CHAPTER 10The Mole

Atomic Mass

• Atomic mass• Atoms of different elements have different masses.

• Mass of a single atom is incredibly small so a special unit called atomic mass unit (amu) is used.

Atomic Mass

• Atoms are composed of three particles:• Electrons• Protons• Neutrons

• Electron mass is too small to matter.• Protons + Neutrons = mass of atoms

• Units = atomic mass units (amu)

Atomic Mass

• Hydrogen – has only one protons • Mass = 1 amu

• Oxygen - 8 neutrons and 8 protons• Mass = 16 amu

• Carbon – 6 protons and 6 neutrons• Mass = 12 amu

Atomic Mass

• How to find the mass of an entire molecule of a compound:• Example: H2O

• 2 hydrogen atoms and 1 oxygen atom. • Atomic mass of hydrogen = 1.0amu• Atomic mass of oxygen = 16.0amu• 2(1.0amu) + 16amu = 18 amu

• The sum of the atomic masses of all the atoms in a compound is the formula mass of the compound.

Sample Problems

•Find the formula mass of baking soda (NaHCO3)

What is a Mole?

•Atomic mass units are not practical for using in the lab. • Easier to work with grams. • In the early 1900s chemists looked for a way to relate the atomic mass of 1 atom of an element in atomic mass units to an amount of that element in grams.

What is a mole?

• A mole is a unit of measurement.

• Used to count extremely small particles, atoms, elements, electrons…

• A way to translate between grams and atomic mass units (amu’s)

• Used for measuring the amount of particles in something.

Understanding the Mole

• Units are used to quantify something.• Example:

• 1 dozen = 12 of something• 3 dozen eggs = 36 eggs.

• 1 mole = 602,200,000,000,000,000,000,000 of something

• A mole is just a large number of something.

The Mole

• 6.022 x 1023 = Avagadro’s number

• Based on the number of atoms in 12 g of Carbon-12. • 1 mole of Carbon-12 has 602,200,000,000,000,000,000,000 carbon atoms.

• Just like 1 dozen of eggs has 12 eggs.

Understanding The Mole

• 1 mole of anything has 6.022 x 1023 particles.• 1 mole of anything will have the same number of particles, but a different weight. • Just like a dozen eggs vs. a dozen elephants.

• 1 mole of an element will equal its atomic mass.• 1 mole of carbon has 6.022 x 1023 atoms and weighs =

12 grams• 1 mole of hydrogen has 6.022 x 1023 atoms and

weighs = 1 gram

The Mole• The mole established a relationship between the atomic

mass unit and the gram.

• The mass in grams of 1 mole of a substance is numerically equal to its atomic mass or formula mass in atomic mass units.

• Atomic mass of oxygen = 16 amu• 1 mole of oxygen = 6.022 x 10 23 atoms• 1 mole of oxygen = 16 grams

Mole Summary

• The number of atoms in 1 mole of an element is always 6.02 x 10 23

• The number of molecules (covalently bonded atoms) in a mole of any molecular compound is 6.02 x 10 23

• Example: 1 mole of H2 contains 6.02 x 10 23 H2 molecules.

Formula units and moles• Mole is also used to describe number

of ions in an ionic compound.

• Ionic compounds exist in crystals not as single-bonded compounds.

• Ionic compounds are represented by formula units. • Lowest whole number ratio.

• 1 mole of an ionic compound contains 6.02 x 10 23 formula units.

Formula units and moles• Example:

• Sodium Chloride• Na+ Cl-

• Lowest ratio = NaCl• 1 mole of sodium chloride contains 6.02 x 10 23

formula units of NaCl

• Calcium Chloride• Ca 2+ Cl-

• Lowest ratio = CaCl2• 1 mole of calcium chloride contains 6.02 x 10 23

formula units of CaCl2

Molar Mass• *The number of items in a mole of a substance is always

the same, but the mass of that mole varies.

• The mass in grams of 1 mole of a substance is called the molar mass of the substance. • Molar mass = M

• How much does 1 mole of something weigh?• If you have 6.02 x 10 23 of something, how much will it weigh?

