In the preparation of iron from hematite, Fe2O3 reacts with carbon: Fe2O3 + C --> Fe + CO2 Unbalanced (a) Balance the equation. (b) How many moles of carbon are needed to react with 525 g of hematite? (c) How many grams of carbon are needed to react with 525 g of hematite?

Video transcript

Hey everyone, we're told that pure aluminum can be extracted from the reaction of alumina with carbon. And were provided. The chemical equation were asked to balance it out and to calculate the mass of carbon needed to react with 500 g of alumina first. Let's go ahead and balance this out. We have our alumina and this reacts with carbon and we produce aluminum plus carbon dioxide. So let's go ahead and calculate the number of atoms we have of each element on each side, starting with our aluminum. In our reacting side we have two of aluminum. Again in our react inside we have three of oxygen and one of carbon. Now looking at our product side, we have one of aluminum, two of oxygen and one of carbon first. Let's go ahead and balance out our oxygen's We can change the value of our oxygen's into six by adding a coefficient of three prior to our carbon dioxide in our product side. So this will give us six of oxygen. But this will also change the value of carbons and now we have three of carbon in our react inside. We can change our values of oxygen into six by adding a coefficient of two prior to our alumina. This will get us six oxygen's but this will also get us four of aluminum. Now to balance out our aluminum in our product side, we can go ahead and add a coalition of four prior to aluminum and lastly to balance out the carbon in our react inside, we can add a coefficient of three prior to our carbon. And now our chemical equation is completely balanced out. So let's go ahead and calculate the mass of carbon needed to react with 500 g of alumina. We can do so by using our dimensional analysis and using Illumina's molar mass. We know that we have 101.96 g of alumina Per one Mole of Alumina. Next looking at our multiple ratios, we can look at the coefficients in our balanced chemical equation and we see that per two mol of alumina, We have three mole of carbon. And lastly using carbons molar mass, which we can find in our periodic table. We know that one mole of carbon will have 12.0107 g of carbon. And now when we calculate this out and cancel out all of our units, we end up with a mass of carbon of 88.3 g of carbon, which is going to be our final answer. Now, I hope this made sense. And let us know if you have any questions