3.1. Relate weight to moles, moles
to weights, mole to mole ratio, and
numbers of particles in a chemical
formula.
[Readings 3.1- 3.2 Problems 18,
19, 21, 27, 33, 35, 39, 41, 45, 47,
49, 51, & 53]
Weights on the Periodic Table
Average Weights
Relative Weights
C is defined as weighing 12 AMU
ATOMIC MASSES
MASS SPECTROMETER
DETECTOR
LEAST MASS
ACCELERATED
ION BEAM
MOST MASS
MAGNETIC
FIELD
MASS O
MASS
12C
= 1.33333333
3/3
1
Weights on the Periodic Table
Average Weights
Relative Weights
C is defined as weighing 12 AMU
1 H atom weighs 1/ 12 times 1 C atom
1 O atom is 16/12 the weight of 1 C atom
Formula Weights
The relative weight of a molecule or formula
unit is the sum of the AWs.
What is the mass of 1 molecule of HNO3:
1 • H atom = 1.01 amu
1 • N atom = 14.01 amu
3 • O atom = 48.00 amu
63.02 amu
Molar Mass
The masses of individual atoms and molecules
is not on a practical scale.
In the laboratory chemists measure massive
quantities of atoms.
amu are too small to measure.
solution: use enough atoms so a measurable
amount is obtained.
2
Molar Mass
rationale:
1 H atom weighs 1 amu.
1 O atom weighs 16 amu.
∴ O atoms weigh 16 times as much as H atoms.
Also, 1 million O atoms would weigh 16 times as
much as 1 million H atoms.
If I had enough atoms of H to weigh 1 gram;
then the same number of O atoms would weigh 16
grams
Molar Mass
Since the weights listed on the periodic table are
relative weights;
they can be expressed in grams instead of amu.
The number of atoms necessary to scale up from amu
to grams is called a mole and the weight is called a
molar mass.
The actual number atoms necessary to have 1 gram of
H or 16 grams of O is 6.022 x 1023. This number is
called Avogadro’s Number.
Molar masses can be applied to molecules as well as
to atoms.
Summary
1 atom of H weighs 1 amu.
6.02 x 1023 atoms of H weigh 1 g.
1 atom of Cu weighs 63.54 amu.
6.02 x 1023 atoms of Cu weigh 63.54 g.
1 molecule of HNO3 weighs 63.02 amu.
6.02 x 1023 molecules of HNO3 weigh 63.02 g.
3
Mole
Mole (SI unit for amount of a chemical substance)
One mole of any element or compound has the
same number of formula units as there are atoms
in exactly 12 g of carbon-12. (6.022 x 1023)
Samples of elements
containing one mole
(6.022x1023) atoms.
Zn, Hg, Cu, S
One mole size samples of:
NaCl (white), CuSO4·5H2O (blue)
H2O (colorless), K2 CrO4 (yellow)
Practice Problem
• What is the molecular weight of ethanol,
C2H5OH
• wt of C = 2 x 12.0 amu = 24.0 amu
• wt of H = 6 x 1.0 amu = 6.0 amu
• wt of O = 1 x 16.0 amu = 16.0 amu
• MW of C2H5OH
= 46.0 amu
• Molar mass of C2H5OH = ???
The Mole Concept
• Stoichiometric Equivalencies:
• C2H5OH (ethanol)
– 2 C atoms; 6 H atoms; & 1 O atom
– 4 mol C; 6 mol H; & 1 mol O atoms
• Calculate the mols of C atoms contained in
5.25 mol of ethanol
4
The Mole Concept
• Stoichiometric Equivalencies:
• C2H5OH (ethanol)
– 2 C atoms; 6 H atoms; & 1 O atom
– 4 mol C; 6 mol H; & 1 mol O atoms
• Calculate the mols of C atoms contained in
5.25 mol of ethanol
mol C = 0.52 molC 2 H5 OH ∗
2 molC
= 1.04 molC
1 molC 2 H5 OH
Practice Problem
• caproic acid smells like goats and has this
chemical formula CH3(CH2) 4CO2H
• Calculate the number of moles of caproic
acid contained in 65.24 g of caproic acid
Practice Problem
• CH3(CH2) 4CO2H
• Calculate the number of moles of caproic
acid contained in 65.24 g of caproic acid
molscap= 65.24gcap ∗
1molcap
= 0.562 molcap
116.0 gcap
5
Correct Conversion Pathway
Grams A
Grams B
x mol A/ gram A
Moles A
x grams B/mole B
Moles B
x mol B/mol A
Stoichiometric Calculations
All stoichiometric calculations involve center moles A
to moles B step. Mass A to moles A step and mass B to
moles B steps are used as needed.
