In an industrial reaction, iron oxide reacts with carbon to make iron and carbon monoxide. Fe3O4 plus four C react to produce three Fe plus four CO, where the molar mass of iron is 56 grams per mole and oxygen is 16 grams per mole. Calculate, to the nearest whole number, the percentage yield if two kilograms of Fe3O4 produces 800 grams of iron.
The percentage yield is calculated by dividing the actual yield by the theoretical yield and multiplying by 100 percent. The actual yield is the amount of product that is obtained from carrying out a chemical reaction. And the theoretical yield is the maximum amount of product that can be formed from the given amounts of reactants. The question tells us that 800 grams of iron is produced in this reaction. This is the actual yield. The question also tells us that two kilograms of Fe3O4, or iron oxide, produces this iron. This is not the theoretical yield, but we can use this value to work out what the theoretical yield is.
Our first step in calculating the theoretical yield is to calculate the number of moles of starting material, which is the iron oxide. To do this, we can use the equation 𝑛 equals lowercase 𝑚 divided by uppercase 𝑀, where 𝑛 is the number of moles, lowercase 𝑚 is the mass in grams, and uppercase 𝑀 is the molar mass in grams per mole, where the molar mass is the average mass in grams per mole of species.
We know that the mass of iron oxide is two kilograms, but we need to know what this is in grams. Kilo means 1000, so one kilogram equals 1000 grams. We want to know how many grams there are in two kilograms. To go from one kilogram to two kilograms, we need to multiply by two. So, we also need to multiply 1000 grams by two. This gives a value of 2000 grams. Now that we know what the mass is in grams, we need to calculate the molar mass of iron oxide.
We have been given the molar masses for iron and oxygen individually in the question. But we need to work out the molar mass for iron oxide. The molar mass of iron is 56 grams per mole, and we have three equivalents of iron. So, we need to multiply 56 grams per mole by three. The molar mass of oxygen is 16 grams per mole, and there are four equivalents of oxygen in iron oxide. So, we need to multiply 16 grams per mole by four. If we add these together, we get 232 grams per mole. So, the molar mass of iron oxide is 232 grams per mole. If we divide 2000 grams by 232 grams per mole, we get 8.62 moles. We have now calculated the number of moles of starting material.
The next step is to calculate the maximum number of moles of product, which is iron, that could’ve been produced from the moles of starting material, which we’ve already calculated to be 8.62 moles of iron oxide. The equation tells us that one mole of iron oxide will produce three moles of iron. So, the molar ratio between iron oxide and iron is one to three. And to convert between the number of moles of iron oxide and iron, you need to multiply by three. If we multiply the 8.62 moles of iron oxide by three, then we get 25.86 moles. So, hypothetically, we should be able to get 25.86 moles of iron product. So now we’ve calculated the maximum number of moles of product that could’ve been produced from the 8.62 moles of iron oxide.
Our next step is to convert the number of moles of product, which we’ve just calculated to be 25.86 moles, to grams. This will give the value for the theoretical yield, which we need to calculate the percentage yield. To convert the number of moles of product to grams, again, we can use the equation 𝑛 equals lowercase 𝑚 divided by uppercase 𝑀. As lowercase 𝑚, the mass, is in units of grams, we need to make the mass the subject. If we multiply both sides of the equation by capital 𝑀, the molar mass, then the molar mass terms on the right-hand side of the equation will cancel, leaving us with the mass equals the number of moles times the molar mass.
We’ve already calculated 𝑛, the number of moles, to be 25.86. And we’ve been given the molar mass of the product, which is iron, in the question, which is 56 grams per mole. If we perform this calculation, we get 1448.16 grams.
Now that we know the theoretical yield of the product, we can calculate the percentage yield. To calculate the percentage yield, we need to divide 800 grams by 1448.16 grams and multiply by 100 percent. This gives a value of 55.2 percent, but the question asks for the percentage yield to the nearest whole number. 55.2 to the nearest whole number is 55. So, the percentage yield if two kilograms of iron oxide produces 800 grams of iron is 55 percent.