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CHEMISTRY 20
Quantitative Relationships in Chemical Change
BALANCING CHEMICAL REACTIONS
• Every chemical reaction involves the rearrangement of atoms into
different combinations. However, during these reactions, the total
number of atoms of each type of element is the same after the
reaction as it was before the reaction.
• Chemical reactions have to be properly balanced in order to clearly
obey the Law of Conservation of Matter.
• Every chemical reaction must first be written so that each reactant and
product has the correct chemical formula and state of matter.
• Coefficients are then used in order to balance the various atoms. All
coefficients must be in the simplest whole number ratio possible.
BALANCING CHEMICAL REACTIONS
Hints for balancing equations:
• Write out an unbalanced equation, making sure that each reactant and
product formula is written correctly.
• Use coefficients to balance any atoms that are not already balanced.
• If a polyatomic ion is remaining intact, it may be easiest to balance it
as a group.
• Always balance any elements last.
• Make sure that the coefficients have the simplest whole number ratio
possible.
EXAMPLES
Re-write the following word equations as balanced chemical equations.
sodium + chlorine →
Na(s) +
aluminium chlorate
→
Cl(s)
→
sodium chloride
NaCl(s)
aluminium + chlorine + oxygen
EXAMPLES
butane(C4H10(g)) + oxygen → carbon dioxide + water vapour
scandium + copper(II) sulfate → copper + scandium sulfate
hydrochloric acid + barium hydroxide → water + barium chloride
FORMATION REACTIONS
• A formation reaction is a reaction in which two or more
elements react together to form a compound.
• X + Y
→
XY
• N2(g) + 3 H2(g) → 2 NH3(g)
EXAMPLE
• Write a balanced chemical
equation for the formation of
glucose (C6H12O6(s)).
•
Write a balanced chemical equation
for the formation of ammonium
benzoate.
DECOMPOSITION REACTIONS
• A decomposition reaction is a reaction in which a compound
reacts and breaks down into its component elements.
• XY → X + Y
• 2 H2O(l) →
2 H2(g) + O2(g)
EXAMPLE
• Write a balanced chemical
equation for the decomposition of
diphosphorous heptaoxide.
• Write a balanced chemical
equation for the decomposition of
sodium sulfate.
COMBUSTION REACTIONS
• A complete combustion reaction is a reaction in which a
hydrocarbon burns in a plentiful supply of oxygen and the only
products are carbon dioxide and water vapour.
• CH4(g) + 2 O2(g) →
CO2(g) + 2 H2O(g)
EXAMPLE
• Write a balanced chemical
equation for the complete
combustion of hexane (C 6H14(l)).
• Write a balanced chemical
equation for the complete
combustion of methanol
(CH3OH(l)).
HOMEWORK
• Balancing Chemical Reactions practice questions
• page 5 in your notes
SINGLE REPLACEMENT REACTIONS
• A single-replacement reaction involves an atom of one
element taking the place of an atom of another element.
• These reactions typically involve an ionic compound reacting
with an element.
• Either the positive ion or the negative ion of the compound can
be replaced.
A + BX → AX + B
AX + Y → AY + X
Cu(s) + 2 AgNO3(aq) → 2 Ag(s) + Cu(NO3)2(aq)
EXAMPLE
• Write a balanced chemical
equation for the reaction
between zinc and hydrochloric
acid.
• Write a balanced chemical
equation for the reaction
between aluminium chloride and
bromine.
DOUBLE REPLACEMENT REACTIONS
• A double-replacement reaction involves two ionic compounds reacting
together. During the reaction, the positive ions switch places.
• Generally, the ionic compounds are dissolved (if soluble). These reactions
often result in the production of a precipitate (an insoluble ionic
compound).
• Neutralization reactions represent a special case of double-replacement in
which one of the compounds is an acid and the other compound is a base.
