Table 1. The table below displays numerous values and equations utilized when
observing chemical kinetics for numerous reactions types
Zero-
Order
First-Order
Second-Order
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Rate Law
Rate= k
Rate= k[A]
Rate= k[A]2
Integrated Rate Law
[A]
t
=
−kt+[A]
0
ln[A]
t
=
−kt+ln[A]
0
1[A]
t
=−kt+1[A]
0
Units of Rate Constant
(k):
molL
−1
s
−1
s
−1
Lmol
−1
s
−1
Linear Plot to Determine
(k):
[A] versus
time
ln[A] versus
time
versus time
Relationship of Rate
Constant to the Slope of
Straight Line:
slope=
−k
slope=
−k
slope= k
Half-life:
Sample Problems
1. Define Reaction Rate
2. TRUE or FALSE: Changes in the temperature or the introduction of a
catalyst will affect the rate constant of a reaction
For sample problems 3-6, use Formula 6 to answer the questions
H2O
⟶2H2+O2(6)(6)H2O⟶2H2+O2
*Assume the reaction occurs at constant temperature
3. For the given reaction above, state the rate law.
4. State the overall order of the reaction.
5. Find the rate, given k = 1.14 x 10
-2
and [H
2
O] = 2.04M
6. Find the half-life of the reaction.
Answers
1. Reaction Rate is the measure of the change in concentration of the
disappearance of reactants or the change in concentration of the appearance of
products per unit time.
2. FALSE. The rate constant is not dependant on the presence of a catalyst.
Catalysts, however, can effect the total rate of a reaction.
3. Rate= k[H
2
O] Rate= k[H
2
O]
4. First - Order
5. 2.33 x 10
-2
s
-1
6. 29.7 s
3.3. A chemical equation is the symbolic representation of a chemical reaction
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in the form of symbols and formulae, wherein the reactant entities are given on the
left-hand side and the product entities on the right-hand side.
[1]
The coefficients next
to the symbols and formulae of entities are the absolute values of the stoichiometric
numbers. The first chemical equation was diagrammed by Jean Beguin in 1615.
[2]
A chemical equation consists of the chemical formulas of the reactants (the
starting substances) and the chemical formula of the products (substances formed in
the chemical reaction). The two are separated by an arrow symbol (
, usually read
as "yields") and each individual substance's chemical formula is separated from
others by a plus sign.
As an example, the equation for the reaction of hydrochloric acid with sodium
can be denoted:
2 HCl +2 Na
→2 NaCl + H 2
This equation would be read as "two HCl plus two Na yields two NaCl and H
two." But, for equations involving complex chemicals, rather than reading the letter
and its subscript, the chemical formulas are read using IUPAC nomenclature. Using
IUPAC nomenclature, this equation would be read as "hydrochloric acid plus sodium
yields sodium chloride andhydrogen gas."
This equation indicates that sodium and HCl react to form NaCl and H
2
. It also
indicates that two sodium molecules are required for every two hydrochloric acid
molecules and the reaction will form two sodium chloride molecules and one
diatomic molecule of hydrogen gas molecule for every two hydrochloric acid and two
sodium molecules that react. Thestoichiometric coefficients (the numbers in front of
the chemical formulas) result from the law of conservation of mass and the law of
conservation of charge
Chemical reactions happen all around us: when we light aMATCH , start a
car, eat dinner, or walk the dog. A chemical reaction is the process by which
substances bond together (or break bonds) and, in doing so, either release or consume
energy (see our Chemical Reactions module). A chemical equation is shorthand that
scientists use to describe a chemical reaction. Let's take the reaction of hydrogen with
oxygen to form water as an example. If we had a container of hydrogen gas and
burned this in the presence of oxygen, the two gases would react together, releasing
energy, to form water. To write the chemical equation for this reaction, we would
place the substances reacting (the reactants) on the left side of an equation with an
arrow pointing to the substances being formed on the right side of the equation (the
products). Given this information, one might guess that the equation for this reaction
is written:
H + O
→ H
2
O
The plus sign on the left side of the equation means that hydrogen (H) and
oxygen (O) are reacting. Unfortunately, there are two problems with this chemical
equation. First, because atoms like to have full valence shells, single H or O atoms
are rare. In nature, both hydrogen and oxygen are found asdiatomic molecules, H
2
and O
2
, respectively (in forming diatomic molecules the atoms shareelectrons and
complete their valence shells). Hydrogen gas, therefore, consists of H
2
molecules;
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oxygen gas consists of O
2
. Correcting our equation we get:
H
2
+ O
2
→ H
2
O
But we still have one problem. As written, this equation tells us that one
hydrogen molecule (with two H atoms) reacts with one oxygen molecule (two O
atoms) to form one water molecule (with two Hatoms and one O atom). In other
words, we seem to have lost one O atom along the way! To write a chemical equation
correctly, the number of atoms on the left side of a chemical equation has to be
precisely balanced with the atoms on the right side of the equation. How does this
happen? In actuality, the O atom that we "lost" reacts with a second molecule of
hydrogen to form a second molecule of water. During the reaction, the H-H and O-O
bonds break and H-O bonds form in the water molecules, as seen in the simulation
below.