Molar Mass

• The molar mass of a substance can be determined from its atomic mass of formula mass.

• 1 mole of any element is the amount of that substance that has a mass in grams numerically equal to the atomic mass or formula mass.

Molar Mass• What is the molar mass of glucose? (C6H12O6)

• Meaning – how much does 1 mole of glucose weigh?

• Given: Chemical formula: C6H12O6

• Need: Molar Mass

• Known: molar mass (g) = formula mass (amu)

• Solve for formula mass: • C = 12.0amu x 6 = 72 amu• H = 1.0 amu x 12 = 12 amu• O = 16.0 amu x 6 = 96 amu

• Formula mass = 180 amu• Molar mass of 1 mole of glucose = 180 g/mol

Practice Problems:• Find the molar mass of :

• Sulfur Dioxide (SO2)

• Benzene (C6H6)

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MOLE CONVERSIONS10-2

Mole Conversion

• The mole measures both a mass and a number of particles so it is the central unit in converting the amount of a substance from one type of measurement to another.

Mole Conversion

• Review your Conversions

• Examples:• 1 m = 100 cm• 1 kg = 1000 g• 1 dm = 10 cm • 1 m = 1000 mm• Remember that 1 dm3 = 1 L = 1OOO cm3.

Mole Conversion

• The factor-label method treats labels as factors.• These factors divide out.

• There are two main rules to solving science problems with the factor-label method:• 1. Always carry along your units with any measurement

you use.• 2. You need to form the appropriate labeled ratios

(equalities).

Mole Conversion

• Example Problem:• How many centimeters in 2 meters?• You will see from the metric conversion chart that 1 meter = 100 cm

• we turn this into a ratio by writing it like this:

Or

Mole Conversion

•Once you have the equalities you must pick the one that will cancel out the units leaving the desired units.

•Then multiply your starting quantity (2 meters) by the equality that will give you your desired units.

• As a rule of thumb your problem set up should look like this:

Practice Problems• 1. How many wheels on 350 Ford pickups (use the

equality 1 pickup = 4 tires) - the starting units are pickups, the ending units need to be wheels.

Practice Problems

• What is the mass of 3.20 moles of zinc nitrate?

Practice Problems

• What is the mass of 5.50 moles of NaOH?

• How many moles of PbSO4 are in 158.1g of the compound?

SIGNIFICANT DIGITS• In scientific notation, all numbers are expressed as the

product of a number between 1 and 10 and a whole-number power of 10.

SIGNIFICANT DIGITS

• In addition and subtraction, the answer may contain only as many decimal places as the measurement having the least number of decimal places.

• In multiplication and division, the answer may contain only as many significant digits as the measurement with the least number of significant digits.

Significant Digit Rules• 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are

ALWAYS significant. • 2) ALL zeroes between non-zero numbers are

ALWAYS significant. • 3) ALL zeroes which are SIMULTANEOUSLY to the

right of the decimal point AND at the end of the number are ALWAYS significant.

• 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.

Particles and Moles

• Equations are also used to convert between moles and particles.

• The identity of the substance is not important because the number of particles in 1 mole of any substance is always the same Avogadro’s number 6.02 x 10 23

Particles and Moles

• It is important to note that one mole of atoms contains 6.02 x 10E23 atoms.

• One mole of molecules contains 6.02 x 10E23 molecules.

• One mole of formula units contains 6.02 x 10E23 formula units.

• One mole of ions contains 6.02 x 10E23 ions.

Particles and Moles• How many molecules are in 2 moles of water?

• Multiply the number of molecules in 1 mole of of water by 2.• (6.02 x 10 23 ) x 2 = 1.20 x 10 24 molecules of water in 2 moles.

• How many formula units are in 3 moles of Zn(NO3)2

Particles and Moles

• If the number of particles in a sample is given the number of moles of that substance can also be calculated.

• Divide the number of particles by Avogadro’s number.

Practice Problems• A piece of marble contains 8.74 x 10 23 formula units of

calcium carbonate (CaCO3). How many moles of CaCO3 is that?