AX + BY → AY + BX
CuSO4(aq) + 2 NaOH(aq) → Na2SO4(aq) + Cu(OH)2(s)
EXAMPLE
• Write a balanced chemical
equation for the reaction
between aluminium nitrate and
ammonium phosphate.
• Write a balanced chemical
equation for the reaction
between hydrosulfuric acid and
potassium hydroxide.
CALCULATING AMOUNTS
The coefficients in a balanced
chemical equation represent the
relative amounts of the chemicals
that react with each other.
The actual amount of a chemical
can be found by using one of the
following equations:
• when the mass of a pure
substance is given:
m
n=
M
• when the volume and
molar concentration of a
solution is given:
n = cV
• when the pressure,
volume, and temperature
of a gas is given:
n=
PV
RT
EXAMPLE
• Calculate the amount of potassium carbonate in a 33.5 g
sample.
EXAMPLE
• Calculate the amount of zinc nitrate that must be dissolved to
prepare 750 mL of a solution that has a concentration of 15.8
mmol/L.
EXAMPLE
• Calculate the amount of helium in a 8.00 L balloon if it has a
pressure of 103 kPa at 22.0oC.
HOMEWORK
• Balancing Chemical Reactions practice questions
• Page 8-9 in your notes
Chemistry 20
NET IONIC EQUATIONS
NET IONIC EQUATIONS
• In replacement reactions, many of the reactants and products
exist as dissociated ions.
• Some of these dissociated ions remain unchanged in any way
throughout the reaction.
• For example, in the reaction between solutions of silver nitrate
and sodium chloride:
AgNO3(aq) + NaCl(aq) → NaNO3(aq) + AgCl(s)
• The Ag+ and Cl- react to form a solid precipitate.
• However, the Na+ and NO3- remain dissolved in both the
reactants and the products.
• They are classified as spectator ions, because they are left
unchanged by the reaction itself.
DEMO
• Potassium iodide + lead (II) nitrate
• https://www.youtube.com/watch?v=DITY2rXYU-I
DEMO
• Potassium iodide + lead (II) nitrate
• https://www.youtube.com/watch?v=DITY2rXYU-I
• The complete balanced equation for this reaction would be
2 KI(aq) + Pb(NO3)2(aq) → 2 KNO3(aq) + PbI2(s)
• An ionic equation shows all soluble ionic compounds as dissociated
ions. Strong acids are also shown as being completely ionized.
• The ionic equation for the previous reaction would be
2 K+(aq) + 2 I-(aq) + Pb2+(aq) + 2 NO3-(aq) → 2 K+(aq) + 2 NO3-(aq) + PbI2(s)
• The K+(aq) and NO3-(aq) are the spectator ions. They remain
unchanged throughout the reaction.
• The net ionic equation omits the spectator ions.
• The net ionic equation for this reaction is:
• Pb2+(aq) + 2 I-(aq) → PbI2(s)
EXAMPLE
• Write a complete balanced equation, ionic equation, and net
ionic equation for the reaction between barium hydroxide and
hydrochloric acid.
EXAMPLE
• Write a complete balanced equation, ionic equation, and net
ionic equation for the reaction between aluminium and copper(II)
nitrate.
QUALITATIVE VS QUANTITATIVE ANALYSIS
• Qualitative analysis involves determining by experiment
whether a certain substance is present in a sample.
• Quantitative analysis involves determining how much of a
certain substance is present in a sample.
• For aqueous solutions, typical qualitative analytic techniques
include observing solution colour, flame tests and precipitation
reactions.
• When certain ions are dissolved in water, they give the solution
a distinct color.
QUALITATIVE VS QUANTITATIVE ANALYSIS
• The more concentrated the ion is in the solution, the more
evident this characteristic colour will appear.
• Many metal ions produce a distinct colour of flame when they
are heated.
• One way to test for the presence of metal ions in solution is to
heat a drop of the solution in a hot flame and observe the
colour. This is called a flame test.
• The different colours that fireworks can have are due to the
explosive ignition of different metals and metal salts.
