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Chapter 2 Atoms & Elements CHE 123: General Chemistry I Dr. Jerome Williams, Ph.D. Saint Leo University Overview • • • • • Fundamental Chemical Laws Dalton’s Atomic Theory Isotopes Chemical Formulas & Molar Mass The Mole: A Counting Unit Example 2.1: Show that two samples of carbon dioxide obey the Law of Definite Proportions Given: Find: Conceptual Plan: Relationships: Sample 1: 25.6 g O and 9.60 g C Sample 2: 21.6 g O and 8.10 g C proportion O:C g O 1, g C1 g O 2, g C2 O:C in each sample all samples of a compound have the same proportion of elements by mass Solution: Check: both samples have the same O:C ratio, so the result is consistent with the Law of Definite Proportions Tro: Chemistry: A Molecular Approach, 2/e 3 Practice – If a 10.0 g sample of calcite contains 4.0 g of calcium, how much calcite contains 0.24 g of calcium? Tro: Chemistry: A Molecular Approach, 2/e 4 Practice – How much calcite contains 0.24 g of calcium? Given: Find: Conceptual Plan: Sample 1: 4.0 g Ca and 10.0 g calcite Sample 2: 0.24 g Ca mass calcite in Sample 2, g g Ca1, g calcite1 g Ca2 g calcite2 because Relationships: Solution: Sig Figs & Round: Tro: Chemistry: A Molecular Approach, 2/e 0.6 g calcite = 0.60 g calcite 5 Practice – Decide if each statement is correct according to Dalton’s model of the atom • Copper atoms can combine with zinc atoms to make gold atoms • Water is composed of many identical molecules that have one oxygen atom and two hydrogen atoms Tro: Chemistry: A Molecular Approach, 2/e 6 Practice – Decide if each statement is correct according to Dalton’s model of the atom • Copper atoms can combine with zinc atoms to make gold atoms – incorrect; according to Dalton, atoms of one element cannot turn into atoms of another element by a chemical reaction. He knew this because if atoms could change it would change the total mass and violate the Law of Conservation of Mass. Tro: Chemistry: A Molecular Approach, 2/e 7 Practice – Decide if each statement is correct according to Dalton’s model of the atom • Water is composed of many identical molecules that have one oxygen atom and two hydrogen atoms – correct; according to Dalton, atoms combine together in compounds in small whole-number ratios, so that you could describe a compound by describing the number of atoms of each element in a molecule. He used this idea to explain why compounds obey the Law of Definite Proportions. Tro: Chemistry: A Molecular Approach, 2/e 8 Practice – Decide if each statement is correct according to Dalton’s Model of the Atom • Some carbon atoms weigh more than other carbon atoms • Because the mass ratio of Fe:O in wüsite is 1.5 times larger than the Fe:O ratio in hematite, there must be 1.5 Fe atoms in a unit of wüsite and 1 Fe atom in a unit of hematite Tro: Chemistry: A Molecular Approach, 2/e 9 Practice – Decide if each statement is correct according to Dalton’s model of the atom • Some carbon atoms weigh more than other carbon atoms – incorrect; according to Dalton, all atoms of an element are identical. Tro: Chemistry: A Molecular Approach, 2/e 10 Practice – Decide if each statement is correct according to Dalton’s Model of the Atom • Because the mass ratio of Fe:O in wüsite is 1.5 times larger than the Fe:O ratio in hematite, there must be 1.5 Fe atoms in a unit of wüsite and 1 Fe atom in a unit of hematite Tro: Chemistry: A Molecular Approach, 2/e 11 Practice – Decide if each statement is correct according to Dalton’s model of the atom • Because the mass ratio of Fe:O in wüsite is 1.5 times larger than the Fe:O ratio in hematite, there must be 1.5 Fe atoms in a unit of wüsite and 1 Fe atom in a unit of hematite – incorrect; according to Dalton, atoms must combine in small whole-number ratios. If you could combine fractions of atoms, that would mean the atom is breakable