A and B are any species, reactant or product, in reaction.
Practice Problem
• Calculate the number of copper atoms
contained in .635 g of copper
6
Thermite Reaction Stoichiometry
2Al(s) + Fe 2O3(s)
Al2O3(s) + Fe(l)
This reaction generates so much heat
that the iron formed is a liquid.
In order to produce 100 g of Fe find:
1. Mass of Fe2O3 required.
2. Mass of Al required.
3. Mass of Al2O3 produced.
3.2. Calculate the percent
composition of a compound.
[Readings 3.3 Example 3.9,
Practice ex. 10, Problems 55, 57, &
59]
Quantitative Decomposition of HgO
HgO is a red
solid.
2HgO(s)
2Hg(l) + O2(g)
Upon heating
HgO decomposes
to Hg and O 2.
After heating the
Hg(l) is observed
in this U bend
which was in a
0 oC ice bath.
Click picture to view animation
7
Percent Composition
• Percentage of one element in a compound
%element =
mass of element
*100%
mass of sample
Percent Composition
• A 3.052 g sample of a liquid is found to
contain 1.145 g carbon, 0.382 g of
hydrogen, and 1.526 g of oxygen. What is
the percent composition of each element?
3.3 . Given data, calculate the
empirical and the molecular
formulas of a compound.
[Readings 3.4 Problems 63, 65,
67, 71, 75, & 79]
8
Empirical Formula
• Empirical formula gives the smallest whole
number ratio of moles of atoms in a formula
unit.
• e.g. a 1.358 g sample of hydrazine contains
1.187 g of nitrogen and the rest is hydrogen.
What is the empirical formula of hydrazine?
Molecular formula
• The molecular formula results from
multiplying the Empirical formula by a
whole number scalar.
• You must know the molecular mass of the
compound in order to calculate the
molecular formula
• From previous problem: Hydrazine could
be (NH2)n
• N2H4 or N3H6 …NnH2n
Sample problem
• The empirical formula of hydrazine is NH2
and its molecular mass is 32.0. What is the
molecular formula of hydrazine?
n=
molecular formula weight
empirical formula weight
9
Sample problem
• The empirical formula of hydrazine is NH2
and its molecular mass is 32.0. What is the
molecular formula of hydrazine?
• Molecular formula is (NH2)n
• N2H4
3.4 . Write and balance chemical
equations.
[Readings 3.5 Problems 83, 85,
87,& 89]
Chemical Equations
• A balanced chemical equation describes
symbolically a chemical reaction.
• An equation is balanced when all of the
reactant atoms are also present in the
products.
• Reactions are balanced by adjusting the
coefficients - NOT the chemical formulas
10
Chemical Equations
• Balancing Chemical Equations
• Step 1: Write the unbalanced equation.
Make sure that each formula is written
correctly.
• Step 2: Adjust the coefficients to get equal
numbers of each kind of atom on both sides
of the arrow.
Chemical Equations
• Tips
• 1. Balance for elements other than O and H
first.
• 2. Balance polyatomic ions as a group
• 3. When elements appear in the equation
separately, balance them separately.
• The process is TRIAL AND ERROR!!
Chemical Equations
• A chemical equation represents a chemical reaction:
•
Before → After
•
Reactants → Products
Atoms in Before → Atoms in After
Arrangement
Arrangement
• Conservation of atoms: there are the same number and
kind of atoms after a chemical reaction as before the
reaction.
