# 4.1: Stoichiometry: Mass Relationships in Chemical Reactions

Learning Objective

• Apply stoichiometric coefficients in balanced chemical equations to determining quantities of reactants and products:
• Calculate the mass/number of moles of products formed from reactants and vice versa
• Calculate the mass/number of moles of one reactant needed to consume another reactant

In chapter 3 we were introduced to stoichiometric coefficients and learned how to balance chemical equations. The balanced chemical equation is in effect a series of equivalence statements that relate the relative rates of reactant consumption and product formation. Consider the following equation describing the formation of Aniline (C6H5NH2) from from nitrobenzene (C6H5NO2).

4C6H5NO2 + 9Fe + 4H2O ---> 4C6H5NH2 + 3 Fe3O4

The above equation relates the number of particles. So, for every 4 molecules of nitrobenzene, 9 atoms of iron, and 4 molecules of water consumed you, you create 4 molecules of aniline and 3 formula units of Fe3O4. The problem is the balanced equation describes the number of particles and we can not physically count them, nor do we work on such a small scale in the laboratory.

So how do we "count" chemical entities involved in a chemical reaction?

We count chemical entities in a reaction by measuring macroscopic observables like mass, volume, temperature and pressure. What we measure depends on the state of matter, but we need to relate a measurable property to the number of particles. In this chapter we will learn how to do this for solid substances and for solutes in a solution. In the gas phase chapter we will use the ideal gas law (PV=nRT) to do this for gas phase reactants. The above flow chart describes this process into three steps.

1. Convert measurable quantities to moles (number of particles).
2. Use the balanced equation to relate the moles of what you are given to the moles of what you want..
3. If requested, convert the answer above back to a measurable unit.

## Stoichiometric calculations involving masses of pure solid or liquid phase substances

Mass to Mass or Mass to Mole Conversions

Objective: Given the mass one species be able to predict the mass another species consumed or produced from a balanced chemical equation.

Technique: This is a three step process which should be done in one equation which uses three conversion factors.

• Conversion Factor #1: Use molar mass to convert mass of known material to moles.
• Conversion Factor #2: Use coefficients of balanced reaction equation to convert moles of known material to moles of desired material.
• Conversion Factor # 3: Use molar mass to convert moles of desired material to mass of desired material.

Set up as Dimensional Analysis Problem and solve with one equation (not three)!

### How many grams of oxygen are consumed when 4.0 g butane (C4H10) combusts?

In the following figure we solve this problem with one equation, where each step is a different conversion factor (equivalence statement). I

• Conversion Factor #1: Divide by molar mass of butane. Note, this has significant digits, and the units are included in the numerator and denominator as they are different, but the identity is the same and so not repeated in the denominator (it is implicitly understood that it is the same chemical entity, which in this case in butane)
• Conversion Factor #2: Use coefficients of balanced reaction equation to convert moles of known material to moles of desired material. These are exact numbers that come from the balanced equation and so do not have significant figures, but since they are relating two different entities, the identity of both the numerator and denominator are explicitly stated.
• Conversion Factor # 3: Multiply by molar mass to convert moles oxygen to grams oxygen. Note, this has significant digits, and the units are included in the numerator and denominator as they are different, but the identity is the same and so not repeated in the denominator (it is implicitly understood that it is the same chemical entity, which in this case in butane) Cancel units in the above equation to be sure your answer has the desired units and only round off your final answer to the correct number of significant digits, do not round off during intermediate steps.

How many significant digits should your molar masses be? The measurement with the least number of significant figures determines the number of significant digits that you round your final answer to. Since this problem had 4.0 g of butane, which has 2 significant digits, we used molar masses of 3 significant digits, but rounded the final answer to two. If at all possible, never use a molar mass with fewer significant digits than the measured values you are working with, as stated in the problem.

Do you Always start with the Mass-to-Mole step? NO! If the question was what mass of oxygen is consumed if you combust 4 moles of butane, you do not need to do the first step. Note, both propane and carbon dioxide are gases at ambient conditions and so you can not measure their mass directly. Instead, you need to measure the pressure, temperature and volume of the gas to determine the number of moles. We will learn how to do this when we study gasses, but for now we will use masses in our calculations.

Aniline, (C6H5NH2) can be formed from nitro benzene (C6H5NO2) by the following equation:

4C6H5NO2 + 9Fe + 4H2O ---> 4C6H5NH2 + 3 Fe3O4*

Molar Mass for each substance:

C6H5NO2 : (123.105g/mol)

Fe: (55.845g/mol)

H2O: (18.016g/mol)

C6H5NH2 : (93.121g/mol)

Fe3O4 : (231.535) g/mol

Lets look at some of the questions you could answer. (AND BE CAREFUL TO READ THE QUESTIONS!)

1. How many moles of iron would you need to produce 100 mole of aniline?
2. How many grams of aniline could 100 g nitrobenzene produce?
3. How many moles of Fe3O4 could 100 g of nitrobenzene produce?

(note in all of these questions we have assumed everything else is in excess)

*Note, Fe3O4 is the mineral magnetite, and would be called Iron(II,III) oxide as it has both Iron +2 and Iron +3 in its crystal structure (you will not be responsible for naming it in this class).

### 1. How many moles of iron would you need to produce 100 moles of aniline?

Video 4.1A: 1:25 second YouTube on mole-to-mole stoichiometric problem

### 2. How many grams of aniline could 100 g nitrobenzene produce?

Video 4.1B: (3:03 minute) YouTube on mass-to-mass stoichiometric problem

### 3. How many moles of Fe3O4 could 100 g of nitrobenzene produce?

Video 4.1C: (2:23 minute) YouTube video on mass to mole stoiochometric problem

Exercise $$\PageIndex{1}$$

What is true regarding the following statements made for the following balanced chemical reaction?

4 Al(s) + 3 O2(g) --> 2 Al2O3(s)

A) for every 8 moles of aluminum and 6 moles of oxygen consumed, 4 moles of aluminum oxide are produced.

B) for every 4 molecules of aluminum and 3 molecules of oxygen consumed, 2 molecules of aluminum oxide are produced.

C) for every 4 grams of aluminum and 3 grams of oxygen consumed, 2 grams of aluminum oxide are produced.

D) A and B only

E) A, B, and C

D) A and B only. Stoichiometric ratios in a balanced chemical equations represent a particles/particle ratio that can be scaled up to a mole/mole ratio. So, instead of looking at one molecule at a time, which is not very feasible, we can count by the mole (think by the dozen) of particles at time. Coefficients never represents a mass/mass to ratio because each species in a chemical reaction has a different molar mass. Note: A is still true. We are just doubling the amount of moles, but the ratio is still the same.

Click the following link to complete more practice problems with feedback in hints relating stoichiometric calculations:

http://chemcollective.org/activities/tutorials/stoich/reaction_stoi

Do the Following Worksheet: