Grade 10

Advanced

5 min

Lesson 7 of 12

Mole-to-Mole Conversions

Not Started

The core of stoichiometry: predicting the amount of product formed based on the moles of reactants used.

If you were a chef tasked with baking 5,000 cookies, you wouldn't guess the flour—you'd use a recipe. In chemistry, the balanced equation is your master recipe, allowing you to predict the exact amount of 'ingredients' needed to create a specific amount of 'product' every single time.

Learning Objectives

1.Perform mole-to-mole conversions using stoichiometric factors from balanced equations
2.Predict the moles of product generated from a specific amount of reactant
3.Calculate the required moles of a second reactant needed for a complete reaction

The Mole Ratio: Your Conversion Bridge

In stoichiometry, the coefficients in a balanced chemical equation do more than just balance atoms; they represent the mole ratio. For example, in the reaction

N_2 + 3H_2 \rightarrow 2NH_3

, the coefficients tell us that 1 mole of

N_2

reacts with 3 moles of

H_2

to produce 2 moles of

NH_3

. This relationship is the 'bridge' that allows us to move from one substance to another. We express these as stoichiometric factors, which are ratios like

\frac{2 \text{ mol } NH_3}{1 \text{ mol } N_2}

. Without a balanced equation, this bridge doesn't exist, and calculations become impossible.

Given the balanced equation:

N_2 + 3H_2 \rightarrow 2NH_3

How many moles of $NH_3$ are produced if 2.5 moles of $N_2$ react completely?

1. Identify the Given:

2.5 \text{ mol } N_2

. 2. Identify the Wanted:

\text{mol } NH_3

. 3. Determine the Mole Ratio from the equation:

1 \text{ mol } N_2 : 2 \text{ mol } NH_3

. 4. Set up the calculation:

2.5 \text{ mol } N_2 \times \frac{2 \text{ mol } NH_3}{1 \text{ mol } N_2} = 5.0 \text{ mol } NH_3

Quick Check

In the reaction $2H_2 + O_2 \rightarrow 2H_2O$ , what is the mole ratio of Oxygen ( $O_2$ ) to Water ( $H_2O$ )?

Look at the coefficients in front of the molecules.

Answer

The ratio is 1:2 (or 1 mole of $O_2$ for every 2 moles of $H_2O$ ).

The 'Wanted/Given' Strategy

To solve any mole-to-mole problem, always use the Dimensional Analysis method. You multiply your 'Given' quantity by a fraction where the unit you want to get rid of is on the bottom, and the unit you want to find is on the top. This is the Stoichiometric Factor:

\text{Moles of Given} \times \frac{\text{Coefficient of Wanted}}{\text{Coefficient of Given}} = \text{Moles of Wanted}

This ensures that the units cancel out correctly, leaving you with the desired substance. This logic applies whether you are moving from reactant to product, or reactant to reactant.

Propane burns according to:

C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O

If you have 0.60 moles of $C_3H_8$ , how many moles of $O_2$ are required for a complete reaction?

1. Given:

0.60 \text{ mol } C_3H_8

. 2. Wanted:

\text{mol } O_2

. 3. Ratio:

\frac{5 \text{ mol } O_2}{1 \text{ mol } C_3H_8}

. 4. Calculation:

0.60 \text{ mol } C_3H_8 \times \frac{5 \text{ mol } O_2}{1 \text{ mol } C_3H_8} = 3.0 \text{ mol } O_2

Quick Check

If you are calculating the moles of product from a reactant, which coefficient goes on the top of the stoichiometric factor?

Remember the 'Wanted over Given' rule.

Answer

The coefficient of the product (the 'Wanted' substance) goes on top.

Advanced Reactant Prediction

In industrial chemistry, we often work backwards. If we need to produce a specific amount of product, we must calculate the exact moles of all reactants required. This prevents waste and ensures the reaction goes to completion. If a reaction has multiple reactants, you simply perform the mole-to-mole conversion for each one separately using the same balanced equation. This is the foundation of Green Chemistry, where efficiency is prioritized to reduce environmental impact.

The reaction is:

2Al + Fe_2O_3 \rightarrow Al_2O_3 + 2Fe

You need to produce 12.0 moles of Iron ( $Fe$ ). Calculate the moles of $Al$ and $Fe_2O_3$ required.

1. **For Aluminum (

Al

):**

12.0 \text{ mol } Fe \times \frac{2 \text{ mol } Al}{2 \text{ mol } Fe} = 12.0 \text{ mol } Al

2. **For Iron(III) Oxide (

Fe_2O_3

):**

12.0 \text{ mol } Fe \times \frac{1 \text{ mol } Fe_2O_3}{2 \text{ mol } Fe} = 6.0 \text{ mol } Fe_2O_3

Key Takeaways

1The coefficients in a balanced equation represent the mole ratio between substances.
2The stoichiometric factor is a fraction: $\frac{\text{moles of Wanted}}{\text{moles of Given}}$ .
3Mole-to-mole conversions are the only way to switch from one chemical species to another in a calculation.
4Always ensure the chemical equation is balanced before starting any stoichiometric calculation.

Quick Check

Multiple Choice

In the reaction $4Al + 3O_2 \rightarrow 2Al_2O_3$ , what is the mole ratio of $Al$ to $Al_2O_3$ ?

Multiple Choice

How many moles of $H_2$ are needed to react with 2 moles of $N_2$ in the reaction $N_2 + 3H_2 \rightarrow 2NH_3$ ?

True/False

Stoichiometric factors can be used even if the chemical equation is not balanced.

What's Next?

Review Tomorrow

In 24 hours, try to write down the 'Wanted/Given' formula and explain to yourself why the 'Given' unit must be on the bottom of the fraction.

Practice Activity

Find a balanced equation for the combustion of methane ( $CH_4$ ) and calculate how many moles of $CO_2$ are produced from 5 moles of $O_2$ .

Browse

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Mole-to-Mole Conversions

Learning Objectives

The Mole Ratio: Your Conversion Bridge

The 'Wanted/Given' Strategy

Advanced Reactant Prediction

Key Takeaways

Quick Check

What's Next?

Mole-to-Mole Conversions

Learning Objectives

The Mole Ratio: Your Conversion Bridge

The 'Wanted/Given' Strategy

Advanced Reactant Prediction

Key Takeaways

Quick Check

What's Next?