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# Chemical Stoichiometry

### Skills to develop

• Interpret the mass relationship of reactants and products.
How much is each of the reactants to used in a chemical reaction?
How much will products be form known amounts of reactants?

• Recognize unbalanced and balanced reaction equations.
What are the reactants and products in a reaction?
How to represent the reaction by an equation?
Is the equation properly written up and balanced?
What are the quantitative relations among the reactants and products?

• Balance unbalanced equations.
What principle is applied to balance the equation?
What are the techniques used to balance a reaction equation?

• Describe chemical reactions types and classify them.
How do you classify reactions?
How many types of chemical reactions are there?
Is the classification technique useful for the study of material?

• Explain excess and limiting reactants.
Which reactant will be used up in a reaction mixture?
Which reactant will not be used up in a reaction mixture?
How does limiting reagent affect amounts of products?

• Calculate theoretical and actual yields of chemical reactions.
What are actual and theoretical yields?
For certain amounts of reactants, how much products shall be produced? How much actually is produced?

# Stoichiometry

The quantitative relationship among reactants and products is called stoichiometry. The term stoichiometry is derived from two Greek words: stoicheion (meaning "element") and metron (meaning "measure"). On this subject, you often are required to calculate quantities of reactants or products.

Stoichiometry calculations are based on the fact that atoms are conserved. They cannot be destroyed or created. Numbers and kinds of atoms before and after the reactions are always the same. This is the basic law of nature.

From the atomic and molecular point of view, the stoichiometry in a chemical reaction is very simple. However, atoms of different elements and molecules of different substances have different weights. Thus, simple stoichiometry at the atomic level appears to be complicated when amounts (quantities) are measured in units of g, kg, L or mL. When quantities in moles are used, the relationships (or ratios) are really simple. For example, one mole of oxygen reacts with two moles of hydrogen,

2 H2 + O2 -> 2 H2O
or one mole of hydrogen reacts with half a mole of oxygen, H2 + ½ O2 -> H2O
one mole of carbon reacts with one mole of oxygen. C + O2 -> CO2

This is a major and important topic that you have to master. In order to accomplish this, you have to be able to do several things. First, you have to be able to convert amounts of substances between mass units of g (or kg) to moles and vice versa. Then, you have to understand chemical reactions (changes). In this case, you not only know what are the reactants and products, you can write a balanced equation to explain the reaction. Sometimes you may be told what the reactions are.

There are many chemical reactions, but they can be divided into a few types as a summary.

In a chemical reaction, not all reactants are necessarily consumed. One of the reactants may be in excess and the other may be limited. The reactant that is completely consumed is called limiting reactant, whereas unreacted reactants are called excess reactants.

Amounts of substances produced are called yields. The amounts calculated according to stoichiometry are called theoretical yields whereas the actual amounts are called actual yields. The actual yields are often expressed in percentage, and they are often called percent yields.

Listed with the skills are some general questions. If you are confident in answering all these questions, you have already acquired the skills. Furthermore, we list some diagnostic problems below. Each question test some aspect of stoichiometry. If you find a question difficult, the appropriate topic to study is suggested.

### Typical problems related to Amounts of Substances

• What are the atomic weights of hydrogen (H), oxygen (O), iron (Fe) and gold (Au)?

• The element gold is a precious metal. How many moles of gold have a mass of 1.0 kg?

• The common table salt is a compound with a formula NaCl. What is the mass for a mole of salt? This mass is called molar mass.

• The common sugar has a chemical formula C12H22O11. You dissolved 10.0 g of sugar and made in 250.0 mL of solution in a drink. What is the sugar concentration in the solution?

### Chemical Reactions

Chemical reactions are changes when one or more substances convert to other substances. The best method to represent these changes is a reaction equation. Reaction equations show the molar relationship of reactants and products.

For example, when we exhale via a straw into a solution containing Ca(OH)2, the following reaction takes place.

Ca2+ + H2O + CO2 = CaCO3 + 2H+ This equation shows that a mole of Ca2+ requires a mole of CO2 to react and the products are a mole of solid CaCO3 and 2 moles of H+ ions. Since Ca(OH)2 are basic, the hydrogen ions produced react with the OH- ions to form water.

