Plan, Ppt08(PS4) (Many ideas from Tro, 2.9 & 3.7) I.Subscripts can be used to make “conversion factors”— between two different kinds of FU (atoms or ions) II.A “mole” of a chemical substance is a certain (huge!) number of FUs of it (called “Avogadro’s Number”). III. Avogadro’s Number can be used as a “conversion factor”--between FUs and moles [of FUs] of a given substance IV.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 V.The mass of one mole of a substance (molar mass) is related to the mass of one FU of it. VI. Molar mass can be used as a “conversion factor”-- between grams (of a substance) and moles [of FUs] of it 1Ppt08(PS4)

NOTE: The handout you have that looks like this will be explained / used throughout this PowerPoint grams of A x B y (in the sample) Molar mass of A x B y Avogadro's # (# of things/mol of things) formula units of A x B y (in the sample) moles of A x B y (in the sample) Molar mass of A, Molar mass of B (g/mol) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) Avogadro's # (# of things/mol of things) (Mole) Ratio Using Subscripts from the Chemical Formula (Atom / Ion) Ratio Using Subscripts from the Chemical Formula 2Ppt08(PS4)

I. Before we get to moles…subscripts can be used to form “conversion factors” How many O atoms are in 125 FU of CO 2 ? How many Cs ions are in 3.4 x FU of Cs 3 PO 4 ? 3Ppt08(PS4)

From handout sheet formula units of A x B y (in the sample) atoms / ions of A, atoms / ions of B (in the sample) (Atom / Ion) Ratio Using Subscripts from the Chemical Formula 4Ppt08(PS4)

Subscripts → “conversion factor” (cont.) How many O atoms are in a sample of P 4 O 10 containing 7.2 x 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) 5Ppt08(PS4)

II. Introduction to Moles Which sample has more “basic units” (formula units) of the substance described: Sample A: A million P 4 O 10 molecules OR Sample B: Two million Hg atoms 6Ppt08(PS4) What if I asked the same question for: Sample A: A mole of P 4 O 10 OR Sample B: Two moles of Hg What if I asked the same question for: Sample A: One gram of P 4 O 10 OR Sample B: One gram of Hg atoms Can answer without any additional info or calculation! Can (still) answer without any additional info or calculation! (Same “thing”)! Can NOT answer without additional info and calculation!

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 CO 2, the number of atoms of O is always twice the number of atoms of C The ratio of H 2 O molecules to anhydrous compound FU’s in a hydrate is fixed. –In CuSO 4  5 H 2 O, the number of H 2 O molecules is always 5 times the number of FU’s of CuSO 4 We will see that whenever chemical reaction occurs, the ratio of FU’s of substances that react is fixed as well (coefficients)! 7Ppt08(PS4)

Moles (of things) 1 mole of “things” = x things (6.022 x 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 CO 2 molecules Na 2 S formula units 8Ppt08(PS4)

Moles (of things) continued Dozen analogy –1 dozen O means _____________ –1 dozen CO 2 means ___________________ –1 dozen Na 2 O means _______________________ 9Ppt08(PS4) “One mole of: –O” means __________________________________ –CO 2 ” means ________________________________ –Na 2 O” means _______________________________ “12 O atoms” “12 CO 2 molecules” “12 Na 2 O formula units” “6.022 x O atoms” (in a sample) “6.022 x CO 2 molecules ( “ ) “6.022 x Na 2 O FU’s ( “ )

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 C atoms –A “mole of CH 4 ” is “a moleion CH 4 ’s” i.e., ~6 x CH 4 molecules 10Ppt08(PS4)

Avogadro’s Number can be used as a conversion factor (between FUs and moles [of FUs]) 1 mole of XXX’s = x XXX’s How many atoms are in (a sample of) 2.68 mol C? How many moles of C is 8.45 x atoms of C? E.g.: 1 mole of C (atoms) = x C atoms 11Ppt08(PS4)

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) 12Ppt08(PS4)

