THE MOLE CONCEPT

• Chemists find it more convenient to use mass relationships in the laboratory, while chemical reactions depend on the number of atoms present.
• In order to relate the mass and number of atoms, chemists use the SI unit mole (abbreviated mol).
• The number of particles in a mole is called Avogadro's number and is .
  

  

\(\mathbf{1 ~ m o l}\) of H atoms. . . . . . . . . contains: \(\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}} \mathrm{H}\) atoms
\(\mathbf{1 ~ m o l}\) of \(\mathrm{H}_{2}\) molecules. . . . . . . . . contains: \(\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}} \mathrm{H}_{2}\) molecules
\(\mathbf{2} \mathbf{x}\left(\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}}\right)\) H atoms
\(\mathbf{1 ~ m o l}\) of \(\mathbf{H}_{\mathbf{2}} \mathbf{O}\) molecules....contains: \(6.02 \times 10^{23} \mathrm{H}_{2} \mathrm{O}\) molecules
    \(\mathbf{2} \boldsymbol{\times}\left(\mathbf{6 . 0 2} \times 10^{23}\right) \mathbf{H}\) atoms
    \(\mathbf{1} \boldsymbol{\times}\left(\mathbf{6 . 0 2} \times 10^{23}\right) \mathbf{O}\) atoms
\(\mathbf{1 ~ m o l}\) of \(\mathrm{Na}^{+}\)ions...........contains: \(\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}} \mathrm{Na}^{+}\)ions

• The atomic mass of one atom expressed in amu is numerically the same as the mass of one mole of atoms of the element expressed in grams.

MOLAR MASS

• The mass of one mole of a substance is called molar mass and is measured in grams.

Examples:

1. Lithium carbonate
2. Salicylic acid

• The molar mass to convert between mass and moles.
• Avogadro's number to convert between moles and number of entities.
  

  

  
  

  

  
  

  

Examples:

1. How many moles of iron are present in 25.0 g of iron?

2. What is the mass of 5.00 mole of water?
3. How many magnesium atoms are present in 5.00 g of Mg ?

4. How many molecules of HCl are present in 25.0 g of HCl ?

MOLES OF ELEMENTS IN A FORMULA

• The subscripts in a chemical formula of a compound indicate the number of atoms of each type of element. For example, in a molecule of aspirin, , there are 9 carbon atoms, 8 hydrogen atoms and 4 oxygen atoms.
• The subscript also indicates the number of moles of each element in one mole of the compound. For example, one mole of aspirin contains 9 moles of carbon atoms, 8 moles of hydrogen atoms and 4 moles of oxygen atoms.
  

  

• Using the subscripts from the aspirin formula, one can write the following conversion factors for each of the elements in 1 mole of aspirin:

Examples:

1. Determine the moles of C atoms in 1 mole of each of the following substances:
   a) Acetaminophen used in Tylenol,
   b) Zinc dietary supplement,
2. How many carbon atoms are present in 1.50 moles of aspirin, ?
3. How many chlorine atoms are present in 15.0 g of ?

SUMMARY OF MASS-MOLE CALCULATIONS

Examples:

1. How many nitrogen atoms are present in 5.00 g of magnesium nitride?
2. How many phosphorus atoms are present in 1.00 g of calcium phosphate?

PERCENT COMPOSITION

• The percent composition of a compound in the mass percent of each element in the compound.

Examples:

1. Determine the percent composition of .

2. 1.63 g of zinc combines with 0.40 g of oxygen to form zinc oxide. Determine the percent composition of the compound formed.

USING PERCENT COMPOSITION AS A CONVERSION FACTOR

• The mass percent composition of an element in a compound is a conversion factor between mass of the element and mass of the compound. For example, given that the mass percent of Cl in is , the following two conversion factors can be written:

Examples:

1. The FDA recommends that a person consume less than 2.4 g of sodium per day. How many grams of sodium chloride can a person consume and still be within this guideline? Sodium chloride is sodium by mass.
2. What mass (in grams) of iron (III) chloride contains 58.2 g of iron?

DETERMINING EMPIRICAL FORMULAS

• Mass composition data can be used to determine the chemical formula of a compound. The formula obtained by this means is the empirical formula. The steps for this determination are listed below:

1. Convert composition data to mass by assuming 100 g of sample.
2. Determine the mass of each element from data.
3. Calculate the moles of each element from its mass
4. Determine the smallest ratio between the moles of each element. If ratio is fractional, multiply by an integer till whole.

Examples:

1. Arsenic (As) reacts with oxygen (O) to form a compound that is As and oxygen by mass. What is the empirical formula for this compound?
   

   

DETERMINING EMPIRICAL FORMULAS

• Empirical formula for a compound can also be calculated from experimental data on composition of compound. The steps for this determination are listed below:

1. Determine the mass of each element from data.
2. Calculate the moles of each element from its mass
3. Determine the smallest ratio between the moles of each element. If ratio is fractional, multiply by an integer till whole.

Examples:

2. A sample of a compound is decomposed in the laboratory and found to contain 165 g of carbon, 27.8 g of hydrogen and 220.2 g of oxygen. Calculate the empirical formula of this compound.
3. A 3.24 -g sample of titanium reacts with oxygen to form 5.40 g of the metal oxide. What is the formula of the metal oxide?

CALCULATING MOLECULAR FORMULA FROM EMPIRICAL FORMULA

• Molecular formula can be calculated from empirical formula if molar mass is known:

Examples:

1. A compound of N and O with a mass of 92.0 g has the empirical formula of . What is its molecular formula?

2. Butane is a compound used as lighter fluid. Its empirical formula is and its molar mass is . Find the molecular formula for butane.
3. Caffeine, a stimulant found in coffee and soda, has the following mass percent composition: . The molar mass of caffeine is . Find the empirical and molecular formulas for caffeine.
4. Maleic acid is an organic compound composed of , and the rest oxygen. If 0.129 mol of maleic acid has a mass of 15.0 g , what are the empirical and molecular formulas of maleic acid?