HOMEWORK
• Practice Questions on page 11 and 14 in your notes
Chemistry 20
SELECTIVE PRECIPITATION
SELECTIVE PRECIPITATION
• Precipitation reactions can determine whether an ion is present
in solution or not.
• A precipitation reaction is another term for a doublereplacement reaction in solution that produces a solid product
(the precipitate).
• Chemists add dissolved substances to unknown solutions and
observe whether a precipitate forms.
• https://www.youtube.com/watch?v=PaA5LOawjpE
At each stage, the colour of the solution is observed and the resulting
precipitate is removed.
Flame tests can be used to identify the precipitates.
EXAMPLE
• You are given an unidentified solution and are told that it may or
may not contain sulfide ions. How could you confirm or deny
the presence of S 2-(aq) in this solution?
EXAMPLE
• You are given an unidentified solution and are told that it may or
may not contain zinc ions. How could you confirm or deny the
presence of Zn2+(aq) in this solution?
• If a solution contains more than one dissolved ion, it is
essential to design the technique carefully so that only
one precipitate is formed.
EXAMPLE
• You are given an unidentified solution and are told that it may or
may not contain acetate ions and/or sulfate ions. How could
you confirm or deny the presence of CH 3COO-(aq) and/or
SO42-(aq) in this solution?
EXAMPLE
• You are given an unidentified solution and are told that it may or
may not contain lead(II) ions and/or aluminium ions. How could
you confirm or deny the presence of Pb 2+(aq) and/or Al3+(aq) in this
solution?
• Flame test demo
• Homework: Practice Questions pg 17/18
• Remember you have a quiz on Wednesday, up to and including
today!
Chemistry 20
STOICHIOMETRY
STOICHIOMETRY
• Balanced chemical equations are essential to doing calculations
and making predictions related to quantities in a chemical
reaction.
• The balancing coefficients in a chemical equation illustrate the
relative number of particles of each chemical involved.
• For example, the production of nitrogen dioxide has the
following balanced chemical equation:
2 NO(g) + O2(g) → 2 NO2(g)
2 NO(g) + O2(g) → 2 NO2(g)
For every 2 molecules of NO 2(g) that are produced, 2 molecules of
NO(g) and 1 molecule of O 2(g) have been consumed.
• Because of the large numbers of molecules involved in any
chemical reaction, it is more convenient to compare the amount
(number of moles) of the reactants and products.
• For every 2 mol of NO2(g) that are produced, 2 mol of NO(g) and
1 mol of O2(g) have been consumed.
• In a reaction, the actual amounts involved may vary but this
ratio will always be observed.
EXAMPLE
• Use the following reaction to determine the missing amounts.
C3H8 (g)
+
5 O2 (g)
→
3 CO2 (g)
+
4 H2O (g)
EXAMPLE
• What amount of zinc will be produced by the decomposition of
0.40 mol of zinc phosphate?
EXAMPLE
• During the formation of benzoic acid, 0.366 mol of carbon is
consumed. What amount of hydrogen will have been consumed
during this reaction?
HOMEWORK
• Practice problems in your notes pg 21-22
Chemistry 20
GRAVIMETRIC STOICHIOMETRY
GRAVIMETRIC STOICHIOMETRY
• Gravimetric stoichiometry is the analysis of the various masses
of reactants and/or products involved in a chemical reaction.
• However, the coefficient ratio can only be used to compare
amounts of chemicals.
• For example, in the formation of carbon dioxide gas,
C(s) + O2(g) → CO2(g)
it would be correct to say that 1 mol of carbon reacts with 1 mol
of oxygen, but it would be incorrect to say that 1 g of carbon
reacts with 1 g of oxygen.
STOICHIOMETRIC PROCESS
1. Write a balanced chemical equation.
2. Using the information given, calculate the amount of the given
substance (ngiven) by the following equation:
3. Calculate the amount of the required substance (nrequired)
using the mole ratio from the balanced equation and the ngiven
you calculated in step 2.