and Dalton’s first premise would be incorrect. You can get the Fe:Fe mass ratio to be 1.5 if the formula for wüsite is FeO and the formula for hematite is Fe2O3. Tro: Chemistry: A Molecular Approach, 2/e 12 Isotopes • Isotopes (Two Definitions) – Atoms that have the same atomic number (Z) but different mass numbers (A). – Atoms that have the same #p+ but differ in #no. • Mass Number (A) – This is the sum of the number of protons and neutrons in an atom. (A = #p+ + #no) Isotopes • Isotope Format – Standard Format vs. Element # Isotopes • An atom of element X contains 47 protons and 62 neutrons. Identify the element, and write the symbol for the isotope in the standard format. Answer to Exercise • Atomic No. (Z) = #p = 47 = Ag (Silver) • Mass No. (A) = 47 p + 62 n = 109 109 Ag 47 Isotopes • Calculating Atomic Masses – To find atomic mass for an element one needs to have the individual isotopic masses and the relative percent abundance of each isotope. Isotopes • Atomic Mass = Σ (fraction of isotope n) x (mass isotope n) Isotopes • Calculating Atomic Masses: An Example – Carbon has two naturally occurring isotopes. Carbon 12 has an isotopic mass of 12.000 amu and an abundance of 98.89% while carbon 13 has an isotopic mass of 13.0034 amu and an abundance of 1.11%. Calculate the atomic mass of carbon. Isotopes • Solution to Example • Atomic Mass = [ (0.9889 x 12.000 amu) + (0.0111 x 13.0034 amu) ] • Atomic Mass = 11.867 amu + 0.144 amu • Atomic Mass = 12.011 amu Isotopes • Chlorine has two naturally occurring isotopes: chlorine 35 with an abundance of 75.77% and an isotopic mass of 34.969 amu, and chlorine 37 with an abundance of 24.23% and an isotopic mass of 36.966 amu. What is the atomic mass of chlorine? Chemical Formulas & Molar Mass • A formula unit is one unit, (atom, molecule, or ion), corresponding to a given formula. H2O, CO2, CaCO3, Na3PO4 Chemical Formulas & Molar Mass • Since molecules are so small, it is necessary to convert a number ratio of reactant molecules into a mass ratio for a chemical reaction to be useful. • Mass ratios are determined by using atomic masses for the elements. Chemical Formulas & Molar Mass • Formula mass (FM) represents the sum of atomic masses of all atoms in a formula unit of any compound (ionic or molecular). • Alternate terms that you will see include Molecular Mass, Molar Mass, Formula Weight (FW), and Molecular Weight (MW). Chemical Formulas & Molar Mass • Calculating Formula Masses: Examples HCl 1.01 amu + 35.45 amu = 36.46 amu NaCl 23.00 amu + 35.45 amu = 58.45 amu MgF2 24.31 amu + 2 (19.00 amu) = 62.31 amu Chemical Formulas & Molar Mass • Find the formula mass of the following. Glucose (C6H12O6) Sodium dihydrogen phosphate Silicon tetrabromide Formula Mass Example • Answers • Glucose 180.18 amu • NaH2PO4 119.98 amu • SiBr4 347.69 amu The Mole: A Counting Unit • The mole is the SI unit for the amount of a substance. • A mole is defined as the amount of a substance that contains as many “entities” as there are in exactly 12 g of carbon-12. The Mole: A Counting Unit • More useful relationships based on the mole that belong in the chemist toolbox. 1 mole of X = NA units (units = atoms, ions, molecules) NA = Avogadro’s Number = 6.022 x 1023 units/mole mass of 1 mole of a substance X = molar mass of X in grams. Molar mass is equal to formula (molecular) mass of X in grams. Molar mass values are expressed in grams/mole. The Mole: A Counting Unit • Review: What are the first two axioms? • Axiom #3 “Moles are the vehicle that carry us everywhere we want to go in chemistry.” The Mole: A Counting Unit • Example Problems involving moles: • How many moles are in 23.5 g of iron? – Answer 0.421 moles Fe The Mole: A Counting Unit • Example Problems involving moles: • How many moles of zinc are there in a sample that has 3.45 x 1026 atoms of zinc? – Answer 573 moles Zn