Unit 2 Topic 1
Quantitative Chemistry
CDO IB Chemistry SL/HL
Trimble
Measurement and units
• Standardized system of measurement – Systeme
International
• SI Units
2
Property
Unit
Symbol for Unit
Mass
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
volume
Cubic metre
m3
Pressure
Pascal
Pa
Measurement and units
• Typical units used in the lab
Property
Unit
Symbol for Unit
Mass
Gram
g
Time
Minute
min
Temperature
Degree celcius
oC
Volume
Cubic centimetre
cm3 (mL)
Cubic decimeter
dm3 (L)
atmosphere
atm
Pressure
3
Measurement and units
• SI Prefixes –
converts a base unit
to a unit that is
appropriate for the
measurement
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Temperature
By definition
temperature is a
measure of the
average kinetic
energy of the
particles in a sample.
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Temperature
• In scientific measurements,
the Celsius and Kelvin scales
are most often used.
• The Celsius scale is based on
the properties of water.
• 0C is the freezing point
of water.
• 100C is the boiling point
of water.
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Temperature
• Kelvin is the SI unit of
temperature.
• It is based on the
properties of gases.
• There are no negative
Kelvin temperatures.
•
K = C + 273
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Dimensional Analysis
• We use dimensional analysis to
convert one quantity to another.
• Most commonly dimensional analysis
utilizes conversion factors (ex: 1 in. =
2.54 cm)
1 in.
or
2.54 cm
2.54 cm
1 in.
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Dimensional Analysis
• Use the form of the conversion factor that puts the sought-for unit
in the numerator. Conversion factors do not count for significant
figures.
Given unit 
desired unit
given unit
Conversion factor
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 desired unit
Problem Solving In Chemistry
• Answers will always include
• Correct numerical value
• Correct significant figures
• Estimated Uncertainty (If stated)
• Correct units
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Examples: Dimensional Analysis
• Convert 8.00 m to inches.
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Example
An aspirin tablet contains 325 mg acetaminophen. How
many grams is this equivalent to?
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Example: Units to a Power
How many m3 is 1500 cm3?
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Example: Converting Multiple Units
The density of aluminum is 2.70 g/cm3. Express this value in
units of kilograms per cubic meter.
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Amounts of a Substance
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CDO IB Chemistry SL
What is a mole?
• An amount of substance that contains the same number of
particles as 12 g of C-12
• Analogy
• A dozen is 12
• A ream is 500
• A mole is 6.02 x 10 23
Avogadro’s Number
• 6.02 x 1023 (L)
• Example: Determine
the number of atoms in
12 g of C-12 if the
mass of 1 atom of C -12
is 1.99252 x 10 -23 g.
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CDO IB Chemistry SL
Relative Molecular Mass (Mr)
• By definition, Mr is the mass of 1 mol of a substance
(i.e., g/mol).
• The relative molecular mass of an element is the
average mass for the element that we find on the
periodic table.
• The Mr of a compound is the sum of each of the
relative molecular mass of each element multiplied by
the number of the atoms in the formula
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CDO IB Chemistry SL
Example: Calculating Molar Mass
Calculate the molar mass for each of the following elements/compound:
1.
CO2
2. H2SO4
3. S
4. Ca(C2H3O2)2
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White Board Practice
• Find the Mr for each of the following compounds or atoms:
• HNO3
• H2O
• O2
• Mg
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Using Moles
• Moles provide a bridge from the molecular scale to the
real-world scale.
• If the substance is an element we will count atoms using
Avogadro's number if the substance is a compound we will
count molecules, formula units or ions
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CDO IB Chemistry SL
Converting to Determine number of Particles
• Equation:
n=N
L
N
Where
n = moles
N = # of particls
L = Avogadros #
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n
L
Examples: Using Avogadro’s Number
• How many atoms of Au are there in 0.36 moles of Au?
• How many moles are there in 3.46 x 1028 molecules of
water?
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Converting Between Mass and Moles
• Equation:
n=m
Mr
m
Where
n = moles
m = grams
Mr = relative molar mass
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n
Mr
Example: Using Moles in Calculations – Molar Mass
• How many moles of tin are there in 250 grams of tin?
• How many moles of SO2 is present in 0.45 grams of sulfur
dioxide?
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White Board Practice
• How many moles are there in 36 g of Sulfur?
• How many grams are there in 3.2 moles of CO2?
• How many atoms are there in 1.62 moles of Calcium?
• How many moles is 3.61 x 10
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molecules of sulfuric acid?
