Lecture #7 - (a) The Mole Concept,

(b) Formula of an Unknown

Chemistry 142 B

James B. Callis, Instructor

Autumn Quarter, 2004

Figure 3.1: Mass spectrometer

Figure 3.2 (a): Peaks of neon injected

Figure 3.2 (b): Bar graph of neon injected

Problem 7-1: Isotopic Composition

The two isotopes of potassium with significant abundance in nature are 39K (isotopic mass 38.9637 amu, 93.258%) and 41K (isotopic mass 40.9618 amu, 6.730%). Fluorine has only one naturally occurring isotope, 19F (isotopic mass 18.9984 amu). Use this information to calculate the formula mass of potassium fluoride.

Solution:

MOLE

• Definition: The amount of substance that contains as many elementary particles (atoms, molecules, ions, or other ?) as there are atoms in exactly 12 grams of carbon 12.

• 1 Mole = 6.022145 x 1023 particles (atoms, molecules, ions, electrons, or…) = NA particles

• NA is Avogado’s Number. (~100 million x 100

million x 100 million)

The Mole is a Chemical Concept

• It represents a fixed number of chemical entities

• A mole of a chemical entity has a fixed, unique mass. (Molar Mass)

• Thus, the mole allows the mass balance to count chemical entities.

Counting objects of fixed relative mass

12 red marbles @ 7g each = 84g12 yellow marbles @4e each=48g

55.85g Fe = 6.022 x 1023 atoms Fe32.07g S = 6.022 x 1023 atoms S

Mole - Mass Relationships of Elements

Element Atomic Mass Molar Mass Number of Atoms

1 atom of H = 1.008 amu 1 mole of H = 1.008 g = 6.022 x 1023 atoms

1 atom of Fe = 55.85 amu 1 mole of Fe = 55.85 g = 6.022 x 1023atoms

1 atom of S = amu 1 mole of S = g = atoms

1 atom of O = amu 1 mole of O = g = atoms

Molecular mass:1 molecule of O2 = amu 1 mole of O2 = g = molecules1 molecule of S8 = amu 1 mole of S8 = g = molecules

Mole - Mass Relationships of Elements

Element Atomic Mass Molar Mass Number of Atoms

1 atom of H = 1.008 amu 1 mole of H = 1.008 g = 6.022 x 1023 atoms

1 atom of Fe = 55.85 amu 1 mole of Fe = 55.85 g = 6.022 x 1023 atoms

1 atom of S = 32.07 amu 1 mole of S = 32.07 g = 6.022 x 1023 atoms

1 atom of O = 16.00 amu 1 mole of O = 16.00 g = 6.022 x 1023 atoms

Molecular mass:1 molecule of O2 = 16.00 x 2 = 32.00 amu 1 mole of O2 = 32.00 g = 6.022 x 1023 molecule1 molecule of S8 = 32.07 x 8 = 256.56 amu 1 mole of S8 = 256.56 g = 6.022 x 1023 molecules

Molecular Mass - Molar Mass ( M )

The Molecular mass of a compound expressed in amu is numerically the same as the mass of one mole of the compound expressed in grams, called its molar mass.For water: H2O Molecular mass = (2 x atomic mass of H ) + atomic mass of O = 2 ( amu) + amu = amu Mass of one molecule of water = amu

Molar mass = ( 2 x molar mass of H ) + (1 x molar mass of O) = 2 ( g ) + g = g g H2O = 6.022 x 1023 molecules of water = 1 mole H2O

The Molecular mass of a compound expressed in amu is numerically the same as the mass of one mole of the compound expressed in grams , called its molar mass.For water: H2O Molecular mass = (2 x atomic mass of H ) + atomic mass of O = 2 ( 1.008 amu) + 16.00 amu = 18.02 amu Mass of one molecules of water = 18.02 amu

Molar mass = ( 2 x molar mass of H ) + (1 x molar mass of O) = 2 ( 1.008 g ) + 16.00 g = 18.02 g 18.02 g H2O = 6.022 x 1023 molecules of water = 1 mole H2O

Molecular Mass - Molar Mass ( M )

One moleof commonsubstancesCaCO3

100.09 gOxygen, O2

32.00 gCopper 63.55 gWater 18.02 g

Calculating the Number of Moles and Atoms in a Given Mass of Element

Problem 7-2: Tungsten (W) is the element used as the filament in light bulbs, and has the highest melting point of any element 3680oC. How many moles of tungsten, and atoms of the element are contained in a 35.0 mg sample of the metal?Plan: Convert mass into moles by dividing the mass by the atomic mass of the metal, then calculate the number of atoms by multiplying by Avogadro’s number.Solution: Converting from mass of W to moles: Moles of W =

