The Mole

Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second?

Measuring the Amount of “Stuff”• Suppose you needed to measure the amount

of sand in a child’s sandbox…

– You could count each grain of sand (the number of particles)

– You could weigh the sand (mass)

– You could measure how many bucket-fulls of sand there are (volume)

– You could use moles to convert the number of particles to mass or to volume and vice versa

1 Mole = 6.02 x 1023 particles

• Defining particles…

• Elements have particles called Atoms

• Compounds have particles called Molecules

• Moles are like measuring cups

MollionaireQ: how long would it take to spend a mole of

$1 coins if they were being spent at a rate of 1 billion per second?

A: $ 6.02 x 1023 / $1 000 000 000 = 6.02 x 1014 payments = 6.02 x 1014 seconds

6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes1.003 x 1013 minutes / 60 = 1.672 x 1011 hours1.672 x 1011 hours / 24 = 6.968 x 109 days6.968 x 109 days / 365.25 = 1.908 x 107 years

A: It would take 19 million years

Comparing sugar (C12H22O11) & H2O

No, sugar has more (45:3 ratio)

Yes (6.02 x 1023 in each)

Yes.

No, molecules have dif. masses

No, molecules have dif. sizes.

1 mol each

Yes, that’s what grams are.

mass?

No, they have dif. molar masses# of moles?

No, they have dif. molar masses

# of molecules?

No# of atoms?

No, they have dif. densities.

volume?

1 gram eachSame

Example: How many moles of magnesium is 1.25 x 1023 atoms of magnesium?• 1 mole Mg = 6.02 x 1023 atoms Mg

• Use as a conversion factor in a t-table

= 2.08 x 10-1 mol Mg

Round Table Practice1. What is Avogadro’s Number?

2. How many moles of sodium is 6.482 x 1023 atoms of sodium?

3. If there are 1.03 x 105 mol cesium, then how many atoms are there?

4. If there are 8.925 x 10-3 mol of sulfur, then how many atoms are there?

5. How many atoms are in 2.12 mol of propane (C3H8)?

6. You have 1.14 mol SO3. a)What is the name of this compound. b) How many atoms are there?

7. a) How many moles are there in 4.65 x 1024 molecules of NO2 b)What is the name of this compound?

Answers to Round Table Practice

1. 6.02 x 1023 particles of a substance

2. 1.08 x 1010 mol Na

3. 6.20 x 1028 atoms Cs

4. 5.37 x 1021 atoms S

5. 1.40 x 1025 atoms in this sample of propane

6. a) sulfur trioxide, b) 2.75 x 1024 atoms

7. a) 7.72 mol NO2 b) nitrogen dioxide

Homework Assignment

• Section 10.1 wksht,

• 9-14 pg. 296

• 3-4 pg. 291

• 5-6 pg. 292

• Finish Naming Compounds Review

Molar Mass – Use the Periodic Table• The mass of one mole is called “molar mass”• Example: 1 mol Li = 6.94 g Li• This is expressed as 6.94 g/mol• What are the following molar masses?

S SO2

Cu3(BO3)2

32.06 g/mol 64.06 g/mol308.27 g/mol

Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

Cu x 3 = 63.55 x 3 = 190.65B x 2 = 10.81 x 2 = 21.62O x 6 = 16.00 x 6 = 96.00

308.27

Molar mass• The mass of one mole is called “molar mass”• E.g. 1 mol Li = 6.94 g Li• This is expressed as 6.94 g/mol• What are the following molar masses?

S SO2

Cu3(BO3)2

32.06 g/mol 64.06 g/mol308.27 g/mol

Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

110.98 g/mol (Ca x 1, Cl x 2)96.11 g/mol (N x 2, H x 8, C x 1, O x 3)32.00 g/mol (O x 2)

811.54 g/mol (Pb x 3, P x 2, O x 8)180.18 g/mol (C x 6, H x 12, O x 6)

Molar Mass – Don’t be fooled by other names!

• Gram Atomic Mass (GAM) – molar mass of an element (all atoms are identical)

• Gram Molecular Mass (GMM) – molar mass of a compound (atoms that are covalently bonded)

• Gram Formula Mass (GFM) molar mass of an ionic compound (ions bound in specific simple mole ratios)

Converting between grams and moles• If we are given the # of grams of a compound

we can determine the # of moles, & vise-versa• In order to convert from one to the other you

must first calculate molar mass• Use a t-table to decide which conversion factor to

use.

0.25HCl

53.15H2SO4

3.55NaCl1.27Cu

mol (n)gg/molFormula9.136.46

0.541998.0820758.44

0.020063.55

Homework Assignment

• 10.2 wksht (mole mass problems – we’ll finish the rest tomorrow)

• 7,8,15 pg. 296

• 18-19 pg. 299

• 24, 26, 27 pg. 303

Mole Mass Practice Problems1. How many moles are represented by 16.0 g of

ethanol, C2H5OH?