Mole Relationships
• One mole of atoms, ions, or molecules contains Avogadro’s number of
those particles.
• One mole of molecules or formula units contains Avogadro’s number
times the number of atoms or ions of each element in the compound.
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Molecules and Chemical Formulas
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Molecules
• Molecules are groups of atoms chemically
bonded together.
• Molecules may be elements or compounds.
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Molecular Elements and Allotropes
• Some Elements exist as molecules
• Diatomic elements (molecules)
• Phosphorus exists as a tetratomic molecule
• Some elements exist in a variety of forms (Allotropes)
• Carbon: graphite; diamond; buckminsterfullerine
• Phosphorus - red and white
• Sulfur - S6 and S4
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Diatomic Molecules
These seven elements occur naturally as molecules containing two
atoms.
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Molecules and Molecular Compounds
• Molecular compounds - molecules containing atoms
from two or more different elements
• Covalent bonds - the force holding the atoms
together in a molecular compound by the sharing
of electrons
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Formulas
• A compound is represented by using the symbols for the
elements of which it is composed
• Subscripts are used to indicate how many atoms of a
particular element exist in the compound
• If there is only one atom of a particular element, the one
is assumed
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Formulas, con’t
• Changing the subscripts changes the compound
• consider H2O and H2O2
• Two different compounds can, however, share the
same chemical formula
• dimethyl ether and ethyl alcohol both have the
formula C2H6O
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Ions
• When atoms lose or gain electrons, they become ions.
• Cations are positive and are formed by elements on the left side of
the periodic table
• Anions are negative and are formed by elements on the right side
of the periodic table
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How charged species arise
• Neutral atoms and molecules have the same
number of protons and electrons
• Cations have more protons than electrons
resulting from the loss of an electron
• Anions have more electrons than protons resulting
from the gain of an electron
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Common Monatomic Ions
• Main Group Elements
• Group 1, 2 – All Metals – Group # = Charge of the
Cation
• Group 3 – Metals (doesn’t include B) – Group # = Charge
of Cation
• Group 5 – Non Metals – Group # - 8 = Charge of Anion
Metal – Bi – Group # = Charge
• Group 6, 7 – Non Metals Group # - 8 = Charge of Anion
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• Group 0 – Doesn’t Form Ions!!
CDO IB Chemistry SL
Common Variable Charge Cations
• Copper – Cu 1+ and Cu 2+
• Iron – Fe
2+ and
Fe 3+
• Lead – Pb 2+ and Pb 4+
• Gold – Au
• Tin – Sn
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1+ and
2+ and
Au 3+
Sn 4+
Ionic Bonds
• Ionic compounds (such as NaCl) are generally
formed between metals and nonmetals.
(Cation and Anions) due to electrostatic
attraction
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Writing Formulas
• Because compounds are electrically neutral, one can
determine the formula of a compound this way:
• The charge on the cation becomes the subscript on the
anion.
• The charge on the anion becomes the subscript on the
cation.
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• If these subscripts are not in the lowest whole-number
them by the greatest common factor.
CDOratio,
IB Chemistry divide
SL
Examples: Writing the Formula for Ionic Compounds
• Ca and Cl
• Ba and F
• Na and S
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CDO IB Chemistry SL
Polyatomic ions
• Cations or anions consisting of groups of atoms that are
covalently bonded to each other
• When more than one appears in a formula unit - the
polyatomic ion is put in between parentheses, and a
subscript is used to indication the number of the ions that
appear in the formula unit
• example: Ba(ClO3)2
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CDO IB Chemistry SL
Polyatomic Ions to Memorize
• Ammonium
• Acetate (Ethanoate)
• Hydrogen Carbonate
(Bicarbonate)
• Phosphate
• Carbonate
• Nitrate
• Hydroxide
• Sulfate
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CDO IB Chemistry SL
Types of Ionic Compounds
• Ionic compounds will always consist of one of the following
combinations:
• a metal and a nonmetal
• a polyatomic ion and a nonmetal
• a metal and a polyatomic ion or
• two polyatomic ions
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CDO IB Chemistry SL
Properties of Ionic Compounds
• High melting points that correlate with charges
on ions
• Most ionic solids do not conduct electricity but
molten ionic compounds do.
• Most ionic compounds dissolve in water
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Properties cont.
• Solutions of ionic compounds in water
conduct electricity (electrolytes)
• In ionic substances, each ion has its own
characteristics, and these are different
from the characteristics of the atom from
which the ion was derived (NaCl)
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CDO IB Chemistry SL
Binary Compound Nomenclature
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Ionic Nomenclature
• Write the name of the cation.
