# Video: Comparing the Atom Economies of Reactions

Which of the following reactions has the greatest atom economy for the production of hydrogen? [A] 2Al + 2NaOH + 6H₂O ⟶ 2Na[Al(OH)₄] + 3H₂ [B] Zn + 2HCl ⟶ ZnCl₂ + H₂ [C] CO + H₂O ⟶ CO₂ + H₂ [D] CH₄ + H₂O⟶ CO + 3H₂ [E] C₆H₁₀O₅ + 7H₂O⟶ 12H₂ + 6CO₂

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### Video Transcript

Which of the following reactions has the greatest atom economy for the production of hydrogen? 2Al + 2NaOH + 6H₂O react to form 2Na[Al(OH)₄] + 3H₂. Zn + 2HCl react to form ZnCl₂ + H₂. CO + H₂O react to form CO₂ + H₂. CH₄ + H₂O react to form CO + 3H₂. Or C₆H₁₀O₅ + 7H₂O react to form 12H₂ + 6CO₂.

This question is asking us about atom economy. So let’s review what we mean by atom economy. The atom economy of a reaction is a measure of the amount of reactants which go on to end up as useful products at the end. You could think of this a bit like a measure of a reaction’s efficiency. In our question, we’re aiming to produce hydrogen. So that’s the useful product that we’re going to focus on. It might be tempting to look through all of our reactions and pick the bottom one since that has 12H₂ molecules produced. However, it’s not just about which reaction produces the most hydrogen. We’re looking for the reaction which produces the most hydrogen in the most efficient way using the reactants.

We can calculate the atom economy by taking the total molecular mass of the desired product, in our case hydrogen, and dividing it by the total molecular mass for all the reactants. And then timesing by 100 to give us a percentage. This tells us what percentage of our starting materials actually go on to end up being useful. You can think of this a little bit like looking at how much waste we produce in everyday life.

Let’s imagine that we buy a piece of cake. When we go to buy our piece of cake, we have two options. One piece of cake is presented purely on a small paper plate. The other identical piece of cake is in a huge box with lots of Ribbons and decorations. Ultimately, when we get them home, each set of packaging contains exactly the same piece of cake. However, we also have the packaging to get rid of. The cake is our desired product. And the packaging is our waste.

In the first instance, we simply have a small paper plate to get rid of. In the second instance, we have lots of material to get rid of, lots of waste. So which one of these is more efficient? It’s clear that the top reaction here produces the least waste. So this would have the highest atom economy. If we were to weigh the piece of cake on its small paper plate, the majority of that weight would then go on to simply be the cake in our products. So we need to do something similar here with our reactions. In order to work out the molecular mass of both our desired product and all our reactants, we’re going to need our periodic table.

From our periodic table, we’re going to take the atomic masses of each of the atoms in our reactants and add them all together. So let’s do this for the first example. Let’s start with the aluminum. On our periodic table, we can see that the atomic mass for aluminum is 26.982. In our reaction, we have two aluminum atoms. So we multiply this by two. Now, let’s look at the NaOH. Again, from our periodic table, we can see that the atomic mass of sodium is 22.990. The atomic mass of oxygen is 15.999. And the mass of hydrogen is 1.008. We add all these up and multiply by two for the total. Finally, we come to water. Here, we have six water molecules. So we do six lots of two masses of hydrogen and one mass of oxygen.

Once we’ve calculated all of these reactants, we can add them all together to get the total mass of our reactants. For the first reaction, this comes to 242.048. Now, to work out the atom economy for this reaction, we need the total mass of our desired product which is hydrogen. And we have three hydrogen molecules. We work this out by adding two masses of a hydrogen atom, two times 1.008, and multiplying by three since we have three molecules. This has a mass of 6.048. Substituting these values for masses into our atom economy equation, we get 6.048 divided by 242.048, all multiplied by 100. This gives us 2.499 percent.

Now, we need to repeat this for the second reaction. The atomic mass of zinc is 65.38. And the mass of two HCl molecules is two lots of a hydrogen plus a chlorine, which gives us 72.916. By adding these masses together, we get a total mass for the reactants of 138.296. In this reaction, we produce one molecule of hydrogen, which is two times 1.008. Now, we can put these values into our atom economy equation. So the atom economy equals 2.016 divided by 138.296 times 100 percent, which gives us an atom economy of 1.458 percent.

Now, on to the third reaction, we can work out the reactant masses in the same way as the two reactions before. And we get a total of 46.025. We calculate the mass of one hydrogen molecule and divide that by the total mass of our reactants multiplied by 100 percent, which gives us an atom economy of 4.380 percent. Now let’s look at the fourth reaction. When we add the masses of all the reactants, we get a total of 34.058. In this reaction, we produce three hydrogen molecules, which is a total of six hydrogen atoms. So the mass of our desired product is 6.048. Divide that by the total of the masses of reactants, 34.058, and multiply it by 100. This gives us an atom economy of 17.758 percent.

And now on to the final reaction. By adding up all our reactants in this last reaction, we get a total mass of 288.246. For this atom economy, we need the mass of 12 hydrogen molecules divided by the total mass of the reactants multiplied by 100, which gives us an answer of 8.393 percent. So, going back to our question, we’re looking for the reaction which has the greatest atom economy for the hydrogen production. From the values we’ve just worked out, we can see that it’s the fourth reaction which has the greatest atom economy, with an atom economy of 17.758 percent. Notice that this is not the reaction which produces the most molecules of hydrogen. So our answer is option four, CH₄ + H₂O ⟶ CO +3H₂.