Unit 10 – The Mole
The mole Measuring Matter
What do you ask for when you buy:
2 shoes 1 pair
12 eggs 1 dozen 48 doughnuts 4 dozen
500 sheets of paper 1 ream Pair, Dozen, Ream
These are all ways to batch a group of objects to make them easier to count! The object may change Eggs to Doughnuts But the number they represent is always constant! What do eggs have to do with Chemistry? How many carbon atoms are in a teaspoon of carbon?
200,666,666,666,666,666,666,667 atoms!!! Can you even pronounce this? 200,666,666,666,666,666,666,667 atoms!!!
It would be nice if chemists had a batch like a dozen (but muuuucchh bigger) to handle this kind of number! Meet the Mole!
S/He is the Chemist’s “dozen”! What is a mole?
The chemist’s “dozen” is called the: MOLE (or the unit mol) 1 dozen atoms = 12 atoms 1 mole atoms = 602213670000000000000000 atoms Or 1 mole = 6.02 1023 How many moles are in 1 teaspoon of carbon atoms? .33 moles Measuring Matter – Moles and Avogadro’s number • Mole (mol) – the amount of a substance that contains the same number of particles as the number of atoms in 12 g of carbon-12. Like doughnuts are counted in dozens, the mole is a SI unit for counting the amount of a substance. – 1 dozen pencils have the same number of particles as 1 dozen doughnuts – 1 mole of carbon atoms have the same number of particles as 1 mole of water molecules
This does not mean they both weigh the same, only that they have the same number of units or particles. Measuring Matter – Moles and Avogadro’s number • Avogadro’s Number – the number of particles (6.02 1023) in exactly one mole of a pure substance. – 1 mole pencils = 6.02 1023 pencils – 1 mole water molecules = 6.02 1023 molecules of water
1 mole of Guaca-”mole” Measuring Matter – Moles and Avogadro’s number If Avogadro’s number is the number of particles in 1 mole, how do you know what kind of particle you have? Remember… Particles can be an atom, molecule, or formula unit? What kind of particle?
Particles can be an atom, molecule, or formula unit? • Atom – one atom • Molecule – more than one nonmetal atom • Formula unit - compound with a metal or + NH4
Measuring Matter – Moles and Avogadro’s number How do you know what kind of particle you have? Examples 1. NaCl formula unit (form.unit)
2. H2O molecule molecule 3. H2 4. Na atom Measuring Matter – Moles and Avogadro’s number Avogadro’s number is really an equality!
1 mole C = 6.021023 atoms C
What can you use equalities to do?
Equalities are conversion factors in Dimensional Analysis problems! Measuring Matter – Moles and Avogadro’s number
How many atoms are in 3.2 mol of C?
6.021023 atoms C 3.2 mol C = 1.9 10 24 atoms C 1 mol C Measuring Matter – Moles and Avogadro’s number How many moles of water molecules are in 21 3.7 10 molecules of H2O?
3.7 1021 molecules H O 1 mol H O 2 2 .0061 = mol H2O 23 6.0210 Molecules H2O Mass and the Mole • Molar mass – the mass, in grams, of one mole of a substance.
How do you find this mass?
The atomic mass printed on the periodic table has two meanings! 1. It is the average mass of one atom in atomic mass units (u). 2. It is also the mass of one mole of atoms of a given element in grams. Mass and the Mole
• Finding molar mass – Atoms – the mass of 1 mole of any atom is the same as the atomic mass in grams. (Round your masses to the tenths)
1mole H atoms = 1.008 g 1.0 g 1mole C = 12.011 g 12.0 g 1mol Cu = 63.546 g 63.5 g Mass and the Mole
• Molar mass continued – Compounds – the mass of 1 mole of a compound is the sum of the masses of the atoms.
1mole H2O = 18.0g 2 H = 2(1.0g) = 2.0g 1 O = 16.0g 2.0g + 16.0g = 18.0g As a molar mass, it would be expressed as 18.0 g/mol Mass and the Mole
Molar mass is really an equality!
For water:
1mole H2O = 18.0 g
What can you use equalities to do?
Equalities are conversion factors in Dimensional Analysis problems!
Mass and the Mole
How many moles are in 242 g of water?
1 mol H O 242 g H2O 2 = 13.4 mol H2O
18.0 g H2O Mass and the Mole
What is the mass of 3.77 mol of gold?
3.77 mol Au 197.0 g Au = 743 g Au 1 mol Au The Last Conversion Factor! What do you do if you are asked to find atoms (or ions) and your representative particle is NOT an atom (or ion)? The Formula Conversion Factor
Think about what a formula really tells you!
1 molecule of H2O
Doesn’t this mean:
1 molecule H2O = 2 hydrogen atoms
The formula is a conversion factor between atoms (or ions) and compounds!