• If the cation is a polyatomic ion, write the name of the
polyatomic ion
• If the cation can have more than one possible charge, write the
charge as a Roman numeral in parentheses.
• If the anion is an element, change its ending to -ide;
• If the anion is a polyatomic ion, simply write the name of the
polyatomic ion.
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Examples Formula to Name
• NaCl
• MgCl2
• KBr
• CuCl
• CuCl2
• Al(NO3)3
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Example Name to Formula
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White Board Practice
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Binary Molecular Nomenclature
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Nonmetals + nonmetals
• Name nonmetal further to the left of the
periodic table first with no changes
• Name nonmetal further to the right of the
periodic table second with the -ide suffix
• Use Greek prefixes to indicate the number
of each one
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Greek prefixes
Number
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Prefix
1
2
3
Mono
Di
Tri
4
5
6
Tetra
Penta
Hexa
7
8
9
Hepta
Octa
Nona
10
Deca
CDO IB Chemistry SL
Examples
• N2O3
• CO2
• P2O5
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Acids
• Binary acids – H with one other non metal
• name begins with hydro
• then add stem of nonmetal plus -ic
• end with acid
• Examples
• HCl –
• H2S -
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CDO IB Chemistry SL
Oxyacids
• Take polyatomic suffix and convert
• change -ate to -ic
• change -ite to -ous
• Do not use hydro- in the beginning
• Examples
• H2SO4 –
• H2SO3 57
CDO IB Chemistry SL
Hydrates
• Some ionic compounds can have water
molecules attached within the structure
• These compounds are termed hydrates and
have properties distinct from the
unhydrated form
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Naming Hydrates
• Hydrates are named by naming the ionic
compound and then using a Greek prefix to
indicate the number of water molecules
followed by the word hydrate
• Example
CuCl2 5H20
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Formula Calculations
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Types of Formulas
• Empirical formulas give the lowest
whole-number ratio of atoms of each
element in a compound.
• Molecular formulas give the exact
number of atoms of each element in a
compound.
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Empirical Formula
• Simplest whole number ratio of atoms in the
compound
• All ionic formulas are empirical
• Molecular formulas are either equal to the
empirical or a whole number multiple
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The composition of compounds
• Mole composition is the number of moles of each
of the elements that make up the compound
• CO2 - one mole of C and two moles of O
• Mass composition is the mass of each element in
the compound
• CO2 - 12.0 g of C and 32.0 g of O
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Percent composition
• Equation
x(Molar
Mass of Element A)
x
100
Molar Mass Compound
• Example
Find the mass % of each element in CH2O (formaldehyde)
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White Board Practice
• Find the percent by mass of carbon in CO2
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Calculating Formulas
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Determination of Empirical formula
• Problem Solving Process:
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Example
• Example: A compound contains 63.6% N and 36.4% O,
determine the compounds empirical formula
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Example
• Determine the empirical formula for a compound which is 26.6% K, 35.4%
Cr, 38.0% O
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White Board Practice
• What is the empirical formula of a compound which is 26.4% N, 5.66% H
and 67.9 % C
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Molecular formula
• The actual number of each atom in a formula
unit
• Consider acetylene and benzene
• both have the empirical formula CH
• acetylene is actually C2H2
• benzene is actually C6H6
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Molecular Formula from Empirical
• Molecular formula must be integral multiple
of empirical formula
• Therefore the mass of the molecular
formula must be the same integral multiple
of the mass of the empirical formula.
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Example
• A compound has the following composition
20.0% C, 2.2 % H, 77.8 % Cl. The molar mass of
the compound is 545 g/mol. What is the
molecular formula of the compound
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White Board Practice
• A compound is composed f 1.65 g N and 3.78
g S, its molar mass is 184 g/mol, what is the
molecular formula?
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States of Matter
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States of Matter
• The three states of matter are described in terms of molecular motion, arrangement of the
particles and the forces between them
• The state of matter is dependent on the interparticle (intermolecular) forces
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Changes of State
• When the temperature increases enough for the particles to have sufficient
energy to overcome the interparticle forces a state change (physical change)
occurs
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Chemical Reactions
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What is a Chemical Equation?
• Shows the reactants
and
products and
their relative amounts in a reaction.
