## Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

# Chemical Quantities

Mole—Mole Relationships

**Objective**

· To learn to use a balanced equation to determine relationships between moles of reactants and moles of products.

Now that we have discussed the meaning of a balanced chemical equation in terms of moles of reactants and products, we can use an equation to predict the moles of products that a given number of moles of reactants will yield. For example, consider the decomposition of water to give hydrogen and oxygen, which is represented by the following balanced equation:

This equation tells us that moles of yields moles of and mole of .

Now suppose that we have moles of water. If we decompose moles of water, how many moles of products do we get?

One way to answer this question is to multiply the entire equation by (which will give us moles of ).

Now we can state that

which answers the question of how many moles of products we get with moles of .

Next, suppose we decompose moles of water. What numbers of moles of products are formed in this process? We could answer this question by rebalancing the chemical equation as follows: First, we divide *all coefficients* of the balanced equation

by , to give

Now, because we have moles of , we multiply this equation by .

This gives

(Verify that this is a balanced equation.) Now we can state that

This procedure of rebalancing the equation to obtain the number of moles involved in a particular situation always works, but it can be cumbersome. In **Example 9.2** we will develop a more convenient procedure, which uses a conversion factor, or **mole ratio** , based on the balanced chemical equation.

**Interactive Example 9.2. Determining Mole Ratios**

What number of moles of will be produced by the decomposition of moles of water?

**Solution**

**Where Are We Going?**

We want to determine the number of moles of produced by the decomposition of moles of .

**What Do We Know?**

· The balanced equation for the decomposition of water is

· We start with moles of .

**How Do We Get There?**

Our problem can be diagrammed as follows:

To answer this question, we need to know the relationship between moles of and moles of in the balanced equation (conventional form):

From this equation we can state that

which can be represented by the following equivalence statement:

We now want to use this equivalence statement to obtain the conversion factor (mole ratio) that we need. Because we want to go from moles of to moles of , we need the mole ratio

so that mol will cancel in the conversion from moles of to moles of .

So if we decompose moles of , we will get moles of .

**Reality Check** Note that this is the same answer we obtained earlier when we rebalanced the equation to give

We saw in **Example 9.2** that to determine the moles of a product that can be formed from a specified number of moles of a reactant, we can use the balanced equation to obtain the appropriate mole ratio. We will now extend these ideas in Example 9.3.

**Interactive Example 9.3. Using Mole Ratios in Calculations**

Calculate the number of moles of oxygen required to react exactly with moles of propane, , in the reaction described by the following balanced equation:

**Solution**

**Where Are We Going?**

We want to determine the number of moles of required to react with moles of .

**What Do We Know?**

· The balanced equation for the reaction is

· We start with moles of .

**How Do We Get There?**

In this case the problem can be stated as follows:

To solve this problem, we need to consider the relationship between the reactants and . Using the balanced equation, we find that

which can be represented by the equivalence statement

This leads to the required mole ratio

for converting from moles of to moles of . We construct the conversion ratio this way so that mol cancels:

We can now answer the original question:

**Reality Check** According to the balanced equation, more is required (by moles) than by a factor of . With about moles of , we would expect about moles of , which is close to our answer.

**Self-Check: Exercise 9.1**

· Calculate the moles of formed when moles of reacts with the required moles of .

**Hint** Use the moles of , and obtain the mole ratio between and from the balanced equation.

See **Problems 9.15** and 9.16.