In this example question, it asks how many moles of hydrogen gas were produced when 38.74 milliliters of 0.275 molar water react with excess sodium. Alright. So we know that this is a balanced chemical equation. They're providing information on one compound and asking for information on another. This is the definition of stoichiometry. The chemical equation gives us information on at least one compound, and we use stoichiometry to find the other. Now here, we're going to follow the steps to deal with this stoichiometric question.

For step 1, it says to convert the given quantity into moles of the given compound. If a compound is said to be in excess, then just ignore it. So here, they're telling us that sodium is in excess, so sodium doesn't matter here. Now, up above, I said that moles equals liters times molarity. So we have to convert our milliliters here into liters. So we have 38.74 milliliters, and we're going to say here for every 1 milliliter it's \(10^{-3}\) liters. Now that we have liters, the next thing we can say is that molarity, remember, represents a conversion factor. So that 0.275 molar of water really means we have 0.275 moles of water per 1 liter of solution. So at this point, we've just isolated our moles of given.

Now step 2 says we're going to do a mole-to-mole comparison to convert the given into moles of the unknown. So at this point, remember when we do a mole-to-mole comparison, we look at the coefficients in the balanced equation. It's 2 moles of water for every 1 mole of \(H_2\), which is what we're looking for. So then, moles of water down here, moles of \(H_2\) here. At this point, we're done because they're only asking us to find the moles of hydrogen gas. But let's just look at the other steps. If necessary, convert the moles of unknown into the final desired mole units. So here they only wanted moles of \(H_2\) we can stop, but if they wanted us to go to grams, we'd have to go a little bit further. If they wanted us to find molecules, we'd go a little bit further.

Now step 4, if you calculate more than one final amount, then you must compare them to determine the theoretical yield. The smaller amount will equal your limiting reagent, so the reactant that makes less product will be the limiting reagent. The one that says it can make more product will be the excess reagent. In this question, we don't have to worry about step 3 because we only needed moles, and we don't have to worry about step 4 because only one compound had a given amount. So all we're going to do here is we're going to plug this into our calculator and when we do, we get \(5.33 \times 10^{-3}\) moles of \(H_2\) as our final product for this stoichiometric solution type.