### Limiting Reagents and Theoretical Yield

So far, we have assumed that reactants are present in the proper ratios; for example, in the equation below, we assume that we have one mole of hydrogen and half a mole of oxygen.

H2 (g) + 1/2 O2 (g) --> H2O (g)

However, this ideal situation is very rare in real chemistry--you will almost never see reagents present in their stoichiometric ratios in "real-world" applications. Instead, one reactant is often present in a less-than-ideal amount. Consider the water-formation reaction that we have discussed so often. When you burn a balloon of hydrogen in a room, there is obviously more oxygen present than hydrogen; the only hydrogen available for combustion is the amount in the balloon, whereas all the oxygen in the room is available to react. When the reaction goes, it will progress until all the hydrogen is combusted; oxygen will remain after the reaction. Therefore, we say that hydrogen is the limiting reagent, since it is the amount of hydrogen that determines (or limits) how far the reaction can go. The oxygen is said to be in excess, since there is more oxygen present than necessary. In other words, a given amount of hydrogen was reacted with excess oxygen.

Once you determine the limiting reagent of a reaction, assume all of this reactant is consumed. Thus, you can predict the amounts of reactants consumed and products generated by the reaction. Returning to the example reaction, let's say you have a 5-liter balloon of hydrogen (which has a density of about 24.4 liters per mole at room temperature) that you ignite, using proper safety equipment. Let's assume your room has volume of 200 liters (about 5 meters by 3 meters by 13 meters), of which 20% by volume is oxygen. BOOM! Once the explosion is complete, how many moles of water were made? Using simple division, you have (5 l) / (24.4 l/mol) = 0.205 moles of hydrogen. Since oxygen gas also has a molar density of 24.4 moles per liter at room temperature, we find that you have about (200 l) * (20% O2) / (24.4 l/mol) = 1.64 moles of oxygen.

When combustion occurs, all 0.205 moles of hydrogen are consumed, along with half that amount of oxygen (about 0.1025 moles). Therefore, 0 moles of hydrogen and about 1.54 moles of oxygen remain after the reaction, with 0.205 moles of water vapor being generated.

Previously, we have made a second assumption: that all reactions proceed to 100% completion. However, some reactions do not go as far as expected; that is, the amounts of reactants consumed and products generated are different from those predicted. This may occur because the reaction naturally does not proceed to completion, or because of peculiar circumstances, such as abnormal pressures, temperatures, or contamination of the sample. In chemistry, the amount of any given product that would be expected at the conclusion of a reaction is called the theoretical yield. The amount of product actually produced is called the actual yield, and may be expressed in moles or as a percentage of the theoretical yield.

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