Download Unit D: Quantitative Relationships in Chemical Change

CHRIST THE
REDEEMER
CATHOLIC
SCHOOLS
UNIT D: QUANTITATIVE
RELATIONSHIPS IN CHEMICAL CHANGE
Chemistry 20 | Mrs. Sample
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.

Hints for balancing equations:
1. Write out an unbalanced equation, making sure that each reactant and product formula
is written correctly.
2. Use coefficients to balance any atoms that are not already balanced.
3. If a polyatomic ion is remaining intact, it may be easiest to balance it as a group.
4. Always balance any elements last.
5. Make sure that the coefficients have the simplest whole number ratio possible.

EX: Re-write the following word equations as balanced chemical equations.
(a) sodium + chlorine →
(b) aluminium chlorate
→
(c) butane(C4H10(g)) + oxygen
sodium chloride
aluminium + chlorine + oxygen
→ carbon dioxide + water vapour
(d) scandium + copper(II) sulfate → copper + scandium sulfate
→
(e) hydrochloric acid + barium hydroxide
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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
N2(g) + 3 H2(g) →
XY
2 NH3(g)

EX: Write a balanced chemical equation for the formation of glucose (C6H12O6(s)).

EX: 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)

EX: Write a balanced chemical equation for the decomposition of diphosphorous
heptaoxide.

EX: Write a balanced chemical equation for the decomposition of sodium sulfate.
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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)

EX: Write a balanced chemical equation for the complete combustion of hexane (C6H14(l)).

EX: Write a balanced chemical equation for the complete combustion of methanol
(CH3OH(l)).
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PRACTICE: BALANCING CHEMICAL
REACTIONS
1. Balance the following chemical equations by correctly filling in the coefficients.
a) _____ Ni (s) + _____ Br2 (l)
b) _____ Al2(CO3)3 (s)
→
→
_____ NiBr3 (aq)
_____ Al2O3 (s) + _____ CO2 (g)
_____ C5H12 (aq) + _____ O2 (g)
→
_____ CO2 (g) + _____ H2O (g)
d) _____ CrCl2 (aq) + _____ Sn (s)
→
_____ SnCl4 (aq) + _____ Cr (s)
c)
e)
_____ ZnCl2 (aq) + _____ (NH4)3PO4 (aq)
→
_____ NH4Cl (aq) + _____ Zn3(PO4)2 (s)
2. Write a balanced chemical equation for each of the following.
a) The complete combustion of dodecane (C12H26(l))
b) The formation of calcium dihydrogen phosphate
c) The decomposition of titanium(IV) cyanide
d) The formation of sulfur trioxide
e) The complete combustion of benzoic acid.
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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)

EX: Write a balanced chemical equation for the reaction between zinc and hydrochloric acid.

EX: 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)
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
EX: Write a balanced chemical equation for the reaction between aluminium nitrate and
ammonium phosphate.

EX: 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:
n
m
M
ncV
n
PV
RT
use when the mass of a pure substance is given
use when the volume and molar concentration of a
solution is given
use when the pressure, volume, and temperature of a gas
is given
EX: Calculate the amount of potassium carbonate in a 33.5 g sample.
EX: 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.
EX: Calculate the amount of helium in a 8.00 L balloon if it has a pressure of 103 kPa at
22.0oC.
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PRACTICE: BALANCING CHEMICAL REACTIONS
1. Change each of these word equations into a balanced chemical equation. Classify each of
these reactions as one of the five common types of reactions.
a. carbon + hydrogen + oxygen → benzoic acid
b. ethanol(C2H5OH(l)) + oxygen → carbon dioxide + water
c. lead(II) chlorate + germanium → germanium chlorate + lead
d. cobalt(III) hydrogen sulfate → cobalt + hydrogen + sulfur + oxygen
e. chromium(III) sulfate + calcium nitrate →
calcium sulfate + chromium(III) nitrate
2. Write a balanced chemical equation for each of the following reactions:
a. The decomposition of nickel(II) dichromate.
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b. The combustion of C6H13OH(l).
c. The formation of titanium(IV) thiosulfate.
d. The reaction between aluminium and iron(III) nitrate.
e. The reaction between ammonium sulfide and nickel(III) chlorate.
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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: Mix together a test tube of potassium iodide with a test tube of lead(II) nitrate.