2. How many grams of glucose are in 6.63 x 1023 molecules of glucose, C6H12O6?

3. How many moles of methanol, CH3OH, are in 6.53 x 1023 molecules of methanol?

4. How many moles of sodium chloride are in 16.0 g of sodium chloride?

5. How many molecules, of potassium hydroxide are in 40.6 g?

6. How many grams of chromic chloride are in 7.14 moles of chromic chloride?

Volume of a Mole of Gas• Volume varies with a change in temperature of pressure

• The volume of a gas is usually measured at Standard Temperature and Pressure, STP

• Standard Temperature: 0 C

• Standard Pressure: 101.3 kPa or 1 atm

• At STP, 1 mole of any gas fills 22.4 L (molar volume of a gas)

• 22.4 L of a gas at STP has 6.02 x 1023 particles

Molar Density• Density = Mass . = grams .

Volume milliliters

• Molar Density will always have the same t-table except for the first square

Example Problems• Humans take in oxygen to burn glucose and

gain energy. The water and carbon dioxide produced in this reaction, called cellular respiration, are exhaled. – If 28 g of water is produced in this reaction,

what volume of water vapor could be exhaled?

– How many atoms are exhaled if 44.8 L of CO2 is released?

– How many grams of oxygen is consumed in the reaction if the volume of oxygen inhaled was 250.0 mL?

Homework Assignment

• Finish 10.2 wksht

• 20-21 pg. 301

• 22-23 pg. 302

• 25, 28-31 pg. 303

Percent Composition: The relative amounts of each element in a compound expressed as a percent

• Also called “percent by mass”

• % means “part over whole”

• Example: 8.2 g of Magnesium reacts completely with 5.40 g of Oxygen to form a compound. What is the percent composition of each element in the compound?

Solution

• Mass of MgO = 8.2 g + 5.40 g = 13.60 g

• (because the law of conservation of mass is ALWAYS true)

If all you are given is the formula or name of a compound, then you must use Molar Mass from the Periodic Table• Example: Calculate the % composition of

propane, C3H8.

• Molar mass of C3H8 = 44.0 g/mol

• Mass of carbon = 3 x 12 = 36 g/mol

• Mass of hydrogen = 8 x 1 = 8 g/mol

Percent Composition can also be used as a conversion to solve for mass.

• Calculate the mass of carbon in 82.0 g of propane C3H8

• Molar mass of C3H8 = 44 g/mol

• Mass of carbon = 3 x 12 = 36 g/mol

• %C in propane = 81.8%... So if there were 100 g of propane, 81.8g would be C

= 67.1 g of C

Empirical and Molecular FormulasConsider NaCl (ionic) vs. H2O2 (covalent)

Cl Na

Na Cl

Cl

Cl

Na

Na

• Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular”. Ionic compounds are always expressed as simplest whole number ratios, or formula units.

• Covalent compounds can either be molecular formulas (H2O2) or empirical formulas (HO)

HOO

H HOO H H

OO H

Steps to Calculate the Empirical Formula

• What is the empirical formula of a compound that is 25.9% nitrogen and 74.1% oxygen?

1.Assume that the % given is equal to the number of grams.

N = 25.9 g O = 74.1 g

2.Convert the number of grams to moles using GAM.

3. Divide by the lowest number of moles to obtain the simplest whole number ratio

4. If necessary, multiply by a whole number to obtain a whole-number ratio

1 mol N x 2 = 2 mol N

2.5 mol O x = 5 mol O

5. Write the chemical formula using these whole number ratios

N2O5

• Q - Write empirical formulas for propene (C3H6), ethene (C2H2), glucose (C6H12O6), octane (C8H14)

• Q - Identify these as empirical formula, molecular formula, or both H2O, C4H10, CH, NaCl

AnswersQ - Write simplest formulas for propene (C3H6),

C2H2, glucose (C6H12O6), octane (C8H14)

Q - Identify these as simplest formula, molecularformula, or both H2O, C4H10, CH, NaCl

A - CH2

A - H2O is both simplest and molecular

C4H10 is molecular (C2H5 would be simplest)

CH is simplest (not molecular since CH can’t form a molecule - recall Lewis diagrams)

NaCl is simplest (it’s ionic, thus it doesn’t form molecules; it has no molecular formula)

CH CH2O C4H7

Determine the Molecular Formula• You must know the empirical formula.• You must also know the molar mass of the compound.• Divide the molar mass of the compound by the empirical

formula mass• Example: Calculate the molecular formula of a compound

whose molar mass is 60.0 g and empirical formula is CH4N.

• CH4N = 30 g/mol (using periodic table)

• ? = 60 g/mol• Need twice as much… multiply subscripts in chemical

formula by two

• C2H8N2

Homework Assignment

• 10.3 wksht

• 32-33 pg. 306

• 34-35 pg. 307

• 36-37 pg. 310

• 38-39 pg. 312

• Pre-Lab Digenite Lab

Digenite Lab – Choose Your Role• Alchemist – measures out materials, combines

them, and heats them up

• Mathematician – guides team through the calculations and provides calculator-support

• Troubadour – tells the story of the lab through careful and detailed observations

• Scribe – records team data on the class data table and ensures accurate information is recorded by each team member