4 Al(s) + 3 O2(g)  2 Al2O3(s)
State Symbols
• Solid (s)
• Liquid (l)
• Gas (g)
• Aqueous (aq) – compound dissolved in water
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Chemical Equations
4 Al(s) + 3 O2(g)  2 Al2O3(s)
• This equation means
4 Al atoms + 3 O2 molecules give  2 molecules of Al2O3
OR
4 moles of Al + 3 moles of O2 give  2 moles of Al2O3
Chemical Equations
• Because the same atoms are present in a reaction at the
beginning and at the end, the amount of matter in a system does
not change.
• This represents the Law of the Conservation of Matter
• Chemical reactions are balanced to show the conservation of
matter is true
Tips for Balancing Equations
• You can never change a subscript to balance a reaction, you
can only add a coefficient
• The coefficient applies as a multiplier to each element in the
compound directly behind it, but not compounds separated by
a+
• Atoms on the same side of the reaction but in different
compounds add
• Balance H and O Last
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Balancing Equations
___ Al(s) + ___ Br2(l)  ___ AlBr3(s)
Examples: Balancing Equations
____C3H8(g)
+
_____ O2(g)

_____CO2(g)
+
_____ H2O(g)
____B4H10(g) + _____ O2(g) ___ B2O3(g) + _____ H2O(g)
White Board Practice
Balance each of the following reactions:
• N2 + H2  NH3
• Al + HCl  AlCl3 + H2
• BaCl2 + Na3PO4  Ba3(PO4)2 + NaCl
• C3H8 + O2  CO2 + H2O
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Stoichiometry
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STOICHIOMETRY
• the study of the
quantitative aspects
of chemical reactions
• It rests on the
principles of the
conservation of mass
Problem Solving Process
1. Write the balance chemical equation
2. Convert given amounts into moles, if amounts for each reactant is
given convert both amounts into moles to determine the limiting
reactant (more on this later)
3. Use the mole – mole relationships from the reaction to convert from
the moles you have to the moles of the other substance you want
4. Convert to the desired quantity requested and be sure your answer
has the correct units and correct significant figures. (this is called a
theoretical yield)
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Example
• If 454 g of NH4NO3 decomposes, how much H2O is formed? What
is the theoretical yield of the water?
NH4NO3  N2O + H2O
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Finding the Theoretical Yield
• % Yield = Actual Yield
Theoretical Yield
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x 100
Example
• Ethyne (Acetylene) is used in welding as its combustion gives a lot of heat.
2 C2H2 + 5O2  4CO2 + 3H2O
Calculate the mass of CO2 produced from the complete combustion of 1.00g
of C2H2?
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White Board Practice
• Iron is produced in a blast furnace by reduction of iron (III) oxide.
Fe2O3 + 3 CO  2 Fe + 3 CO2
Calculate the minimum mass iron (III) oxide needed to produce 800 g of Fe.
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Reactions Involving a
LIMITING REACTANT
LIMITING REACTANTS
Reactants
2 NO(g) + O2 (g)
Products
2 NO2(g)
Limiting reactant = ___________
Excess reactant = ____________
Limiting Reactants: An Analogy
• If you were going to make pb and j
sandwiches, and you had a new loaf of bread
and a large jar of pb and a large jar of jelly,
how many sandwiches can you make?
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Example: Limiting Reactants
• Mix 5.40 g of Al with 8.10 g of Cl2. What mass of AlCl3 can form?
Al(s) + Cl2(g)  AlCl3 (s)
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How much of which reactant will remain when reaction is
complete?
• Cl2 was the limiting reactant.
• Therefore, Al was present in excess. But how
much?
• First find how much Al was required.
• Then find how much Al is in excess.
Calculating Excess Al
2 Al + 3 Cl2
2 AlCl3
Reacting Gases
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Volumes of Reacting Gases
• Gay – Lussac’s Law – through observation he found
that when gases react, their volumes and that of any
products are in simple whole number ratios equal to
the ratio’s of moles in the balanced chemical
equation
Example – Reacting Gases
• 40 cm3 of carbon monoxide reacts with 40 cm3 of oxygen according to the
following reaction. What volume of carbon dioxide is produced? Assume
that the reaction takes place at the same temperature and pressure.
2CO(g) + O2(g)  2CO2(g)
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Molar Volume of Gas
Molar Volume
• Molar Volume – at standard temperature and pressure (STP
= 273K and 1 atm) the volume of 1 mole of gas = 22.4 dm3.
At room temperature (298K, RTP) molar volume = 24 dm3.
• Use – to calculate the mole of gas if you know the volume of
the gas (at STP or RTP)
Example – Molar Volume
Calculate the amount in moles of chlorine gas in 44.8 cm3 of the gas at STP.