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)

EX: Write a complete balanced equation, ionic equation, and net ionic equation for the
reaction between barium hydroxide and hydrochloric acid.

Ionic and net ionic equations can also be written for single replacement reactions.

EX: Write a complete balanced equation, ionic equation, and net ionic equation for the
reaction between aluminium and copper(II) nitrate.
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PRACTICE: IONIC AND NET IONIC EQUATIONS
1. Write a complete balanced equation for the following reactions:
a. The formation of manganese(II) phosphate
b. The decomposition of potassium hydrogen oxalate
c. The complete combustion of benzene (C6H6(l))
2. Write an ionic equation for each of the following replacement reactions:
a. The reaction between aluminium and iron(III) nitrate.
b. The reaction between ammonium sulfide and nickel(III) chlorate.
3. Write a net ionic equation for each of the following replacement reactions:
a. The reaction between chromium(II) sulfate and sodium hydroxide.
b. The reaction between magnesium and titanium(IV) chloride.
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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.
Anions
Cations
Ions
Symbol
Colour
chromium(II)
Cr2+(aq)
copper(II)
Cu2+(aq)
chromium(III)
Cr3+(aq)
copper(I)
Cu+(aq)
iron(II)
Fe2+(aq)
nickel(II)
Ni2+(aq)
iron(III)
Fe3+(aq)
pale yellow
cobalt(II)
Co2+(aq)
pink
manganese(II)
Mn2+(aq)
chromate
CrO42-(aq)
yellow
dichromate
Cr2O72-(aq)
orange
permanganate
MnO4-(aq)
purple
blue
green

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.
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
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.
Ions
Symbol
Colour
lithium
Li+(aq)
red
sodium
Na+(aq)
yellow
potassium
K+(aq)
violet
calcium
Ca2+(aq)
yellowish-red
strontium
Sr2+(aq)
red
barium
Ba2+(aq)
yellowish-green
copper(II)
Cu2+(aq)
bluish-green
DEMO: FLAME TEST OF VARIOUS SOLUTIONS
Lab Design:

A variety of unidentified solutions will be provided.

A metal loop will be dipped into a solution and then placed into the blue flame of a Bunsen
burner.

The colour of the flame will be observed.

The metal loop will be cleaned by dipping it into hydrochloric acid and then being placed into
the flame. This will be repeated 3 times.

The remaining solutions will then be tested, with the metal loop being cleaned in between
each test.
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PRACTICE: NET IONIC EQUATIONS
For each of the following chemical reactions, write a complete balanced equation and a net ionic
equation.
1. The reaction between zirconium and aluminium chlorate.
2. The reaction between cobalt(II) sulfate and ammonium hydroxide.
3. The reaction between gallium acetate and potassium.
4. The reaction between magnesium bromide and sodium phosphate.
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SELECTIVE PRECIPITATION

Precipitation reactions can determine whether an ion is present in solution or not.

A precipitation reaction is another term for a double-replacement reaction in solution that
produces a solid product (the precipitate).

Chemists add dissolved substances to unknown solutions and observe whether a precipitate
forms.

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.

EX: 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 S2-(aq) in this solution?

EX: 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?
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
If a solution contains more than one dissolved ion, it is essential to design the technique
carefully so that only one precipitate is formed.

EX: 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 CH3COO-(aq)
and/or SO42-(aq) in this solution?