• Determine the number of atoms that are in 0.58 mol of Se.

Multistep Conversions

• Converting between mass and particles requires multiple steps.

• Example: A sample of Ca has 7.2 x 1022

atoms. What is the mass of this sample?

Multistep Conversion• Step 1: Convert the number of atoms to moles.• Step 2: Convert the number of moles to mass.

Practice Problems

• 2. How many millimeters in 34 hectometers (use the equality 10,000 mm = 1 hectometer)?

• Sometimes you will need to multiply by more than one ratio to get to your desired units, you can do this by using linking units. Your setup will look like this:

Practice Problems• 3. How many inches in 1 meter given the equality 1 inch =

2.54 cm and 1 meter = 100 cm? (note the linking unit in this problem is cm)

Practice Problems• 4. How many grams in 150 pounds given the equalities 1

pound = 0.454 kg and 1 kg = 1000 grams?

Practice Problems

• You need 250 grams of sugar (C12H22O11) to bake a cake. How many sugar molecules will be in the cake?

Moles and Gases• In a gas particles are spread out from one another. • Avogadro stated that at the same temperature and

pressure, equal volumes of gases contain the same number of gas particles.

• 1 mole of a gas occupies the same volume as 1 mole of any other gas at the same temperature and pressure.

• Molar volume = 22.4 L• 1 mole of any gas at standard temperature and pressure has a

volume of 22.4 L

Practice Problems• How many molecules of carbon dioxide are in a 1.0-L

flask?

Mole Conversions:

MOLES

MASS PARTICLES

VOLUME

Molar Mass

Number of particles in 1 mole

Molar volume (22.4 L/mol)

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EMPIRICAL AND MOLECULAR FORMULAS10-3

Formulas

• The formula for a compound indicates the number and kind of each atom in a particle of the compound.

• How is a chemical formula determined?

Percentage Composition• The percentage composition of a compound is a

statement of the relative mass each element contributes to the mass of the compound as a whole

Percentage Composition• Salt is composed of two elements, sodium and chlorine.

• We know they are always present in the same ratio by mass.

• The ratio in which they are present is the ratio of their atomic masses.

• Therefore, the percentage of sodium in any sample of sodium chloride would be the atomic mass of the element divided by the formula mass and multiplied by 100.

Percentage Composition• Often, because we round off answers, we may find that

the percentages total one or two-tenths more or less than 100%.

Percentage Composition• The mass of a compound is made up of smaller amounts

of different elements. • We can determine what part of the total mass of a compound is

made up by each element in a compound.

• The mass of each element in a compound compared to the entire mass of the compound and multiplied by 100 percent is called the percentage composition of the compound.

• The percentage composition tells you the percent of the mass made up by each element.

Percentage Composition• The percentage composition can be determined in two ways:

• By calculating percentage composition from a given formula. • Example: 1 mole of water – mass equals 18 grams. • 1 mole of water is composed of 2 moles of hydrogen

and 1 mole of oxygen: H2O.

• To find percentage composition: determine what part of the total mass is made up of hydrogen atoms and what part is made up of oxygen atoms.

• Step 1: find mass of hydrogen atoms: 2.0 grams• Step 2: divide the mass of the hydrogen atoms by the

total mass of the compound and multiply by 100 percent.

Percentage Composition

• By experimental analysis:• The mass of the sample is measured. • Sample is decomposed into its components. • The masses of the components are determined and

percentage composition is calculated.

Sample Problems• A sample of 2.45 g of aluminum oxide decomposes into

1.30g of aluminum and 1.15g of oxygen. What is the percentage composition of the compound?

• Find the percentage composition of a compound that contains 1.94g of carbon, 0.48g of hydrogen, and 2.58g of sulfur in a 5.00g sample of the compound.

Empirical Formula• Elements are made of atoms, and compounds are made of elements. Half an atom does not exist.

• Therefore, we can state that the elements in a compound combine in simple whole number ratios, such as 1 to 1, 1 to 2, 2 to 3, and so on.