4. Calculate the mass of the required substance using the
nrequired you calculated in step 3 by the following equation:
EXAMPLE
• What mass of oxygen must be available in order to burn 120 g
of ethane (C2H6(g))?
EXAMPLE
• Solid lithium hydroxide reacts with carbon dioxide gas to
produce lithium carbonate and water vapour. What mass of
lithium carbonate will be produced when 5.00 g of lithium
hydroxide is used up?
EXAMPLE
• Solutions of sodium bromide and lead(II) acetate are mixed
together. The precipitate is filtered, dried, and found to have a
mass of 2.17 g. What minimum mass of lead(II) acetate was
dissolved in the original solution?
HOMEWORK
• Practice problems in your notes pg 25-26
Chemistry 20
SOLUTION STOICHIOMETRY
SOLUTION STOICHIOMETRY
• Reactions taking place in aqueous environments are typically
between solute particles. Generally, the water solvent
molecules are not involved in the reaction itself.
• Solution stoichiometry follows the same general process as
gravimetric stoichiometry except that molar concentrations and
volumes can be used to calculate amounts.
• These questions typically include the use of the following
equation:
n = cV
EXAMPLE
• What volume of 0.214 mol/L sodium hydroxide would be
required to completely neutralize 500 mL of 0.0104 mol/L
hydrochloric acid?
EXAMPLE
• A 100 mL portion of hydrochloric acid is able to react with 5.00 g
of zinc. What is the concentration of the hydrochloric acid
solution?
EXAMPLE
• A student mixes 225 mL of 0.078 mol/L cobalt(II) nitrate with an
excess volume of sodium hydroxide. Predict the mass of
precipitate that should be made.
HOMEWORK
• Practice problems in your notes pg 28-29
Chemistry 20
GAS STOICHIOMETRY
n
PV
RT
GAS STOICHIOMETRY
• With gases, we use the Ideal Gas Law:
PV
n=
RT
EXAMPLE
• A solution of hydrochloric acid is able to react completely with
5.00 g of zinc. What volume of hydrogen gas will be produced
at 21.0oC and 99.6 kPa?
EXAMPLE
• A sample of cyclopentane (C5H10(l)) is burned completely.
During the reaction, 125 L of oxygen at SATP is consumed.
What mass of cyclopentane has been burned?
HOMEWORK
• Practice problems in your notes page 31-32
Chemistry 20
LIMITING AND EXCESS REACTANTS
STOICHIOMETRIC AMOUNTS
• The coefficients of a balanced chemical equation are often called the
stoichiometric coefficients because they are used in stoichiometric
calculations.
• If the reactants are present in the amounts that correspond exactly to
the mole ratios, they are said to be present in stoichiometric
amounts.
• When the reactants are in stoichiometric amounts, then absolutely no
trace of any of the reactants will be left at the end of the reaction .
• In most reactions, one of the reactants may run out before the others.
There will usually be one or more of the reactants left over without
getting a chance to completely react.
• In these cases, the amount of product that results from a chemical
reaction is limited by the reactant that is used up or completely
consumed first.
• The reactant that is completely used up in the reaction is called the
limiting reactant. It is also known as the limiting reagent.
• Any reactant(s) that are left over are called the excess reactant.
• The limiting reactant does not need to be the reactant present in
fewer moles. Rather, it is the reactant that will form fewer moles of
product(s).
LIMITING REACTANTS
• For example, the reaction of 1.5 mol of hydrogen with 1.0 mol of
oxygen to produce water
2 H2(g) + O2(g) →
2 H2O(l)
would find that the hydrogen is fully used up first, creating a
maximum amount of 1.5 mol of water.
• To identify the limiting reactant, you must have a balanced
chemical equation and calculated amounts of how much of each
reactant there is. Use these amounts to calculate the maximum
amount of product that can be created.
EXAMPLE
• A 1.25 g piece of magnesium is placed into 80.0 mL of 0.113
mol/L hydrochloric acid. Which reactant is the limiting reactant?