EX: 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 Pb2+(aq)
and/or Al3+(aq) in this solution?
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PRACTICE: SELECTIVE PRECIPITATION
1. What amount of calcium nitrate would be found in a 300 g sample?
2. What volume would 650 g of dinitrogen tetroxide gas occupy in order to exert a pressure
of 650 mm Hg at 212oC?
3. Write a complete balanced equation, an ionic equation and a net ionic equation for the
reaction between silver nitrate and titanium(IV) acetate.
4. You have been given a clear, colourless solution. You do several qualitative
experimental tests on the solution and get the following results: (1) the flame test shows
a bit of a red colour; and (2) a precipitate is formed when ammonium sulfate is added.
What cation(s) might be present in this solution? What additional test could you do that
would help you to be more certain as to which cation is actually present?
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5. You have been given a solution that contains chloride ions and/or iodate ions. Design a
selective precipitation procedure that would allow you to determine which of these ions
(if either at all) are present.
6. You have been given a solution that contains lead(IV) ions and/or zinc ions. Design a
selective precipitation procedure that would allow you to determine which of these ions
(if either at all) are present.
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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)

For every 2 molecules of NO2(g) that are produced, 2 molecules of NO(g) and 1 molecule of
O2(g) have been consumed.

Because of the large numbers of molecules involved in any chemical reaction, it is more
convenient to compare the amount 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.
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
EX: Use the following reaction to determine the missing amounts.
C3H8 (g)
A
B
C
+ 5 O2 (g)
→
3 CO2 (g)
+ 4 H2O (g)
1.28 mol
0.38 mol
6.2x10-3 mol
D
758.3 mol

EX: What amount of zinc will be produced by the decomposition of 0.40 mol of zinc
phosphate?

EX: During the formation of benzoic acid, 0.366 mol of carbon is consumed. What amount
of hydrogen will have been consumed during this reaction?
20
PRACTICE: STOICHIOMETRY
For each of the following questions, write a balanced chemical equation and then use the mole
ratio to answer the question.
1. A student mixes together a solution of silver nitrate with a solution of sodium chromate
and a precipitate forms. What amount of precipitate will form if the student has reacted
0.314 mol of silver nitrate?
2. When ammonia (NH3(g)) is mixed with carbon dioxide, the products are water vapour and
urea (NH2CONH2(s)). What amount of water vapour is formed when 6.00 mol of carbon
dioxide has reacted?
3. Ammonia can react with sulfuric acid to produce ammonium sulfate. What amount of
ammonia is required to react fully with 3.28 mol of sulfuric acid?
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4. The decomposition of titanium(III) sulfate produces 0.914 mol of sulfur. What amount
of the compound has reacted?
5. The complete combustion of lauric acid, CH3(CH2)10COOH(s), produces carbon dioxide
and water vapour. Calculate the amount of oxygen that must react if this combustion
reaction produces 4.55 mol of carbon dioxide.
6. What amount of aluminium will be able to react completely with 2.19 mol of zinc nitrate?
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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:
a. Write a balanced chemical equation.
b. Using the information given, calculate the amount of the given substance (ngiven)
by the following equation:
n
m
M
c. Calculate the amount of the required substance (nrequired) using the mole ratio
n required
n given
from the balanced equation and the ngiven you calculated in step 2.
n required  n given x mole ratio
d. Calculate the mass of the required substance using the nrequired you calculated in
step 3 by the following equation:
m required  n required x M

EX: What mass of oxygen must be available in order to burn 120 g of ethane (C2H6(g))?
23

EX: 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?

