# Section 7.1 The Mole: A Measurement of Matter

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Section 7.1 The Mole: A Measurement of Matter
OBJECTIVES: Describe how Avogadro’s number is related to a mole of any substance. Calculate the mass of a mole of any substance.

What is a Mole? You can measure mass, or volume,
or you can count pieces. We measure mass in grams. We measure volume in liters. We can count pieces by counting atoms, formula units or molecules.

Moles (abbreviated: mol)
Defined as the number of carbon atoms in exactly 12 grams of carbon-12 (C-12 an isotope that has mass of 12). 1 mole is 6.02 x particles. Treat it like a very large dozen 6.02 x is called Avogadro’s number.

Representative particles
The smallest pieces of a substance. For a molecular compound: it is the molecule. For an ionic compound: it is the formula unit (ions). For an element: it is the atom. Remember the 7 diatomic elements (made of molecules)

Types of questions How many oxygen atoms in the following? CaCO3 3
Al2(SO4)3 12 How many ions in the following? CaCl2 NaOH 2 5

Types of questions (Particles)
How many moles of water is 5.87 x molecules? How many moles is 7.78 x 1024 formula units of MgCl2? Units MUST be the same so they can cancel out. Units for final answer. 5.87 x 1022 molecules 1 mole = mol 1 6.02 x 1023 molecules 7.78 x 1024 formula units 1 mole = 12.9 mol 1 6.02 x 1023 formula units

Types of Questions (to Moles)
How many molecules of CO2 are there in 4.56 moles of CO2? 4.56 mol 6.02 x 1023 molecules = 2.75 x 1024 molecules 1 1 mole

Measuring Moles Remember relative atomic mass?
The amu was one twelfth the mass of a carbon-12 atom. Since the mole is the number of atoms in 12 grams of carbon-12, the decimal number on the periodic table is also the mass of 1 mole of those atoms in grams.

Gram Atomic Mass (gam) Equals the mass of 1 mole of an element in grams 12.01 grams of C has the same number of pieces as grams of H and grams of iron. We can write this as g C = 1 mole C We can count things by massing them.

Examples How much would 1.00 moles of carbon weigh? 12.01 grams
How many moles of magnesium is g of Mg? 1 mol How many atoms of lithium is 1.00 g of Li? 8.67 x 1022 atoms How much would 3.45 x 1022 atoms of U weigh? 13.64 grams

What about compounds? in 1 mole of H2O molecules there are two moles of H atoms and 1 mole of O atoms To find the mass of one mole of a compound determine the moles of the elements they have Find out how much they would weigh add them up

What about compounds? What is the mass of one mole of CH4?
1 mole of C = g 4 mole of H x 1.01 g = 4.04g 1 mole CH4 = = 16.05g The Gram Molecular Mass (gmm) of CH4 is 16.05g this is the mass of one mole of a molecular compound.

Gram Formula Mass (gfm)
The mass of one mole of an ionic compound. Calculated the same way as gmm. What is the GFM of Fe2O3? 2 moles of Fe x g = g 3 moles of O x g = g The GFM = g g = g

Note! Gram Atomic Mass, Gram Molecular Mass, Gram Formula Mass are all generally called Molar Mass. As it sounds, molar mass is the mass of exactly 1 mole (in grams) of that substance.

Section 7.2 Mole-Mass and Mole-Volume Relationships
OBJECTIVES: Use the molar mass to convert between mass and moles of a substance.

Section 7.2 Mole-Mass and Mole-Volume Relationships
OBJECTIVES: Use the mole to convert among measurements of mass, volume, and number of particles.

Molar Mass Molar mass is the generic term for the mass of one mole of any substance (in grams) The same as: 1) gram molecular mass, 2) gram formula mass, and 3) gram atomic mass- just a much broader term.

Examples Calculate the molar mass of the following and tell what type it is: Na2S N2O4 C Ca(NO3)2 C6H12O6 (NH4)3PO4 78.04 g/mol ionic compound 92.02 g/mol molecular compound 12.01 g/mol atom 164.1 g/mol ionic compound g/mol molecular compound g/mol ionic compound

Molar Mass The number of grams of 1 mole of atoms, ions, or molecules.
We can make conversion factors from these. To change grams of a compound to moles of a compound.

For example How many moles is 5.69 g of NaOH?

For example How many moles is 5.69 g of NaOH?

