Reactions and Reactivity: Chemical Calculations and Yields

Chemical Calculations

The coefficients in a balanced equation represent the number of molecules or atoms that are reacting and are produced. For example, in the formation of water, 2 molecules of hydrogen gas react with 1 molecule of oxygen producing 2 molecules of water. If 4 molecules of hydrogen gas are present, then 2 molecules of oxygen gas will be needed to produce 4 molecules of water.

2H2(g) + O2(g) → 2H2O(l)

But what if there are 400 molecules of hydrogen gas? How much oxygen gas would be required to use up all the hydrogen gas?

It can be seen that the ratio of hydrogen molecules to oxygen molecules required is always 2:1. But in the laboratory, when a measurable amount of reactants are necessary, it is advantageous to use moles to count the molecules. So 2 moles of H2 (representing 1.20 × 1024 molecules) would react with 1 mole of O2 (representing 6.02 ×1023 molecules) and produce 2 moles of H2O (representing 1.20 × 1024 molecules).

In other words, all coefficients in a balanced equation represent the number of moles of substances as well as the number of molecules, and can give a ratio between the compounds and elements in a reaction. In the case of the reaction of sodium with chlorine to produce sodium chloride:

2Na(s) + Cl2 (g) → 2NaCl(s)

The ratio of moles of Na to moles of Cl2 is 2:1, but the ratio of moles of Na to moles of NaCl is 2:2, and the ratio of moles of Cl2 to moles of NaCl is 1:2. These mole ratios can be developed for any balanced equation and can be used to determine how much product is made from a given amount of starting material.

Sample Problem

How many moles of Cl2 would be required if 5.0 mol of Na was completely reacted?

The mole ratio of Na:Cl2 is 2:1, so we multiply the 5.0 reacted moles of Na by the mole ratio:

Please note that the mole ratios used have an infinite number of significant figures and the number of significant figures in the answer will be determined by the number in the starting figure.

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