EX: 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?
24
PRACTICE: MASS STOICHIOMETRY
1. Write a balanced chemical equation for the formation of iron(II) thiocyanate.
a) What mass of the compound can be produced when 50.0 g of iron completely reacts?
b) What mass of the compound can be produced when 50.0 g of nitrogen completely reacts?
c) What mass of sulfur must have reacted in order to produce 75 g of the compound?
2. Write a balanced chemical equation for the combustion of butane (C4H10).
a) What mass of oxygen is required to completely react with 30.0 g of butane?
b) What mass of carbon dioxide will be produced when 75.00 g of butane is burned?
c) What mass of water vapor will be produced during a reaction in which 3.85 g of carbon
dioxide is also produced?
25
3. Write a balanced chemical equation for the reaction between zinc and silver nitrate.
a) What mass of zinc is required to completely react with 14 g of silver nitrate?
b) What mass of silver can be produced when 40.0 g of zinc is completely reacted?
c) What mass of zinc nitrate will be produced if 11.0 g of silver nitrate is completely
consumed?
26
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 that 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:

EX: What volume of 0.214 mol/L sodium hydroxide would be required to completely
neutralize 500 mL of 0.0104 mol/L hydrochloric acid?

EX: 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?

EX: 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.
ncV
27
PRACTICE: SOLUTION STOICHIOMETRY
1. Ethanoic acid, CH3COOH(l), is produced according to the following chemical equation:
CH3OH(l) + CO(g) → CH3COOH(l)
Calculate the mass of ethanoic acid that would be produced by the reaction of 6.0 x 106 g of
CO(g) with sufficient CH3OH(l)
2. Sulfuric acid can be neutralized by reacting it with potassium hydroxide. What volume
of 0.676 mol/L sulfuric acid can be neutralized by 41.7 mL of 0.442 mol/L potassium
hydroxide?
3. When solutions of lead(II) nitrate and sodium iodide are mixed, a bright yellow
precipitate appears.
a. What volume of 0.125 mol/L sodium iodide is necessary to precipitate all the
aqueous lead(II) ions in 25.0 mL of 0.100 mol/L lead(II) nitrate?
b. What mass of precipitate is formed in this reaction?
28
4. Calculate the mass of the compound produced when 323 g of Cl2(g) reacts completely
during the formation of phosphorus trichloride.
5. When heated, calcium carbonate decomposes into calcium oxide and carbon dioxide.
What mass of calcium carbonate must be decomposed in order to produce 500 kg of
calcium oxide?
6. What minimum volume of 0.50 mol/L aqueous magnesium chloride to you need to add to
60 mL of 0.30 mol/L aqueous silver nitrate to remove all of the chloride ions?
29
GAS STOICHIOMETRY

These questions use:
n
PV
RT

EX: 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?

EX: 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?
30
PRACTICE: GAS STOICHIOMETRY
1. a) What is the volume of 2.0 mol of chlorine gas at 75 kPa and 27oC?
b) What amount, in moles, of an unknown gas occupies 3.2 L at 16.6 kPa and 127oC?
c) What amount, in moles, of C3F8(g) occupies 12.5 mL at 620 mm Hg and -120oC?
2. The formation of magnesium oxide takes place, producing 2.55 g of compound. What
volume of oxygen gas at 93.7 kPa and 27.0oC has been consumed?
3. During a combustion reaction, 25.0 g of propane (C3H8(g)) is burned in a 75.0 L steel
tank. At the end of the reaction, the internal temperature of the tank is measured to be
275oC. Calculate the pressure of the carbon dioxide gas produced by this reaction.
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4. If 85.0 g of nitrogen gas reacts with an excess of chlorine gas in a formation reaction,
what volume (in L) of nitrogen trichloride gas at 35.0oC and 98.9 kPa would be
produced?
5. What volume (in L) of chlorine gas at 2.30 atm and 36.5oC is required to completely react
with 140 g of sodium bromide?
6. What mass (in g) of sulfur dioxide gas must be decomposed in order to produce 13.0 L of
oxygen gas at 18.5oC and 2.44 bar?
32
LIMITING AND EXCESS REACTANTS

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).

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.

EX: 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?

