Chapter 4

Chemical Composition

Shaun Williams, PhD

The Mole and Molar Mass

The Mole

The unit that acts as a bridge between the microscopic world and the macroscopic world
Contains \( 6.022 \times 10^{23} \) particles (molecules, atoms, ions, formula units, etc.)
- This number is called Avogadro's number.
The amount of substance that contains as many basic particles (atoms, molecules, or formula units) as there are atoms in exactly 12 g of carbon-12

Molar Mass

Describes the mass of 1 mole of a substance
We obtain the Molar Mass (MM) from the periodic table by assigning different units to the atomic mass.
- Instead of assigning the atomic mass units of amu, we assign the atomic mass units of grams per 1 mole.
Molar mass is the conversion factor between mass and moles.

\[ \text{Mass of 1 mol of S} = 1\,mol \times 32.07\,\bfrac{g}{mol} = 32.07\,g \] \[ \text{Mass of 2 mol of O} = 2\,mol \times 16.00\,\bfrac{g}{mol} = 32.00\,g \] \[ \text{Mass of 1 mol of } \chem{SO_2} = 64.07\,g \]

Percent Composition

Percent Composition by Mass

An expression of the portion of the total mass contributed by each element
To find the percent composition of E (E is any element):

The percentage breakdown of a generic compound.

\[ \text{%E} = \frac{\text{mass of E}}{\text{mass of sample}} \times 100% \]

Conversion with Molar Mass and Avogadro's Number

To convert from moles to grams or from grams to moles, use a molar mass (MM) as your conversion factor.
To convert from moles to particles (molecules, atoms, ions, or formula units) or from particles to moles, use Avogadro's number as your conversion factor.

\[ 1\,mol = 6.022 \times 10^{23}\, atoms \]

Determining Empirical and Molecular Formulas

Empirical and Molecular Formulas

Empirical formula
- Expresses the simplest ratios of atoms in a compound
- Written with the smallest whole-number subscripts
Molecular formula
- Expresses the actual number of atoms in a compound
- Can have the same subscripts as the empirical formula or some multiple of them

Example of Empirical and Molecular Formulas

Two molecules both having the same empirical formula, CH, but with very different molecular formulas, C6H6 and C2H2.

Empirical and Molecular Formulas - Practice

For which of these substances is the empirical formula the same as the molecular formula?

A series of molecules with different formulas.

Some Empirical and Molecular Formulas

Substance	Molecular Formulas	Empirical Formulas
cyclopentane	\( \chem{C_5H_{10}} \)	\( \chem{CH_2} \)
cyclohexane	\( \chem{C_6H_{12}} \)	\( \chem{CH_2} \)
ethylene	\( \chem{C_2H_4} \)	\( \chem{CH_2} \)
hydrogen sulfide	\( \chem{H_2S} \)	\( \chem{H_2S} \)
calcium chloride	This compound does not have a molecular formula	\( \chem{CaCl_2} \)

Finding Empirical Formulas

To find the empirical formula:
1. If starting with a percent composition, find the mass of the element by assigning the percent composition (which has no units but a % instead) the units of grams.
  - If starting with another set of units, then convert the units to masses if necessary.
2. Convert from mass to moles using the MM of the element.

Finding Empirical Formulas - Continued

Repeat for all elements in the compound.
Find whole number subscripts by:
1. Dividing the moles of the each element by the smallest number of moles. The quotients will give whole numbers which are now the subscripts for the empirical formula.
2. If #1 does not give whole numbers, then multiply all numbers by a multiplier that will resolve the quotients into whole numbers.

Determining Molecular Formulas

To determine a molecular formula, the problem must give a piece of experimental data, such as a molar mass, MM.
To find the molecular formula:
1. Find the empirical formula first.
2. Divide the empirical formula's molar mass by the experimental molar mass (which is given).

Comparison between molecular and empirical formulas and their molar masses.

Determining Percent Compositions Using Molar Mass

To determine the percent composition of an element (E) in a compound using molar mass (MM):

\[ \%E= \frac{MM(E) \times \text{# of moles E in compounds}}{\text{Total MM of compound}} \times 100\% \]

Chemical Composition of Solutions

Solutions

are any homogeneous mixture at the molecular or ionic scale
are composed of solutes and solvents
- Solutes
  - Are present in a lesser amount
  - The substances that are dissolved (can be either wet or dry)
- Solvents
  - Are present in the larger amount
  - The substances that dissolve

Making a Solution

A picture sequence of pouring a solid into a flask, adding water, and stirring to make a solution.

Solution Concentration

Is the relative amounts of solute and solvent in a solution
When compared with one another, solutions are classified as dilute or concentrated.
- Dilute solution
  - A solution that contains a relatively small amount of solute
- Concentrated solution
  - A solution that contains a relatively large amount of solute

Effect of Solution Concentration on Color

A picture of less and less concentrated blue solutions. As the concentration drops, the solution becomes less and less blue.

Determining Concentration

Percent by Mass
- Expresses concentration via percentage \[ \%\, mass = \frac{\text{mass solute}}{\text{mass solution}} \times 100\% \]
Molarity (M)
- The moles of solute dissolved in 1 L of solution
- The most common units of concentration \[ M = \frac{\text{moles solute}}{\text{Liters of solution}} \]

Dilution and the Dilution Equation

Dilution
- The process of adding more solvent to solution
The dilution equation: \[ M_{con} V_{con} = M_{dil}V_{dil} \] \[ M_1V_1 = M_2V_2 \]

A picture of diluting a solution. Some concentrated solution is extracted, put into a new flask, water is added to get the neccessary concentration.

Molecular View of Dilution

A molecular view of diluting a solution. Some concentrated solution is extracted, put into a new flask, water is added to get the neccessary concentration.

Chapter 4 Chemical Composition