For example How many moles is 5.69 g of NaOH?
need to change grams to moles

For example How many moles is 5.69 g of NaOH?
need to change grams to moles for NaOH

For example How many moles is 5.69 g of NaOH?
need to change grams to moles for NaOH 1mole Na = 22.99g 1 mol O = g 1 mole of H = 1.01 g

For example How many moles is 5.69 g of NaOH?
need to change grams to moles for NaOH 1mole Na = 22.99g 1 mol O = g 1 mole of H = 1.01 g 1 mole NaOH = g

For example How many moles is 5.69 g of NaOH?
need to change grams to moles for NaOH 1mole Na = 22.99g 1 mol O = g 1 mole of H = 1.01 g 1 mole NaOH = g

For example How many moles is 5.69 g of NaOH?
need to change grams to moles for NaOH 1mole Na = 22.99g 1 mol O = g 1 mole of H = 1.01 g 1 mole NaOH = g

Examples How many moles is 4.56 g of CO2? 0.1 mol
How many grams is 9.87 moles of H2O? g How many molecules is 6.8 g of CH4? 2.55 x 1023 molecules 49 molecules of C6H12O6 weighs how much? 1.47 x grams

Gases Many of the chemicals we deal with are gases.
They are difficult to weigh. Need to know how many moles of gas we have. Two things effect the volume of a gas Temperature and pressure We need to compare them at the same temperature and pressure.

Standard Temperature and Pressure
0ºC and 1 atm pressure abbreviated STP At STP 1 mole of gas occupies 22.4 L Called the molar volume 1 mole = 22.4 L of any gas at STP

Types of Questions (Volume)
How many moles are 3.97 L of STP 1 mole of ALL gases take up 22.4 L of space)? Remember: STP Standard Temperature and Pressure (0°C or 273K temperature and 101.3kPa or 1 atmosphere pressure). 3.97 L 1 mole = mol 1 22.4 L

Examples What is the volume of 4.59 mole of CO2 gas at STP?
L of CO2 How many moles is L of O2 at STP? 0.25 mol of O2 What is the volume of 8.8 g of CH4 gas at STP? L of CH4

Density of a gas D = m / V for a gas the units will be g / L
We can determine the density of any gas at STP if we know its formula. To find the density we need the mass and the volume. If you assume you have 1 mole, then the mass is the molar mass (from PT) At STP the volume is 22.4 L.

Examples Find the density of CO2 at STP. 1.965 g/L of CO2
Find the density of CH4 at STP. 0.716 g/L of CH4

The other way Given the density, we can find the molar mass of the gas. Again, pretend you have 1 mole at STP, so V = 22.4 L. m = D x V m is the mass of 1 mole, since you have 22.4 L of the stuff.

The other way What is the molar mass of a gas with a density of g/L? g/mol 2.86 g/L? g/mol

Summary These four items are all equal: a) 1 mole
b) molar mass (in grams) c) 6.02 x 1023 representative particles d) 22.4 L at STP Thus, we can make conversion factors from them.

Section 7.3 Percent Composition and Chemical Formulas
OBJECTIVES: Calculate the percent composition of a substance from its chemical formula or experimental data.

Section 7.3 Percent Composition and Chemical Formulas
OBJECTIVES: Derive the empirical formula and the molecular formula of a compound from experimental data.

Calculating Percent Composition of a Compound
Like all percent problems: Part whole Find the mass of each component, then divide by the total mass. x 100 %

Example Calculate the percent composition of a compound that is 29.0 g of Ag with 4.30 g of S.

Getting it from the formula
If we know the formula, assume you have 1 mole. Then you know the mass of the pieces and the whole.

Examples Calculate the percent composittion of C2H4?
How about Aluminum carbonate? Sample Problem 7-11, p.191 We can also use the percent as a conversion factor Sample Problem 7-12, p.191

The Empirical Formula The lowest whole number ratio of elements in a compound. The molecular formula = the actual ratio of elements in a compound. The two can be the same. CH2 is an empirical formula C2H4 is a molecular formula C3H6 is a molecular formula H2O is both empirical & molecular

Calculating Empirical
Just find the lowest whole number ratio C6H12O6 CH4N It is not just the ratio of atoms, it is also the ratio of moles of atoms. In 1 mole of CO2 there is 1 mole of carbon and 2 moles of oxygen. In one molecule of CO2 there is 1 atom of C and 2 atoms of O.

Calculating Empirical
We can get a ratio from the percent composition. Assume you have a 100 g. The percentages become grams. Convert grams to moles. Find lowest whole number ratio by dividing by the smallest.

Example Calculate the empirical formula of a compound composed of % C, % H, and %N. Assume 100 g so 38.67 g C x 1mol C = mole C gC 16.22 g H x 1mol H = mole H gH 45.11 g N x 1mol N = mole N gN

Example The ratio is 3.220 mol C = 1 mol C 3.219 molN 1 mol N
The ratio is mol H = 5 mol H molN mol N = C1H5N1 A compound is % P and % O. What is the empirical formula? Caffeine is 49.48% C, 5.15% H, 28.87% N and 16.49% O. What is its empirical formula?

Empirical to molecular
Since the empirical formula is the lowest ratio, the actual molecule would weigh more. By a whole number multiple. Divide the actual molar mass by the empirical formula mass. Caffeine has a molar mass of 194 g. what is its molecular formula?

Example A compound is known to be composed of % Cl, 24.27% C and 4.07% H. Its molar mass is known (from gas density) to be g. What is its molecular formula? C2H4Cl2 Sample Problem 7-14, p.194