EX: 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.
33
PRACTICE: LIMITING REACTANT
1. What would be the limiting reactant if 100.0 mL of a 0.5 mol/L solution of magnesium
nitrate was mixed with 125.0 mL of a 0.8 mol/L solution of sodium phosphate?
Calculate the expected mass of precipitate in this reaction.
2. Would 600 mL of 0.085 mol/L sodium sulfide be sufficient to remove all the mercury(II)
ions from 200 mL of 0.221 HgCl2(aq)? Explain your answer.
3. What volume of hydrogen gas will be produced at SATP when 2.00 g of magnesium
reacts with 300 mL of 0.105 mol/L hydroiodic acid?
4. Calculate the maximum amount of molybdenum sulfate that can be produced by a
formation reaction when 50 g of molybdenum, 50 g of sulfur and 50 g of oxygen react
together.
5. Determine the concentration of the copper(II) ions remaining in solution after the reaction
between 400 mL of 0.300 mol/L copper(II) nitrate and 150 mL of 0.150 mol/L sodium
hydroxide.
34
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 THE EXPERIMENTAL YIELD
1. 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.
2. 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.
3. 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.
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4. 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.
5. 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 THE PERCENTAGE YIELD OF A REACTION

Ideally, a percentage yield is as close to 100% as possible. It can be calculated by the
following equation:
Percentage yield 
Experiment al yield
x 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:
Percentage yield 
Experiment al yield
x 100%
Predicted yield
Percentage yield 
3.96 g
x 100%
4.15 g
Percentage yield  95.4%
36

EX: 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.
37
PRACTICE: PERCENTAGE YIELD
1. For the following reaction:
Fe(s) + CuCl2(aq) →
FeCl2(aq) + Cu(s)
a) What is the predicted yield of copper if 10.0 g of Fe(s) is reacted with an excess amount of
CuCl2(aq)?
b) What would be the percentage yield if 9.0 g of Cu(s) is actually obtained?
2. Calculate the percentage yield if 60 g of sulfur dioxide is produced by a formation
reaction in which 50 g of sulfur was available to react.
3. The fermentation enzymes of baker’s yeast convert a solution of glucose to ethanol and
carbon dioxide based on the following reaction:
C6H12O6(aq)
baker’s yeast
2 C2H5OH(aq) + CO2(g)
If 223 g of ethanol is obtained from the fermentation of 1.63 kg of glucose, what is the
percentage yield?
38
4. The reaction of toluene with potassium permanganate proceeds with significantly less than
100% yield under most conditions:
C7H8(l) + 2 KMnO4(aq) → KC7H5O2(aq) + 2 MnO2(s) + KOH(aq) + H2O(l)
a) If 8.60 g of toluene, C7H8(l), reacts with excess potassium permanganate, what is the
predicted yield, in grams, of potassium benzoate, KC7H5O2(aq)?
b) If the percentage yield is 70.0%, what mass of potassium benzoate would you expect to
be produced?
c) What mass of toluene is needed to produce 13.4 g of potassium benzoate if the
percentage yield is 60.0%?
39
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.

A typical titration set-up is shown here.
burette
burette clamp
titrant
retort stand
stopcock valve
Erlenmeyer Flask

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.
40

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.

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.
The 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.

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.
41
H3O+(aq) + In-(aq)
HIn(aq) + H2O(l)
colour 1
colour 2