• Since atoms have a consistent weight: mass is also
conserved.
•
11
Balancing Equations
• From Experiment
Co(NO3)2 + Na3PO4 --> ?
• Co(NO3)2 + Na3PO4 --> Co3(PO4)2 + NaNO3
• Conservation of Atoms: How? Adjust coefficients.
Method: systematic trial and error.
• __Co(NO3)2 +__Na3PO4 -->__Co3(PO4)2 +
__NaNO3
Examples
__S8 + __O2 --> __SO2
__Pb(NO3)2 +__K2CrO4 -->__PbCrO4 +__KNO3
__Cu +__HNO3 -->__NO2 +__Cu(NO3)2 +__H2O
Rules for Balanced Equations
Same number and kind of atoms on both sides.
Same overall net electrical charge.
Cannot change the subscripts of compounds:
Only change the coefficients.
Coefficients should be the lowest ratio integers.
Mathematically they are similar to algebraic
equations.
12
3.5. Calculate the yield of a
reaction using a chemical
equation. [Readings 3.6
Problems 91, 93, 95, & 96]
Correct Conversion Pathway
Grams A
Grams B
x mol A/ gram A
Moles A
x grams B/mole B
Moles B
x mol B/mol A
Calculations & Equations
•
•
•
•
•
•
__NH3(g) + __O2(g) --> __H2O(l) + __N2(g)
4NH3(g) + 3O2(g) --> 6H2O(l) + 2N2(g)
(a) 3 moles of NH3 will produce ? moles N2?
(b) 1.7 g of NH3 will produce ? moles H2O?
(c) 1.6 g of O2 will produce ? grams H2O?
(d) 2 moles of NH3 and 3 moles of O2 will
produce ? moles N2?
• (e) 5.0 g of NH3 and 5.0 g of O2 will produce ? g
of H2O? How many H2O molecules?
13
3.6. Calculate the yield of a
reaction when one of the
reactants limits the reaction.
[Readings 3.7 Problems 97, 99,
& 100]
Assumptions in Stoichiometry
• 1. All reactions go to completion
• 2. There are ample quantities of all
reactants
• 3. Only the main reaction takes place
• These assumptions are rarely true
Limiting Reactant
• Suppose you had 10 bicycle wheels and 50
frames. How many bicycles could you
produce?
• One frame yields one bicycle, thus, 50
bicycles?
• The amount of wheels limits the number of
bicycles which can be produced!
• How many excess frames are there?
14
Limiting Reactant
2AgNO3(aq) + K2 CrO4(aq)
AgNO3 is limiting
Ag2CrO4(s) + 2KNO3 (aq)
K 2CrO4 is limiting
Click picture to play movie.
Limiting Reactant - The reactant that is completely
consumed limits the amount of product formed.
Limiting Reactant
HC2H3O2 (aq) + NaHCO3(aq)
CO2(g) + H2O + NaC2H3O2(aq)
Adding
NaHCO 3(s)
to 100 mL
of vinegar
Click picture to view animation
After addition
of known
masses of
NaHCO 3(s)
How is limiting reactant
concept shown in animation and experiment?
Example Problem
• Suppose you add 125g of C and 125g of Cl2
to an excess amount of TiO2, how much
TiCl4 can be produced according to the
following reaction.
• TiO2(s) + 2 Cl2(g) + C(s) ––> TiCl4(l) + CO2 (g)
• Step 1: Calculate the moles of product
formed from each reactant
• Step 2: The lesser number is the maximum
product.
15
Example Problem
• Methanol is produced according to the
following reaction
• CO(g) + 2 H2(g) –––> CH3OH(l)
• If 356g CO are mixed with 65.0g hydrogen,
how much methanol can be produced?
• What is the limiting reagent.?
• How much of the excess remains after the
reaction?