What amount of the excess reactant will remain unreacted at the
completion of the reaction?
EXAMPLE
• Calculate the mass of precipitate that should be produced when
200 mL of 0.118 mol/L iron(II) sulfate is mixed with 175 mL of
0.204 mol/L ammonium phosphate.
HOMEWORK
• Practice questions pg 34 in your notes
Chemistry 20
PREDICTED AND EXPERIMENTAL YIELD
PREDICTED AND EXPERIMENTAL YIELD
• Stoichiometry calculations can be used to predict the maximum
quantity of product expected from a reaction. This quantity is known
as the predicted yield (which is also known as the theoretical yield).
• The predicted yield is calculated on the assumption that all the limiting
reactant reacts to make product on the ratio described by the
balanced equation.
• The quantity of product actually obtained by a reaction is called the
experimental yield (which is also known as the actual yield).
• In most reactions, the experimental yield will not match exactly with
the predicted yield. Usually, it is a lower value than the predicted
yield.
FACTORS THAT LIMIT EXPERIMENTAL YIELD
Competing Reactions:
• In some circumstances, the same two reactants can react to give different
products
• For example, when carbon burns in a plentiful supply of oxygen, it reacts to
produce carbon dioxide
C(s) + O2(g) → CO2(g)
• However, even in a plentiful supply of oxygen, carbon monoxide can be
produced
2 C(s) + O2(g) → 2 CO(g)
• This secondary reaction is an example of a competing reaction. Since
some of the carbon reacts to form carbon monoxide, the experimental yield
of carbon dioxide will always be less than predicted.
FACTORS THAT LIMIT EXPERIMENTAL YIELD
Slow Reaction:
• If a reaction is slow and not enough time has been allowed for
the reaction to reach completion, the quantity of products
measured will be less than predicted.
FACTORS THAT LIMIT EXPERIMENTAL YIELD
Collection and Transfer Methods:
• If a precipitate is collected by filtration, some of it may remain
dissolved in the filtrate.
• When a precipitate is rinsed to remove traces of the reactants,
some of the precipitate may dissolve in the rinsing solvent.
• Mechanical losses are the small amount of product that are lost
when they remain stuck to glassware or filter paper as they are
transferred in the lab.
FACTORS THAT LIMIT EXPERIMENTAL YIELD
Reactant Purity:
• Many chemicals used in the laboratory that are reactant-grade
may be close to 100% pure, but there may be trace amounts of
contaminants.
FACTORS THAT LIMIT EXPERIMENTAL YIELD
Reactions That Do Not Proceed To Completion:
• Many reactions reach a point where the reaction appears to stop,
although less than 100% of the reactants have been converted into
products.
• These reactions have reached equilibrium and the products are
reacting to form the reactants at the same rate as the reactants are
reacting to form the products.
• For example, under most conditions, only a small percentage of
hydrogen and iodine molecules have reacted to form hydrogen iodide
at any one time:
H2(g) + I2(g)
 2 HI(g)
CALCULATING PERCENT YIELD
• Ideally, a percentage yield is as close to 100% as possible. It
can be calculated by the following equation:
experimental yield
percentage yield =
× 100%
predicted yield
For example, when magnesium metal is heated strongly in air, it
reacts with oxygen to make magnesium oxide.
• If 2.50 g of magnesium was reacted, the predicted yield of
magnesium oxide from a stoichiometry calculation would be
4.15 g. If the mass of product was measured to be only 3.96 g,
then the percentage yield would be:
experimental yield
percentage yield =
× 100%
predicted yield
3.96 g
percentage yield =
× 100%
4.15 g
percentage yield = 95.4%
EXAMPLE
A student mixes together two solutions in the lab and forms a
precipitate. The following data is recorded:
• Solution A: 85.0 mL of 0.172 mol/L potassium phosphate
• Solution B: 120.0 mL of 0.144 mol/L calcium nitrate
• Mass of filter paper: 1.14 g
• Mass of filter paper + dried precipitate: 2.85 g
Calculate the percent yield for this reaction.
