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# 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):
$\text{%E} = \frac{\text{mass of E}}{\text{mass of sample}} \times 100%$

### 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

### Empirical and Molecular Formulas - Practice

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

### 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

1. Repeat for all elements in the compound.
2. 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).

### 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

### 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

### 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: $M_{con} V_{con} = M_{dil}V_{dil}$ $M_1V_1 = M_2V_2$

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