The Formula Conversion Factor
How many hydrogen atoms are in 6.51014 molecules of water?
14 6.510 molecules H2O 2 atoms H = 1.3 10 15 atoms H
1 molecules H2O
Typically, this type of conversion factor is usually a final step in a multi-step problem! The Formula Conversion Factor
How many ammonium ions are in 14 6.510 formula units of (NH4)2CO3?
14 6.510 form. unit (NH4)2CO3 2 ions NH4 15 = 1.3 10 ions NH4
1 form. unit (NH4)2CO3 Conversion Review
Mass
Particles
Moles Formula
Atoms or ions Multi-step Problems
How many water molecules are in 242 g of water?
23 242 g H2O 1 mol H2O 6.0210 molecule H2O 24 = 8.09 10 molecules H2O 1 mol H O 18.0 g H2O 2
Remember, if the question asked for hydrogen atoms, you would have to do a 3rd step! Percent Composition
How would you calculate the percent females in this room?
# females 100 # people
All percents are calculated in the same way! part 100 whole Percent Composition
• Percent Composition – the percent by mass of each element in a compound.
mass element 100 mass compound
molar mass Percent Composition
What is the percent composition of each element in water? Mass H = 2(1.0 g) = 2.0 g + Mass O = 16.0 g
mass H 18.0 g mass O % H 100 % O 100 mass H2O mass H2O 2.0 g 16.0 g 100 100 18.0 g 18.0 g % H = 11% % O = 88.9% Using Percent Composition
If a glass of water contains 648 g of water, how many grams of hydrogen would it hold?
Remember, water is 11% hydrogen
What is 11% of 648 g? (648 g) (.11) 71.28 g 71 g C H N O 8 10 4 2 Empirical Formula
What does H2O mean?
Does it mean 2 atoms of H for every atom of O?
YES
Does it mean 2 g of H for every 1 g of O?
NEVER Empirical Formula
What does H2O mean?
Does it mean 2 moles of H for every mole of O?
Always!
Formulas are not only ratios of atoms, they are also ratios of MOLES Formulas are ratios of moles!
Formulas are ratios of moles!
Formulas are ratios of moles! Empirical Formula
• Empirical Formula – simplest whole number ratio of moles of the atoms in a substance. Experimental method that is the first step in finding the formula of a compound. Circle the empirical formulas!
H2O NaCl C H 2 6 NO2 C H O H2SO4 6 12 6 N2O4 Empirical Formula
Finding the empirical formula 1. Find the mass of each element in the compound. – Usually given – If given as %, then change % to g. 36% H and 64% C 36 g H and 64 g C 2. Convert masses to moles. – Use molar masses. (Don’t worry about significant digits in this step!)
36 g H 1 mol H = 36 mol H 1.0 g H Empirical Formula
3. Find the smallest whole number ratio of moles. a. Write the results of step 2 like a formula. If C = 1.2 mol and H = 4.8 mol
C1.2H4.8 b. Divide by the smallest mole amount.
C1.2H4.8 CH4 1.2 1.2 c. If not all whole numbers, multiply by 2,3, or 4 … Empirical Formula
Examples for step 3 X = .029 mol X = .009 mol Y = .039 mol Y = .006 mol
X.029Y.039 X.009Y.006 .029 .029 .006 .006
X1Y1.34 X1.5Y1 Multiply by 3 Multiply by 2
X Y 3 4 X3Y2 Empirical Formula
More Examples for step 3 X = 1.47 mol X = 2.4 10-4 mol Y = 3.68 mol Y = 7.3 10-4 mol X Y 1.47 3.68 X -4 Y 4 1.47 1.47 2.410 7.310 2.410-4 2.410-4 X1Y2.5 X Y Multiply by 2 1 3.04
X Y X2Y5 1 3 Empirical Formula - Example
A sample of an unknown gas contains 43.2 g of carbon and 115.8 g of oxygen. What is the empirical formula? 1. Find Masses 43.2 g C 115.8 g O 2. Change to moles 43.2 g C 1 mol C = 3.60 mol C 12.0 g C 115.8 g O 1 mol O = 7.24 mol O 16.0 g O Empirical Formula - Example
3. Get whole numbers
C3.60O7.24 3.60 3.60
C1O2.01
CO2 Molecular Formula
• Molecular formula - is some whole number multiple of the empirical formula. – HO is an empirical formula
– H2O2 is twice HO
– (HO)X and X = 2
– For C6H12O6, the empirical formula is CH2O and X=6
• To convert an empirical formula to a molecular formula you must find X. molar mass X empirical mass Molecular Formula - Example
An unknown gas is found to have an empirical formula of NO2 and a molar mass of 92.0 g/mol. What is the molecular formula? molar mass X empirical mass 92.0 g X 2 46.0 g
Molecular formula = (NO2)X = (NO2)2 = N2O4