PRACTICE
Chemistry 20
ACID-BASE TITRATION
ACID-BASE TITRATION
• In a titration, the concentration of one solution is determined by
quantitatively observing its reaction with a standard solution (ie.
a solution of known concentration).
• The observations can be used to standardize the solution (ie.
determine its unknown concentration).
• The predicted yield is calculated on the assumption that all the
limiting reactant reacts to make product on the ratio described
by the balanced equation.
ACID-BASE TITRATION SET-UP
• The solution that is placed into the
burette is known as the titrant. By
measuring the initial burette volume
(prior to beginning the titration) and
the final burette volume (at the
completion of the titration), the
volume of titrant required to
complete the reaction can be
determined.
• The solution that is placed into the
Erlenmeyer flask is known as the
aliquot. The volume of the aliquot is
pre-determined before the reaction
begins - a volumetric pipette is used
to measure the aliquot.
• Either the aliquot or the titrant can
be the standard solution.
ACID-BASE TITRATION
• The stage of the titration at which the reaction is complete is
called the equivalence point. At this point, stoichiometrically
equivalent amounts of each reactant have been consumed.
• In acid-base titrations, an acid-base indicator is added to the
aliquot to provide visual evidence of the end of the reaction. A
dramatic colour change of the indicator identifies when the
reaction is complete.
• The point at which the indicator changes colour is called the
endpoint.
EQUIVALENCE POINT
• In an acid-base titration, an acid titrant is added to a base
aliquot, or vice versa.
• For monoprotic acids and bases, the point at which equal moles
of reactant acid and base combine is called the equivalence
point of the titration.
EQUIVALENCE POINT
• For example, the titration of sodium hydroxide with hydrochloric
acid.
HCl(aq) + NaOH(aq)
H2O(l) + NaCl(aq)
• The mole ratio is 1:1. Therefore, the equivalence point occurs
when an equal amount of HCl(aq) has been added to the
NaOH(aq).
• In every reaction between a strong monoprotic acid and a strong
base, the equivalence point has a pH of 7 because all
hydronium ions from the acid have been neutralized by an equal
amount of hydroxide ions from the base.
• Acid-base titrations are performed with repeated trials until at
least 3 concordant results are obtained.
• A concordant result means the titrant volumes required to
reach the equivalence point are within a range of 0.2 mL.
• Most neutralization reactions involve colourless solutions with
no obvious visible evidence that a reaction is taking place.
• An acid-base indicator is a substance that changes colour over
a given pH range.
• Usually, indicators are weak monoprotic acids. The molecular
and ionized forms of the indicator have different colours.
• For example, bromothymol blue is a commonly used indicator
for titrations. It is yellow between pH 0 and pH 6. It turns blue
between pH 6 and pH 7.6.
• This indicator is commonly used for titrations between a strong
monoprotic acid and a strong base.
TITRATION DEMONSTRATION
Chemistry 20
PH CURVES
• When a strong base titrant is reacted with a strong acid aliquot,
the characteristic shape that should be predicted is:
• When a strong acid titrant is reacted with a strong base aliquot,
the characteristic shape that should be predicted is:
CHOOSING AN INDICATOR
• Titrations are usually performed with indicators because they
are cheaper than pH meters and have easy to recognize colour
changes at the equivalence point.
• The titration can only be done accurately if a suitable indicator is
chosen.
• The endpoint pH of the indicator must be within the steep rise or
drop in the titration curve.
• Ideally, the endpoint of the indicator would occur right at the
equivalence point of the reaction.
CHOOSING AN INDICATOR
Whenever a titration
is between a strong
monoprotic acid
and a strong
monoprotic base,
the equivalence
point will be
observed at a pH of 7.00.
Therefore, the most appropriate choice for indicator for this type of
titration is either bromothymol blue or phenol red.