least 4 decimal places. So plugging this into our calculator, we get 1.3155 moles of Cr. So again, to avoid rounding errors, it's best to have at least 4 decimal places. We converted grams of chromium into moles. Now let's do the same with grams of oxygen. 31.60 grams of oxygen. We want to get rid of grams of oxygen, so place it on the bottom. We want to convert it into moles of oxygen, so put 1 mole of oxygen on top. Look at the periodic table. The mass of oxygen on the periodic table is 16. So here grams of oxygen cancel out, and when we do that we're going to get 1.9750 moles of oxygen.

Next, this is important, step 4, you're going to divide each mole answer by the smallest mole value in order to obtain whole numbers for each element. So here we have 1.3155 moles of Cr and 1.9750 moles of O. The smaller number is 1.3155, so both will get divided by that number. When we do that, we're gonna get 1 chromium, and when we do that here, we're gonna get 1.5 oxygens. Okay. So we've run into an issue here. Step 5, after dividing by the smallest number, if you get a value that is 0.1, some number 0.1, and some number 0.9, then you can round to the nearest whole number. Unfortunately, we got 0.5 here. We can't just simply round that. So what do we do instead? Well, in these situations, if you can't round, we multiply by a factor to create whole numbers. So think to yourself, 1.5, what number can I multiply that by to get a whole number? If we start out by multiplying by 2, that's gonna give me 3. 3 is a whole number, so we'd have 3 oxygens. But here's the thing, if I multiply the number of oxygens by 2, then I have to multiply the number of chromiums also by 2. So the empirical formula contains 2 chromium atoms and 3 oxygen atoms. So that would mean that the empirical formula here is Cr2O3. So this would be my empirical formula for this question. These are the steps you have to employ to get the empirical formula when given information on the percentages or mass of different elements within.