Plan, Ppt08(PS4) (Many ideas from Tro, 2.9 & 3.8) Subscripts can be used to make “conversion factors”—between two different kinds of FU (atoms or ions) A “mole” of a chemical substance is a certain (huge!) number of FUs of it (called “Avogadro’s Number”). Avogadro’s Number can be used as a “conversion factor”--between FUs and moles [of FUs] of a given substance The Ratio of FUs = the Ratio of Moles of FUs → Subscripts can be used to make “conversion factors”—between moles of two different types of atoms or ions The mass of one mole of a substance (molar mass) is related to the mass of one FU of it. Molar mass can be used as a “conversion factor”--between grams (of a substance) and moles [of FUs] of it Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 NOTE: The handout you have that looks like this will be explained / used throughout this PowerPoint Molar mass of AxBy Avogadro's # (# of things/mol of things) grams of AxBy (in the sample) moles of AxBy (in the sample) formula units of AxBy (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula (Atom / Ion) Ratio Using Subscripts from the Chemical Formula grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Molar mass of A, Molar mass of B (g/mol) Ppt08(PS4)

How many O atoms are in 125 FU of CO2? CHM 121 F, 9/14/07 Week 4 I. Before we get to moles…subscripts can be used to form “conversion factors” How many O atoms are in 125 FU of CO2? How many Cs ions are in 3.4 x 1012 FU of Cs3PO4? Ppt08(PS4)

From handout sheet formula units of AxBy (in the sample) CHM 121 F, 9/14/07 Week 4 From handout sheet formula units of AxBy (in the sample) (Atom / Ion) Ratio Using Subscripts from the Chemical Formula atoms / ions of A, atoms / ions of B (in the sample) Ppt08(PS4)

Subscripts → “conversion factor” (cont.) CHM 121 F, 9/14/07 Week 4 Subscripts → “conversion factor” (cont.) How many O atoms are in a sample of P4O10 containing 7.2 x 1012 atoms of P? → I. Subscripts in a formula can be used to create “conversion factors” (this for thats) because they represent ratios of FUs Between two DIFFERENT kinds of FU (here, O atoms and P atoms) Ppt08(PS4)

II. Introduction to Moles CHM 121 F, 9/14/07 Week 4 II. Introduction to Moles Which sample has more “basic units” (formula units) of the substance described: Sample A: A million P4O10 molecules OR Sample B: Two million Hg atoms Can answer without any additional info or calculation! What if I asked the same question for: Sample A: A mole of P4O10 OR Sample B: Two moles of Hg Can (still) answer without any additional info or calculation! (Same “thing”)! What if I asked the same question for: Sample A: One gram of P4O10 OR Sample B: One gram of Hg atoms Can NOT answer without additional info and calculation! Ppt08(PS4)

II. Introduction to Moles; Ratios of FUs are Important! CHM 121 F, 9/14/07 Week 4 II. Introduction to Moles; Ratios of FUs are Important! The ratio of atoms in a compound is fixed; that ratio is given by the subscripts in a formula In CO2, the number of atoms of O is always twice the number of atoms of C The ratio of H2O molecules to anhydrous compound FU’s in a hydrate is fixed. In CuSO45 H2O, the number of H2O molecules is always 5 times the number of FU’s of CuSO4 We will see that whenever chemical reaction occurs, the ratio of FU’s of substances that react is fixed as well (coefficients)! Ppt08(PS4)

Moles (of things) 1 mole of “things” = 6.022 x 1023 things CHM 121 F, 9/14/07 Week 4 Moles (of things) 1 mole of “things” = 6.022 x 1023 things (6.022 x 1023 is called “Avogadro’s #”) The “things” must be specified! They can be Atoms Molecules Ions Formula Units Other things later (photons, electrons, bonds, etc.) The kind of thing must be specified! O atoms Au atoms CO2 molecules Na2S formula units Ppt08(PS4)

Moles (of things) continued CHM 121 F, 9/14/07 Week 4 Moles (of things) continued Dozen analogy 1 dozen O means _____________ 1 dozen CO2 means ___________________ 1 dozen Na2O means_______________________ “12 O atoms” “12 CO2 molecules” “12 Na2O formula units” “One mole of: O” means__________________________________ CO2” means________________________________ Na2O” means_______________________________ “6.022 x 1023 O atoms” (in a sample) “6.022 x 1023 CO2 molecules ( “ ) “6.022 x 1023 Na2O FU’s ( “ ) Ppt08(PS4)