In solving stoichiometric problems, we often write the molar mass below the formula of the equation. If a sample contains 0.10 gram of Ca2+ ions, then the amount of CO2 required to react with Ca can be evaluated in the following way:

Ca2+ + H2O + CO2 = CaCO3 + 2H+
40.1     18.0     44.0     100.1
0.10                   x
```
44.0 CO2
0.10 g Ca2+ --------- = 0.11 g CO2
40.1 Ca2+
```
The above illustrate how you may approach a stoichiometric problem. It also shows the mass relationship of chemical reactions.

### Types of Chemical Reactions

Two reactants undergo a combination reaction to form a new compound, for example:

H2 + Cl2 = 2 HCl.

The formation of AgCl when NaCl and AgNO3 solutions are mixed give rise to an exchange reaction:

NaCl + AgNO3 = AgCl + NaNO3

Reaction with oxygen or air is often called combustion,

C2H5OH + O2 = 2 CO2 + 3 H2O

A combustion reaction is often an oxidation and reduction reaction. Since the oxidation of one substance involves the reduction of another, this type of reaction is often called redox reaction. In the following reaction,

2 Al + Fe2O3 = 2 Fe + Al2O3

The element Al is oxidized, but Fe is reduced. This reaction is also called a displacement reaction because Al displaces Fe in the oxide.

#### Limiting and Excess Reactants

When one or more reactants (or reagents) react, the one that is exhausted first is called the limiting reactant or limiting reagent. When one reactant is exhausted, no more reaction can take place. The reactants left are called excess reactants or excess reagents. For example, when equal masses of CO and O2 react, CO will be used up first, because the equation is

2 CO + O2 = 2 CO2.

Since equal masses are used, we assume 28 g each of CO and O2 are used. The amount of O2 required can be calculated to be:

```
1 mol CO 1 mol O2  32 g O2
28 g CO ------- --------- --------- = 16 g O2 required
28 g CO 2 mol CO  1 mol O2```

The amount of O2 left will be (28 - 16) g = 8 g O2. Thus, CO is the Limiting reactant and O2 is the excess reactant.

#### Theoretical and Actual Yields

For known amounts of reactants, theoretical amounts of products can be calculated in a chemical reaction or process. Calculated amounts of products are called theoretical yield. In these calculations, the limiting reactant is the limiting factor for the theoretical yields of all products.

However, in a reaction to prepare a compound, you may get less than the theoretical yield, because of incomplete reactions or loss. The amount recovered divided by the theoretical yield gives a percent yield (% yield) or actual yield.

### Confidence Building Questions

• In the reaction,
Zh + 2 HCl = ZnCl2 + H2,
What is oxidized?

Consider...
Well, oxidation state for Zn is zero, but for ZnCl2 the oxidation state for Zn is 2.

Excellent...
The oxidation state increased for Zn.

• At the same temperature and pressure, equal volumes of CO
and O2 are mixed for a reaction. What is the limiting reactant?

Consider...
At the same temperature and pressure, equal volumes of gases contain
the same number of moles.

Consider...
The reaction equation is
2 CO + O2 = 2 CO2.

Excellent...
The required volume for CO is twice the volume for O2.

• 10 g each of Al and Fe2O3 are used for the termite reaction,
2 Al + Fe2O3 = 2 Fe + Al2O3.
How much Fe should be produced when the limiting reactant is exhausted?

Since 10 g Fe2O3 requires 3.4 g Al, we assume Fe2O3 completely reduced.

```            1 mol Fe2O3    2 mol Al  27.0 g Al
10 g Fe2O3 ------------- ----------- --------- = 3.4 g Al
159.6 g Fe2O3 1 mol Fe2O3 1 mol Al

Amount Fe produce is calculated this way:

1 mol Fe2O3  1 mol Fe    55.8 g Fe
10 g Fe2O3 ------------- ----------- --------- = __ g Fe (calculate please)
159.6 g Fe2O3 1 mol Fe2O3 1 mol Al
```