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.
DEMONSTRATION
The titration of 10.0 mL of hydrochloric acid with
0.16 mol/L sodium hydroxide
Trial #
1
2
Initial Burette Volume
(mL)
Final Burette Volume
(mL)
Equivalence Point
(mL)
Use this data to calculate [HCl(aq)].
42
3
4
5
6
PRACTICE: TITRATIONS
1. Find the molar concentration of the sodium carbonate solution, given the following:
Titration of 25.0 mL of sodium carbonate with 0.352 mol/L hydrochloric acid
Trial #
1
2
3
4
Initial buret reading (mL)
0.0
15.9
31.2
1.4
Final buret reading (mL)
15.9
31.2
46.4
16.6
Equivalence point (mL)
2. Find the molar concentration of the potassium hydroxide solution, given the following:
Titration of 10.0 mL of potassium hydroxide with 0.150 mol/L sulfuric acid
Trial #
1
2
3
4
Initial buret reading (mL)
0.2
12.8
25.3
0.6
Final buret reading (mL)
12.8
25.3
37.8
13.3
Equivalence point (mL)
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3. Find the molar concentration of the potassium permanganate solution, given the following:
Titration of 10.0 mL of acidified 0.100 mol/L iron(II) sulfate with
potassium permanganate
Trial #
1
2
3
4
Initial buret reading (mL)
0.1
11.3
21.9
32.5
Final buret reading (mL)
11.3
21.9
32.5
42.9
Equivalence point (mL)
The balanced equation that you will use for this reaction is:
10 FeSO4(aq) + 2 KMnO4(aq) + 8 H2SO4(aq)  5 Fe2(SO4)3(aq) + K2SO4(aq) + 2 MnSO4(aq) + 8 H2O(l)
44
Interpreting pH Titration Curves

When a strong base titrant is reacted with a strong acid aliquot, the characteristic shape that
should be predicted is:

The initial pH of the system is very low because only the strong acid is initially present.

The pH curve will rise as more titrant is added.

Eventually, if you continue to add titrant past the equivalence point, the solution reaches a pH
close to that of the base titrant.

This increase in pH is not linear – it follows a characteristic S-shape.

Prior to the equivalence point, there is only a slight, very gradual increase in pH.

As the reaction approaches completion, there is a steep rise in pH accompanying the complete
neutralization of the strong acid sample.

The middle of the steep rise corresponds to the pH of the reaction mixture at the equivalence
point of the reaction.

As the equivalence point approaches, a very small amount of added titrant results in a large
change in pH.
45

When a strong acid titrant is reacted with a strong base aliquot, the characteristic shape that
should be predicted is:

The initial pH of the system is very high because there is only the strong base initially
present.

The pH curve will drop as more titrant is added.

Eventually, if you continue to add titrant past the equivalence point, the solution reaches a pH
close to that of the acid titrant.

This decrease in pH also has a characteristic S-shape.

Prior to the equivalence point, there is only a slight, very gradual decrease in pH.

There is a steep drop in pH accompanying the complete neutralization of the strong base
sample.

The middle of the steep drop corresponds to the pH of the reaction mixture at the equivalence
point of the reaction.

As the equivalence point nears, the pH will start to drastically decrease.

As the equivalence point approaches, a very small amount of added titrant results in a large
change in pH.
46
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 though 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.