Think of a “mole” as a “moleion”! (analogous to “million”) CHM 121 F, 9/14/07 Week 4 Think of a “mole” as a “moleion”! (analogous to “million”) One mole is not one “thing” it’s a moleion (MOLE-yin) things! A “mole of C” is “a moleion C’s” i.e., ~6 x 1023 C atoms A “mole of CH4” is “a moleion CH4’s” i.e., ~6 x 1023 CH4 molecules Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Avogadro’s Number can be used as a conversion factor (between FUs and moles [of FUs]) 1 mole of XXX’s = 6.022 x 1023 XXX’s E.g.: 1 mole of C (atoms) = 6.022 x 1023 C atoms How many atoms are in (a sample of) 2.68 mol C? How many moles of C is 8.45 x 1020 atoms of C? Ppt08(PS4)

(# of things/mol of things) CHM 121 F, 9/14/07 Week 4 From Handout Sheet moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Ppt08(PS4)

In a sample of H2O: 2 The ratio of H atoms : O atoms is always 2 : 1 CHM 121 F, 9/14/07 Week 4 Importance of Moles (Part I): Any Ratio of Nanoscopic “Units” is equal to the Ratio of the Moles of those Units In a sample of H2O: The ratio of H atoms : O atoms is always 2 : 1 If there are 2.34 x 1019 atoms of O, there must be __________ atoms of H present also If there are 6 x 1023 atoms of O, there must be 2 x (6 x 1023) atoms of H present also If there is one mole of O atoms, there must be ____ moles of H atoms present also 2 x (2.34 x 1019) 2 Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Subscripts can be used to create conversion factors between moles (of FUs) How many moles of P (atoms) are in (a sample of) 5.43 moles of P4O10? Ppt08(PS4)

from the Chemical Formula CHM 121 F, 9/14/07 Week 4 From Handout Sheet moles of AxBy (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Using two conversion factors to get from “moles of compound” to “# of atoms” How many P (atoms) are in (a sample of) 5.43 moles of P4O10? Ppt08(PS4)

From Handout Sheet moles of AxBy moles of A (atoms / ions), moles of B CHM 121 F, 9/14/07 Week 4 From Handout Sheet moles of AxBy (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Ppt08(PS4)

Why is the unit of “mole” so important? (Part II) CHM 121 F, 9/14/07 Week 4 Why is the unit of “mole” so important? (Part II) A mole of any substance is a macroscopic amount It can be seen, handled, and weighed. A formula unit of any substance is a nanoscopic amount It cannot be seen, handled, or weighed Using moles is a way to scale up from the nanoworld to the macroworld. For convenience! The scaling factor is Avogadro’s number! A mole of C is 6.022 x 1023 times as big a sample as one atom of C. It will have 6.022 x 1023 times as much mass…… Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Why is the number of things in a mole 6.022 x 1023? (…the relation to mass) It’s simple: Because 1 g is 6.022 x 1023 times as much mass as 1 amu! When the “mole” was defined, the actual value of Avogadro’s number was not known! Avogadro’s number was defined to be the number of atoms of 12C in exactly 12 grams of 12C. 1 atom of 12C has a mass of exactly 12 amu (definition) Determining Avogadro’s number was the same as determining the mass of 1 amu, in grams! Strict analogy: “a gram is to an amu, as a mole is to a formula unit” Ppt08(PS4)

“A gram is to an amu, as a mole is to a formula unit” CHM 121 F, 9/14/07 Week 4 “A gram is to an amu, as a mole is to a formula unit” If one atom of H weighs 1 amu, then one mole of H atoms will weigh 6.022 x 1023 amus, which equals 1 gram. If one atom of He weighs 4 amus, then one mole of He atoms will weigh 4 x (6.02 x 1023 amus) which equals 4 grams. If one atom of “A” weighs y amus, then one mole of “A” atoms will weigh y x (6.02 x 1023 amus) which equals y grams. TOTALLY GENERAL! Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 The upshot of this definition? Molar mass is obtainable from Periodic Table The mass of one mole of any monatomic element will equal y grams if one atom weighs y amus: Use the number (for average atomic mass) from the periodic table to “tell you” the number of grams in one MOLE of atoms of that element (called “molar mass”). Ne: 20.18 amu/atom  ____ g contains1 mol of Ne atoms 20.18 W: 183.9 amu/atom  _____ g contains1 mol of W atoms 183.9 Convenience Ppt08(PS4) To Slide 26