• If the atoms of the elements are present in simple ratios, then the moles of atoms for each element in the substance will be in small whole number ratios.

Empirical Formula

• Consider the following example:• We find a 2.5-gram sample of a certain substance contains 0.9 gram of calcium and 1.6 grams of chlorine.

• The substance is composed of only two elements.

Empirical Formula• We can calculate the number of moles of calcium and the number of moles of chlorine in the compound.

• Then, we can find the ratio of the number of moles of calcium atoms to the number of moles of chlorine atoms.

• From this ratio, we can find the empirical formula, which is the simplest ratio of atoms in a compound.

Determining Empirical Formula• By knowing the percentage composition the empirical

formula of a compound can be determined.

• Empirical formula – a formula that gives the simplest whole-number ratio of the atoms of the element.

• Example: Hydrogen Peroxide – HO• Shows that a molecule of hydrogen peroxide always has equal

numbers of hydrogen and oxygen atoms. • Does not mean that a molecule of hydrogen peroxide has only 1

of each atom. • Shows ratio: HO – 1:1

Empirical Formula

• Determining empirical formula:• Example: A compound has the following percentage

compositions: 80.0 percent carbon, 20.0 percent hydrogen.

• Assume you are dealing with 100.0 grams. • A 100.0 gram sample contains 80.0grams carbon and

20.0grams hydrogen. • The empirical formula is found by converting the mass

of each element in the sample to the number of moles of atoms of that element.

• Conversion factor is molar mass.

Empirical Formula• 100.0 grams of the compound contains 6.67 moles of

carbon atoms and 19.8 moles of hydrogen atoms. • Smallest whole number ratio is found by dividing each

mole value by the smaller of the two values.

• Empirical formula:

Sample Problems• Determine the empirical formula of a compound

containing 5.75g Na, 3.5g N, and 12.0g O.

• Determine the empirical formula of a compound containing 2.644g of gold, and 0.476g of chlorine.

Empirical Formula• Sometimes by dividing by the smallest number the moles

does not yield a ratio close to a whole number.• Examples:

• 2.33 to 1 = 7 to 3• 1.33 to 1 = 4 to 3• 1.67 to 1 = 5 to 3

Molecular Formula• In order to calculate a molecular formula, we need one

additional piece of data, the molecular mass.

Determining Molecular Formula• The empirical formula for a compound indicates the

simplest ratio of the atoms in the compound. • Does not tell you the actual numbers of atoms in each molecule of

the compound.

• Hydrogen peroxide: • empirical formula: HO • molecular formula: H2O2

• The ratio is 1:1, the number of atoms of each element is not necessarily 1 and 1.

• The exact number of atoms in each molecule of a compound is very important because it determines the properties, or characteristics, of that compound.

Molecular Formula

• The formula that gives the actual numbers of atoms of each element in a molecular compound is called the molecular formula. • The molecular formula is always a whole-number

multiple of the empirical formula.

• Molecular formula can be determined by comparing the molar mass of the unknown compound with the molar mass of the empirical formula.

Molecular Formula

• In one of the examples in the previous section, the empirical formula calculated was CH2O.

• If we know that the molecular mass of the compound is 180 g/mol, how can we find the molecular formula?

Molecular Formula

• The molecular formula shows the number of atoms of each element in a molecule.

• Knowing that the elements will always be present in the ratio 1:2:1, we can calculate the mass of the empirical formula.

Molecular Formula

• Then we can find the number of these empirical units present in one molecular formula. In the substance CH20, the empirical unit has a mass of

12 + 2(1) + 16, or 30

Molecular Formula

• It will, therefore, take six of these units to equal 180 or one molecular formula.

• Thus, the molecular formula is C6H1206.

Practice Problems• Find the molecular formula of a compound that contains

45.56g of palladium and 0.80g of hydrogen. The molar mass of the compound is 216.8g/mol.

• Find the molecular formula for a compound that contains 4.90g N and 11.2 g O. The molar mass of the compound is 92.0 g/mol.

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