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Plan, Ppt08(PS4) (Many ideas from Tro, 2.9 & 3.7)

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- 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
→ Subscriptscan 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)

Avogadro's #

(# of things/mol of things)

Molar mass of AxBy

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

gramsof A

(atoms / ions),

gramsof B

(atoms / ions)

(in the sample)

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof 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 Cs ions are in 3.4 x 1012 FU of Cs3PO4?

How many O atoms are in 125 FU of CO2?

Ppt08(PS4)

formula units

of AxBy

(in the sample)

(Atom / Ion) Ratio Using

Subscripts

from the Chemical Formula

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Ppt08(PS4)

- → 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)

How many O atoms are in a sample of P4O10 containing 7.2 x 1012 atoms of P?

Ppt08(PS4)

- 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)

- 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 CuSO45 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)

- 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

- The “things” must be specified! They can be

Ppt08(PS4)

- 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 CO2molecules ( “ )

“6.022 x 1023 Na2O FU’s ( “ )

Ppt08(PS4)

- 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

- A “mole of C” is “a moleion C’s”

Ppt08(PS4)

- 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?

1 mole of XXX’s = 6.022 x 1023 XXX’s

Ppt08(PS4)

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Avogadro's #

(# of things/mol of things)

Ppt08(PS4)

- 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)

- How many moles of P (atoms) are in (a sample of) 5.43 moles of P4O10?

Ppt08(PS4)

moles

of AxBy

(in the sample)

(Mole) Ratio Using

Subscripts

from the Chemical Formula

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

Ppt08(PS4)

- How many P (atoms) are in (a sample of) 5.43 moles of P4O10?

Ppt08(PS4)

moles

of AxBy

(in the sample)

(Mole) Ratio Using

Subscripts

from the Chemical Formula

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Avogadro's #

(# of things/mol of things)

Ppt08(PS4)

- A moleof 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)

- 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)

- 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 1023amus) which equals 4 grams.

- If one atom of “Y” weighs y amus, then one mole of “Y” atoms will weigh yx (6.02 x 1023amus) which equals y grams. TOTALLY GENERAL!

Ppt08(PS4)

- 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”).

- 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)

This is numerically multiplying by “1”

(if all sig figs were used for both qtys)

Ppt08(PS4)

- How many atoms will it contain?

If you have a sample of 5.6 g of Cu, how many moles of Cu (“moleion” Cu atoms) will it contain?

Ppt08(PS4)

gramsof A

(atoms / ions),

gramsof B

(atoms / ions)

(in the sample)

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Avogadro's #

(# of things/mol of things)

Molar mass of A,

Molar mass of B

(g/mol)

Ppt08(PS4)

“Nanoscopic” amounts of matter

“Macroscopic” amounts of matter

- A FU ≠ a mole !!

- But…..

(Average) Atomic Mass

Molar Mass

Both are “this for that’s”—same ratio

An amu ≠ a gram !!

Ppt08(PS4)

- 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)

Ppt08(PS4)

- (no, you do not need the chemical formula of cholesterol here!)

What is the formula (unit) mass in amu (i.e., mass of one molecule) of cholesterol if 0.5731 mol weighs 221.6 g?

Ppt08(PS4)

- 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)

Molar mass of AxBy

grams

of AxBy

(in the sample)

moles

of AxBy

(in the sample)

Ppt08(PS4)

Ppt08(PS4)

moles

of AxBy

(in the sample)

(Mole) Ratio Using

Subscripts

from the Chemical Formula

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Avogadro's #

(# of things/mol of things)

Ppt08(PS4)

Avogadro's #

(# of things/mol of things)

Molar mass of AxBy

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

gramsof A

(atoms / ions),

gramsof B

(atoms / ions)

(in the sample)

molesof A

(atoms / ions),

molesof B

(atoms / ions)

(in the sample)

atoms / ionsof A,

atoms / ionsof B

(in the sample)

Avogadro's #

(# of things/mol of things)

Molar mass of A,

Molar mass of B

(g/mol)

Ppt08(PS4)

The concepts and skills related toproblems1-13 and problem 21 on PS4have been covered in this PowerPoint. Give them a try now!

Ppt08(PS4)

…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)