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 H 2 O: –The ratio of H atoms : O atoms is always 2 : 1 –If there are 2.34 x atoms of O, there must be __________ atoms of H present also –If there are 6 x atoms of O, there must be 2 x (6 x ) 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 ) 2 13Ppt08(PS4)

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 P 4 O 10 ? 14Ppt08(PS4)

From Handout Sheet moles of A x B y (in the sample) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) (Mole) Ratio Using Subscripts from the Chemical Formula 15Ppt08(PS4)

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 P 4 O 10 ? 16Ppt08(PS4)

From Handout Sheet moles of A x B y (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) (Mole) Ratio Using Subscripts from the Chemical Formula 17Ppt08(PS4)

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 x times as big a sample as one atom of C. It will have x times as much mass…… 18Ppt08(PS4)

Why is the number of things in a mole x ? (…the relation to mass) It’s simple: Because 1 g is x 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 12 C in exactly 12 grams of 12 C. –1 atom of 12 C 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” 19Ppt08(PS4)

“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 x 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 amus) which equals 4 grams. If one atom of “Y” weighs y amus, then one mole of “Y” atoms will weigh y x (6.02 x amus) which equals y grams. TOTALLY GENERAL! 20Ppt08(PS4)

The upshot of this definition? Molar mass is obtainable from Periodic Table The mass of one mole of any chemical species will equal y grams if one formula unit 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”). Convenience o Ne: amu/atom  ____ g contains1 mol of Ne atoms o W: amu/atom  _____ g contains1 mol of W atoms Ppt08(PS4)

“Proof” That “g/mol (of FUs)” = “amu/FU” This is numerically multiplying by “1” (if all sig figs were used for both qtys) 22Ppt08(PS4)

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? 23Ppt08(PS4)

From Handout Sheet Molar mass of A, Molar mass of B (g/mol) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) Avogadro's # (# of things/mol of things) 24Ppt08(PS4)

Caution An amu ≠ a gram !! “Nanoscopic” amounts of matter A FU ≠ a mole !! But….. “Macroscopic” amounts of matter (Average) Atomic Mass Both are “this for that’s”—same ratio Molar Mass 25Ppt08(PS4)

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 26Ppt08(PS4)

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Example: Application of Idea What is the formula (unit) mass in amu (i.e., mass of one molecule) of cholesterol if mol weighs g? (no, you do not need the chemical formula of cholesterol here!) 28Ppt08(PS4)

Example: Using molar mass as a “conversion factor” How many moles of Na 2 S are in 24.3 g? Makes sense: If one mole of Na 2 S has a mass of ~78 g, then a sample with 24.3 g is less than a mole (about a third of a mole) 1 mol Na 2 S has a mass of: 2 x x = g (1 FU Na 2 S has a(n) avg mass of 2 x x = amu) 29Ppt08(PS4)

grams of A x B y (in the sample) Molar mass of A x B y moles of A x B y (in the sample) 30Ppt08(PS4)

Examples: Using subscripts and Avogadro’s number 31Ppt08(PS4)

moles of A x B y (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) (Mole) Ratio Using Subscripts from the Chemical Formula 32Ppt08(PS4)

Relationships between “amounts” of a substance A x B y (and component atoms / ions) grams of A x B y (in the sample) Molar mass of A x B y Avogadro's # (# of things/mol of things) formula units of A x B y (in the sample) moles of A x B y (in the sample) Molar mass of A, Molar mass of B (g/mol) moles of A (atoms / ions), moles of B (atoms / ions) (in the sample) atoms / ions of A, atoms / ions of B (in the sample) grams of A (atoms / ions), grams of B (atoms / ions) (in the sample) Avogadro's # (# of things/mol of things) (Mole) Ratio Using Subscripts from the Chemical Formula (Atom / Ion) Ratio Using Subscripts from the Chemical Formula 33Ppt08(PS4)

PS Sign-Posting The concepts and skills related to problems 1-13 and problem 21 on PS4 have been covered in this PowerPoint. Give them a try now! 34Ppt08(PS4)

If time… …you can now redo the “#FU’s of H 2 O 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”. 35Ppt08(PS4)