No. of W atoms =

Calculating the Moles and Number of Formula Units in a given Mass of Compound

Problem 7-3: Trisodium phosphate is a component of some detergents. How many moles and formula units are in a 38.6 g sample?Plan: We need to determine the formula, and the molecular mass from the atomic masses of each element multiplied by the coefficients.Solution: The formula is Na3PO4. Calculating the molar mass: MM =

Converting mass to moles:

# Formula units =

Flow Chart of Mass Percentage Calculation

Moles of X in one mole of Compound

Mass % of X

Mass fraction of X

Mass (g) of X in onemole of compound

Multiply by M (g / mol of X)

Divide by mass (g) of one mole of compound

Multiply by 100 %

Calculating Mass Percentage and Masses of Elements in a Sample of a Compound - I

Problem 7-4: Sucrose (C12H22O11) is common table sugar. ( a) What is the mass percent of each element in sucrose? ( b) How many grams of carbon are in 24.35 g of sucrose?

(a) Determining the mass percent of each element: mass of C per mole sucrose = mass of H / mol = mass of O / mol = total mass per mole =Finding the mass fraction of C in Sucrose & % C : mass of C per mole mass of 1 mole sucrose

=To find mass % of C =

Mass Fraction of C = =

Calculating Mass Percents and Masses of Elements in a Sample of Compound - II

7-4 (a) continued Mass % of H = x 100% =

Mass % of O = x 100% =

7-4 (b) Determining the mass of carbon: Mass (g) of C = mass of sucrose x ( mass fraction of C in sucrose)

Mass (g) of C =

mol H x M of H mass of 1 mol sucrose

mol O x M of Omass of 1 mol sucrose

Empirical and Molecular Formulas

Empirical Formula - The simplest formula for a compound that agrees with the elemental analysis. The smallest set of whole numbers of atoms.

Molecular Formula - The formula of the compound as it exists. It may be a multiple of the Empirical formula.

Some Examples of Compounds with the same Elemental Ratios

Empirical Formula Molecular Formula

CH2(unsaturated Hydrocarbons) C2H4 , C3H6 , C4H8

OH or HO H2O2

S S8

P P4

Cl Cl2

CH2O (carbohydrates) C6H12O6

Steps to Determine Empirical Formulas

Mass (g) of Element

Moles of Element

Preliminary Formula

Empirical Formula

÷ M (g/mol )

Use no. of moles as subscripts.

Change to integer subscripts: ÷ smallest, conv. to whole #.

Determining Empirical Formulas from Masses of Elements - I

Problem 7-5: The elemental analysis of a sample compound gave the following results: 5.677g Na, 6.420 g Cr, and 7.902 g O. What is theempirical formula and name of the compound?Plan: First we have to convert mass of the elements to moles of the elements using the molar masses. Then we construct a preliminary formula and name of the compound.Solution: Finding the moles of the elements:

Moles of Na =

Moles of Cr =

Moles of O =

Determining Empirical Formulas from Masses of Elements - II

Constructing the preliminary formula:

Converting to integer subscripts (dividing all by smallest subscript):

Rounding off to whole numbers:

CnHm + (n+ )O2(g) n CO2(g) + H2O(g)m 2

m 2

Determining a Chemical Formula from Combustion Analysis - I

Problem 7-6: Erythrose (M = 120 g/mol) is an important chemical compound used often as a starting material in chemical

synthesis, and contains Carbon, Hydrogen, and Oxygen. Combustion analysis of a 700.0 mg sample yielded:

1.027 g CO2 and 0.4194 g H2O. From this data calculate the molecular formula.

Plan: We find the masses of Hydrogen and Carbon using the mass fractions of H in H2O, and C in CO2. The mass of Carbon and Hydrogen are subtracted from the sample mass to get the mass of Oxygen. We then calculate moles, and construct the empirical formula, and from the given molar mass we can calculate the molecular formula.

Determining a Chemical Formula from Combustion Analysis - II

Calculating the mass fractions of the elements:

Mass fraction of C in CO2 =

Mass fraction of H in H2O =

Calculating masses of C and H:

Mass of Element = mass of compound x mass fraction of element

Determining a Chemical Formula from Combustion Analysis - III

Mass (g) of C =

Mass (g) of H =

Calculating the mass of O:

Calculating moles of each element: C = H = O =

Answers to Problems in Lecture #7

1. 58.09 amu

2. 1.90 x 10 - 4 mol, 1.15 x 1020 atoms

3. 0.23545 mol, 1.46 x 1023 formula units

4. (a) 42.10% C, 6.479% H, 51.417% O; (b) 10.25 g C

5. Na2CrO4

6. C4H8O4