3.7. Calculate the percent yield
of a reaction. [Readings 3.8
Problems 101, 103, & 105]
Percent Yield
• Stoichiometry gives the theoretical amount
of product produced by a reaction
• Actual yield is usually measured
Percent Yield =
actual yield
*100%
theoretical yield
16
Example
• Aspirin can be made according to the
following reaction
• C7H6O3(s) + C4H6O3 (l) ––––> C 9H804(S) + CH 3CO2H(l)
• salicylic acid+ acetic anhydride –> aspirin
acetic acid
• You begin with 14.4 g of salicylic acid and
excess acetic anhydride
• 6.26g of aspirin are produced
• Calculate the percent yield
Quantitative Decomposition of HgO
Mass empty
Mass with HgO
2 HgO(s)
Mass with Hg
2 Hg(l) + O2(g)
Use data to find:
1. Empirical formula of HgxOy compound assuming
the formula of the red solid is unknown.
2. The percent yield assuming compound is HgO.
3.8. Calculate the concentration
of a solution made by mixing a
solid in solution and by dilution.
[Readings 3.9 - 3.10 Problems
109, 111, 113, 115, & 117]
17
Concentrations
• It is convenient to measure amounts of
dissolved materials by volume of the solution.
• Concentration: a measure of how much solute
dissolved in what amount of solvent or solution.
• Most common concentration unit in chemistry:
• Molar Unit = M = # moles solute/# L solution
Problem
250 mL volumetric flask
What is the concentration of a solution made
by dissolving 55.3 g of Cu(NO3)2 in enough
water to make 250 mL of solution?
Problem
CuNO 3
250 mL volumetric flask
What is the concentration of a solution made
by dissolving 55.3 g of Cu(NO3)2 in enough
water to make 250 mL of solution?
18
Problem
H2O
250 mL volumetric flask
What is the concentration of a solution made
by dissolving 55.3 g of Cu(NO3)2 in enough
water to make 250 mL of solution?
Problem
250 mL volumetric flask
What is the concentration of a solution made
by dissolving 55.3 g of Cu(NO3)2 in enough
water to make 250 mL of solution?
Problem
H2O
250 mL volumetric flask
What is the concentration of a solution made
by dissolving 55.3 g of Cu(NO3)2 in enough
water to make 250 mL of solution?
19
Sample Problem
• What is the concentration of a solution of
1.70g of AgNO3 dissolved in enough water
to make 250 mL?
• How many grams of NaOH will be
contained in 50 mL of a 0.050 M solution?
Problem
How would you make 150 mL of a 2.70 M
solution of NaC2H3O2?
Problem
How many grams of CaCl2 would react with
100 mL of a 0.15 M solution of AgC2H3O2?
20
Dilution Problems
• How much water needs to be added to 100mL
of a 0.400 M NaBr(aq) solution to make a
0.100 M solution?
• # moles NaBr before dil =# moles NaBr after
dil
•
# moles = M • V
•
MiVi = MfVf
Dilution Problems
• Calculate the concentration of a HCl
solution when 25.0 ml of water is added to
30.0 ml of a 0.05M HCl solution
• How much water would you need to add to
10.0 ml of a 16.0 ml solution in order to
make a 0.050 M HCl solution?
3.9. Calculate the yield of
reactions in solution using
molarity. [Readings 3.11
Problems 119, 121, 123]
21
Solution Stoichiometry
• Calculate the maximum amount of silver
carbonate that could be produced if 50.00
ml of 0.01M AgNO3 is mixed with 75 ml of
a 0.01 M Na2CO3 solution according to the
following reaction.
• 2 AgNO3 (aq)+ Na2CO3 (aq)
•
––> Ag2CO3 (s) + 2 NaNO3 (aq)
Solution Stoichiometry
2 KI(aq) + Pb(NO3 )2(aq)
PbI2(s) + 2 KNO3(aq)
Click pictures to play movies.
If the beaker contains 75.0 mL of a 0.100 M Pb(NO3)2
solution, how many mL of a 5.00 M KI solution must
be added to precipitate as much PbI2 as possible?
Stoichiometry Flowchart
A and B are any species, reactant or product. Central
mole to mole step involved in all stoichiometric calculations.
Green/red steps used as needed.
22