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Example: Molar Volume
• How many liters of hydrogen can be produced by reacting 4.0 g of aluminum
with excess hydrochloric acid if the hydrogen is collected at STP.
2Al(s) + 6 HCl(aq)  2AlCl3(aq) + 3H2(g)
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The Gas Laws
Pressure
• Pressure – result of collisions between the particles with themselves and the
walls of its container.
• SI Unit for Pressure – N m-2 = Pascal
• Helpful conversions
• N = kg m
s2
• 1.00 atm = 1.01 x 105 Pa
• 1.00 atm = 760 mmHg
Boyles Law
• The volume of a fixed quantity of gas at constant temperature
is inversely proportional to the pressure.
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Graphical Representation
•
A plot of V versus P results in a
curve.
PV = k
Since:
V = k (1/P)
This means a plot of V versus
1/P will be a straight line.
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Example: Boyles Law
• The volume of some amount of a gas was 1.00 dm3 when the pressure was
10.0 atm; what would the volume be if the pressure decreased to 1.00 atm?
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Charles Law
• The volume of a fixed amount of
gas at constant pressure is
directly proportional to its
absolute temperature.
• i.e.,
V
=k
T
A plot of V versus T will be a straight line.
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Example: Charles Law
• A gas occupied a volume of 6.54 dm3 at 25°C what would its
volume be at 100°C?
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Amontons Law
• The pressure of a gas is directly related to absolute temperature of gas at
constant volume.
• Relationship
P a kT
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Combined Law
• This law combines Boyle’s Law, Charles’s Law and Amonton’s Law so
that the only constant variable is the amount (moles) of gas.
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Example: Combined Law
• What happens to the volume of a fixed amount of gas when the pressure and
absolute temperature are both doubled?
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Example: Combined Law
• A 1.00 dm3 balloon at 25.0oC has a pressure of 750 mmHg. If the
temperature is increased to 37.0oC and the pressure is decreased to 740
mmHg, what is the new volume?
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Ideal Gas Equation
• So far we have seen that:
• Combining these into one relationship:
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Proportionality Constant R
• The constant of
proportionality is
known as R, the ideal
gas constant.
• IB Uses
8.31 J mol -1 K-1
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Ideal Gas Equation
• The relationship:
• Becomes:
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Example – Ideal Gas Law
• If I have 0.275 moles of gas at a temperature of 275 K and a pressure of 1.75
atmospheres, what is the volume of the gas in dm3?
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Example – Ideal Gas Law
• If I have an unknown quantity of gas held at a temperature of 1195 K in a
container with a volume of 25 dm3 and a pressure of 560 atm, how many
moles of gas do I have?
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Calculating the Molar Mass
• Molar Mass (M)
M = m/n
123
m = grams
n = moles
Calculating the Density
• Density
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Example: Molar Mass
• A gaseous sample of a compound has a gas density of .977 g/L at
710.0 torr and 100oC. What is the molar mass of this compound?
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Example: Finding Density
• What is the density of acetone, C3H6O, vapor at 730 mmHg
and 127oC?
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Solutions
Solutions
• Solute – what is being dissolved, usually present in the smallest amount
• Solvent – what is doing the dissolving, usually present in the largest amount
• Solution – solute and solvent combined
• Aqueous solutions – solutions in which water is the solvent
Concentration
• Concentration – describes how much solute is dissolved in solvent
• Saturated solution – when the solute can no longer dissolve in the given
solvent
• Common Concentration units – g dm-3 or mol dm-3 (aka Molarity)
• [Concentration] = moles of solute
volume of solution (dm3)
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Example: Concentration
• A solution contains 4.10 g of NaCl in 1.00 dm3. What is the solutions
concentration in g dm-3 and mol dm-3.
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Standard Solution
• Definition – a solution of known concentration
• Calculating the amount of solute needed to make a standard solution –
Concentration = mol
dm3
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Example: Making a Standard Solution
• Calculate the mass of NaOH need to make 250 cm3 of a 0.200 mol dm-3
solution.
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Titrations
Titrations
• Laboratory
Technique – which
uses a standard
solution to find the
concentration of
another solution.
Example: Titration
What volume of 0.100 mol dm-3 NaOH is required to titrate 25 mL of 0.300 mole
dm-3 solution of HCl to produce a neutral solution?
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Calculations involving solutions and
Gases
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Example
• Calculate the volume of carbon dioxide produced when 1.00 g of calcium
carbonate reacts with 20.0 cm3 of hydrochloric acid. Assume the volume of
the gas is measured at STP
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