Indicator
pH range
Colour change as pH increases
bromocresol green
3.8 – 5.4
yellow to blue
methyl red
4.8 – 6.0
red to yellow
chlorophenol red
5.2 – 6.8
yellow to red
bromothymol blue
6.0 – 7.6
yellow to blue
phenol red
6.6 – 8.0
yellow to red
phenolphthalein
8.2 – 10.0
colourless to pink
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 of phenol red.
47
PRACTICE: STOICHIOMETRY UNIT REVIEW
1. A chemist adds some zinc shavings to a beaker containing a blue solution of copper(II)
chloride. The contents of the beaker are stirred. After several hours, the chemist
observes that the blue colour has almost, but not completely, disappeared.
a. Write a balanced chemical equation to describe this reaction.
b. What other observations would you expect the chemist to make?
c. According to the chemist’s observations, which reactant was the limiting
reactant?
d. The beaker contained 3.12 g of copper(II) chloride dissolved in water. What
does this tell you, quantitatively, about the mass of zinc that was added?
2. 20.89 g of calcium phosphate, 13.3 g of silicon dioxide and 3.9 g of carbon react
according to the following equation:
2 Ca3(PO4)2(s) + 6 SiO2(s) + 10 C(s) → P4(s) + 6 CaSiO3(s) + 10 CO2(g)
a. What is the limiting reactant?
b. Determine the mass of calcium silicate that is produced.
48
3. Nitroglycerin (C3H5N3O9(l)) is a powerful explosive. Its decomposition may be
represented by:
4 C3H5N3O9(l) → 6 N2(g) + 12 CO2(g) + 10 H2O(g) + O2(g)
a. What is the maximum mass of oxygen that can be obtained from the decomposition
of 200 g of nitroglycerin?
b. Calculate the percentage yield in this reaction if the mass of oxygen generated was
found to be 6.55 g.
c. Based on your answer to part b), what mass of nitrogen was formed in the reaction?
4. The complete combustion of octane, the major component of gasoline for automobiles, can be
described by the equation:
2 C8H18(l) + 25 O2(g) → 16 CO2(g) + 18 H2O(g)
If automobile engines are not properly tuned and the air filter replaced, there is often not
sufficient oxygen for complete combustion. Under these conditions, a competing reaction
occurs along with the complete combustion reaction. The equation for this reaction is shown
below. This reaction is the source of carbon monoxide in automobile exhaust.
2 C8H18(l) + 17 O2(g) → 16 CO(g) + 18 H2O(g)
a. What is the maximum mass of carbon dioxide that can be produced by the complete
combustion of 750 g octane?
b. If 350 g of carbon monoxide are produce by the burning of 750 g of octane, what mass of
carbon dioxide would you predict was also generated?
49
5. The production of copper metal is possible through the reaction of copper(II) oxide and
carbon, which also produces carbon dioxide. What mass of carbon is required to completely
react with 500 kg of copper(II) oxide?
6. Design a selective precipitation technique that would allow you to confirm whether an
unidentified solution contained bromide and/or sulfide ions.
7. Octane (C8H18 (l)) is one of the main components of gasoline. What volume of carbon dioxide
(at STP) will be produced by the complete combustion of 675 g of octane?
8. Silver-plated tableware is popular because it is less expensive than sterling silver. Silver
nitrate solution is used by an electroplating business to replate silver tableware for their
customers. To test the purity of the solution, a technician observes 10.00 mL of 0.500 mol/L
silver nitrate reacting with an excess quantity of 0.480 mol/L sodium hydroxide. The
precipitate is dried and measured to have a mass of 0.575 g. Calculate the percent yield for
this reaction.
50
9. Some antacid products contain aluminium hydroxide to neutralize excess stomach acid.
Determine the volume of 0.10 mol/L stomach acid (assumed to be HCl (aq)) that can be
neutralized by 905 mg of aluminum hydroxide in an antacid tablet.
10. Sulfuric acid is produced on a large scale from readily available raw materials. One step in
the industrial production of sulfuric acid is the reaction of sulfur trioxide with water.
Calculate the molar concentration of the sulfuric acid produced by the reaction of 3.50 Mg of
sulfur trioxide with an excess quantity of water to produce 7.00 kL of acid.
11. In a titration, an average volume of 13.5 mL of 0.161 mol/L sodium hydroxide is needed to
react completely with 10.0 mL of oxalic acid.
a. Calculate the molar concentration of the oxalic acid.
b. Re-write this concentration as a % mass-by-volume concentration.
c. Describe how the standard sodium hydroxide solution could have been prepared in the lab
prior to the titration. Assume that solid solute was dissolved.
51
12. A student reacts zinc with excess hydrochloric acid in order to calculate an experimental
value for the Universal Gas Constant (R). The reaction produces hydrogen gas which is
collected by the downwards displacement of water. The observations that the student makes
are:
mass of zinc reacted = 1.20 g
temperature of gas collected = 20.0oC
pressure of gas collected = 106 kPa
volume of gas collected = 420 mL
a. Use the data collected to calculate the experimental value for the Universal Gas Constant.
b. Calculate the percent error associated with your recorded answer from part a.
52