Interactive Animation:The formation of water
The balanced equation is therefore written:
2H
2
+ O
2
→ 2H
2
O
In writing chemical equations, the number in front of the molecule's symbol
(called a coefficient) indicates the number of molecules participating in the reaction.
If no coefficient appears in front of a molecule, we interpret this as meaning one.
In order to write a correct chemical equation, we must balance all of the atoms
on the left side of thereaction with the atoms on the right side. Let's look at another
example. If you use a gas stove to cook your dinner, chances are that your stove
burns natural gas, which is primarily methane. Methane (CH
4
) is a molecule that
contains four hydrogen atoms bonded to one carbon atom. When you lightthe stove,
you are supplying the activation energy to start the reaction of methane with oxygen
in the air. During this reaction, chemical bonds break and re-form and the products
that are produced are carbon dioxide and water vapor (and, of course, light and heat
that you see as the flame). The unbalanced chemical equation would be written:
CH
4
(methane) + O
2
(oxygen)
→ CO
2
(carbon dioxide) + H
2
O (water)
Look at the reaction atom by atom. On the left side of the equation we find one
carbon atom, and one on the right.
C
H
4
+
O
2
→
C
O
2
+
H
2
O
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↑
1
carbon
↑
1
carbon
Next we move to hydrogen: There are four hydrogen atoms on the left side of
the equation, but only two on the right.
C
4
+
2
→
C
O
2
+
H
2
O
↑
4
hydro
gen
↑
2
hydro
gen
Therefore, we must balance the H atoms by adding the coefficient "2" in front
of the water molecule(you can only change coefficients in a chemical equation, not
subscripts). Adding this coefficient we get:
C
H
4
+
O
2
→
C
O
2
+
2H
2
O
↑
4
hydro
gen
↑
4 hydrogen
What this equation now says is that two molecules of water are produced for
every one molecule of methane consumed. Moving on to the oxygen atoms, we find
two on the left side of the equation, but a total of four on the right side (two from the
CO
2
molecule and one from each of two water molecules H
2
O).
C
H
4
+
O
2
→
C
O
2
+
2H
2
O
↑
2
oxygen
↑
4
oxygen
To balance the chemical equation we must add the coefficient "2" in front of
the oxygen molecule on the left side of the equation, showing that two oxygen
molecules are consumed for every one methane molecule that burns.
C
H
4
+
2O
2
→
C
O
2
+
2H
2
O
↑
4
oxygen
↑
4 oxygen
Dalton's law of definite proportions holds true for all chemical reactions (see
our Early Ideas about Matter: From Democritus to Dalton module). In essence, this
law states that a chemical reactionalways proceeds according to the ratio defined by
the balanced chemical equation. Thus, you can interpret the balanced methane
equation above as reading, "one part methane reacts with two parts oxygen to
produce one part carbon dioxide and two parts water." This ratio always remains the
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same. For example, if we start with two parts methane, then we will consume four
parts O
2
and generate two parts CO
2
and four parts H
2
O. If we start with excess of
any of the reactants (e.g., five parts oxygen when only one part methane is available),
the excess reactant will not be consumed:
C
H
4
+
5O
2
→ C O
2
+
2H
2
+
0
+
3O
2
Excessreactantswill not be consumed.
In the example seen above, 3O
2
had to be added to the right side of the
equation to balance it and show that the excess oxygen is not consumed during the
reaction. In this example, methane is called the limiting reactant.
Although we have discussed balancing equations in terms of numbers of atoms
and molecules, keep in mind that we never talk about a single atom (or molecule)
when we use chemical equations. This is because single atoms (and molecules) are so
tiny that they are difficult to isolate. Chemical equations are discussed in relation to
the number of moles of reactants and products used or produced (see our The Mole
module). Because the mole refers to a standard number of atoms (or molecules), the
term can simply be substituted into chemical equations. Thus, the balanced methane
equation above can also be interpreted as reading, "one mole of methane reacts with
two moles of oxygen to produce one mole of carbon dioxide and two moles of
water."
Lewis Theory
The Lewis definition is the most general theory, having no requirements for
solubility or protons.
Lewis Acids and Bases
1.
An acid is a substance that accepts a lone pair of electrons.
2.
A base is a substance that donates a lone pair electrons.
Lewis acids and bases react to create an adduct, a compound in which the acid
and base have bonded by sharing the electron pair. Lewis acid/base reactions are
different from redox reactions because there is no change in oxidation state.
This reaction shows a Lewis base (NH
3
) donating an electron pair to a Lewis
acid (H
+
) to form an adduct (NH
4
+
).
Amphoterism and Water[edit]
Substances capable of acting as either an acid or a base are amphoteric. Water
is the most important amphoteric substance. It can ionize into hydroxide (OH
-
, a
base) or hydronium (H
3
O
+
, an acid). By doing so, water is
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1.
Increasing the H
+
or OH
-
concentration (Arrhenius),
2.