“Proof” That “g/mol (of FUs)” = “amu/FU” CHM 121 F, 9/14/07 Week 4 “Proof” That “g/mol (of FUs)” = “amu/FU” This is numerically multiplying by “1” (if all sig figs were used for both qtys) Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Example If you have a sample of 5.6 g of Cu, how many moles of Cu (“moleion” Cu atoms) will it contain? How many atoms will it contain? Ppt08(PS4)

(# of things/mol of things) CHM 121 F, 9/14/07 Week 4 From Handout Sheet grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Molar mass of A, Molar mass of B (g/mol) Ppt08(PS4)

Caution An amu ≠ a gram !! A FU ≠ a mole !! But….. (Average) CHM 121 F, 9/14/07 Week 4 Caution An amu ≠ a gram !! “Nanoscopic” amounts of matter “Macroscopic” amounts of matter A FU ≠ a mole !! But….. (Average) Atomic Mass Molar Mass Same ratio doesn’t mean same numerators (or denominators)! Ppt08(PS4)

What is the molar mass of a compound? CHM 121 F, 9/14/07 Week 4 What is the molar mass of a compound? Molar Mass of a monatomic element is “directly” from Periodic Table (previous slide) Molar Mass of a compound? Sum the masses of the moles of atoms it contains (use chemical formula). See next slide Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 The mass of one mole of any chemical species will equal y grams if one formula unit weighs y amus! Ppt08(PS4)

Example: Application of Idea CHM 121 F, 9/14/07 Week 4 Example: Application of Idea What is the formula (unit) mass in amu (i.e., mass of one molecule) of cholesterol if 0.5731 mol weighs 221.6 g? (no, you do not need the chemical formula of cholesterol here!) Hint: What can you calculate knowing both the moles and the grams in a given sample? Ppt08(PS4)

Example: Using molar mass as a “conversion factor” CHM 121 F, 9/14/07 Week 4 Example: Using molar mass as a “conversion factor” How many moles of Na2S are in 24.3 g? 1 mol Na2S has a mass of: 2 x 22.99 + 1 x 32.07 = 78.05 g (1 FU Na2S has a(n) avg mass of 2 x 22.99 + 1 x 32.07 = 78.05 amu) Makes sense: If one mole of Na2S has a mass of ~78 g, then a sample with 24.3 g is less than a mole (about a third of a mole) Ppt08(PS4)

grams of AxBy moles of AxBy (in the sample) Ppt08(PS4) CHM 121 F, 9/14/07 Week 4 Molar mass of AxBy grams of AxBy (in the sample) moles of AxBy (in the sample) Ppt08(PS4)

Examples: Using subscripts and Avogadro’s number CHM 121 F, 9/14/07 Week 4 Examples: Using subscripts and Avogadro’s number Do as practice only Ppt08(PS4)

moles of B atoms / ions of B CHM 121 F, 9/14/07 Week 4 moles of AxBy (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 Relationships between “amounts” of a substance AxBy (and component atoms / ions) Molar mass of AxBy Avogadro's # (# of things/mol of things) grams of AxBy (in the sample) moles of AxBy (in the sample) formula units of AxBy (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula (Atom / Ion) Ratio Using Subscripts from the Chemical Formula grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) Avogadro's # (# of things/mol of things) Molar mass of A, Molar mass of B (g/mol) Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 PS Sign-Posting The concepts and skills related to problems 1-8 on Written PS4, as well as problems in PS4 Mastering Part 1, have been covered in this PowerPoint. Give them a try now! Ppt08(PS4)

CHM 121 F, 9/14/07 Week 4 If time… …you can now redo the “#FU’s of H2O in 150. g” question (from Ppt07) the “traditional” way (g → mol → FU) instead of the more “obscure” way (g → amu → FU) Chemists use moles because we often do not need to know the actual number of FU’s of substances, just the ratio of them. And “grams” is a much more “convenient” mass unit than “amu”. Ppt08(PS4)