Donating or accepting a proton (Brønsted-Lowry), and
3.
Accepting or donating an electron pair (Lewis).
Important A bare proton (H
+
ion) cannot
exist in water. It will form a hydrogen bond to
the
nearest
water
molecule,
creating
thehydronium ion (H
3
O
+
). Although many
equations and definitions may refer to the
"concentration of H
+
ions", that is a misleading
abbreviation. Technically, there are no H
+
ions,
only hydronium (H
3
O
+
) ions. Fortunately, the
number of hydronium ions formed is exactly
equal to the number of hydrogen ions, so the two
can be used interchangeably.
H
+
ions actually exist as hydronium, H
3
O
+
.
Water will dissociate very slightly (which further explains its amphoteric
properties).
The presence of hydrogen ions
indicates an acid, whereas the presence
of hydroxide ions indicates a base.
Being neutral, water dissociates into
both equally.
This equation is more accurate—
hydrogen ions do not exist in water
because they bond to form hydronium.
Helpful Hint!
Although the other halogens make strong acids, hydrofluoric acid (HF) is a
weak acid. Despite being weak, it is incredibly corrosive—hydrofluoric acid
dissolves glass and metal!
Most acids and bases are weak. You should be familiar with the most common
strong acids and assume that any other acids are weak.
Formula
Strong Acid
HClO
4
Perchloric acid
HNO
3
Nitric acid
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H
2
SO
4
Sulfuric acid
HCl, HBr, HI Hydrohalic acids
Within a series of oxyacids, the ions with the greatest number of oxygen
molecules are the strongest. For example, nitric acid (HNO
3
) is strong, but nitrous
acid (HNO
2
) is weak. Perchloric acid (HClO
4
) is stronger than chloric acid (HClO
3
),
which is stronger than the weak chlorous acid (HClO
2
). Hypochlorous acid (HClO) is
the weakest of the four.
Common strong bases are the hydroxides of Group 1 and most Group 2 metals.
For example, potassium hydroxide and calcium hydroxide are some of the strongest
bases. You can assume that any other bases (including ammonia and ammonium
hydroxide) are weak.
Formula Strong Base
LiOH
Lithium hydroxide
NaOH
Sodium hydroxide
KOH
Potassium hydroxide
RbOH
Rubidium hydroxide
CsOH
Cesium hydroxide
Ca(OH)
2
Calcium hydroxide
Sr(OH)
2
Strontium hydroxide
Ba(OH)
2
Barium hydroxide
Acids and bases that are strong are not necessarily concentrated, and weak
acids/bases are not necessarily dilute. Concentration has nothing to do with the
ability of a substance to dissociate. Furthermore, polyprotic acids are not
necessarily stronger than monoprotic acids.
Properties of Acids and Bases
Now that you are aware of the acid-base theories, you can learn about the
physical and chemical properties of acids and bases. Acids and bases have very
different properties, allowing them to be distinguished by observation.
Indicators
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Bromothymol blue is an indicator that turns blue in a base, or yellow in acid.
Made with special chemical compounds that react slightly with an acid or base,
indicators will change color in the presence of an acid or base. A common indicator is
litmus paper. Litmus paper turns red in acidic conditions and blue in basic conditions.
Phenolphthalein purple is colorless in acidic and neutral solutions, but it turns purple
once the solution becomes basic. It is useful when attempting to neutralize an acidic
solution; once the indicator turns purple, enough base has been added.
Conductivity
A less informative method is to test for conductivity. Acids and bases in
aqueous solutions will conduct electricity because they contain dissolved ions.
Therefore, acids and bases are electrolytes. Strong acids and bases will be strong
electrolytes. Weak acids and bases will be weak electrolytes. This affects the amount
of conductivity.
However, acids will react with metal, so testing conductivity may not be
plausible.
Physical properties
The physical properties of acids and bases are opposites.
Acids
Bases
Taste
sour
bitter
Feel
stinging
slippery
Odor
sharp
odorless
These properties are very general; they may not be true for every single acid or
base.
Another warning: if an acid or base is spilled, it must be cleaned up
immediately and properly (according to the procedures of the lab you are working
in). If, for example, sodium hydroxide is spilled, the water will begin to evaporate.
Sodium hydroxide does not evaporate, so the concentration of the base steadily
increases until it becomes damaging to its surrounding surfaces.
Chemical Reactions
Neutralization
Acids will react with bases to form a salt and water. This is a neutralization
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reaction. The products of a neutralization reaction are much less acidic or basic than
the reactants were. For example, sodium hydroxide (a base) is added to hydrochloric
acid.
This is a double replacement reaction.
Acids
Acids react with metal to
produce a metal salt and hydrogen
gas bubbles.
Acids
react
with
metal
carbonates to produce water, CO
2
gas
bubbles, and a salt.
Acids react with metal oxides
to produce water and a salt.
Bases
Bases are typically less reactive and violent than acids. They do still undergo
many chemical reactions, especially with organic compounds. A common reactions is
saponificiation: the reaction of a base with fat or oil to create soap.
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