4. Compounds & Stoichiometry
Terms in this set (37)
molecule is a combination of two or more atoms held together by covalent bonds. Molecules are
the smallest units of compounds that display their identifying properties. Molecules can be composed
of two or more atoms of the same element or may be composed of atoms of
different elements, as in (carbon dioxide), (thionyl chloride), and
Because reactions usually involve a very large number of molecules—far too many
to count individually—we usually measure amounts of compounds in terms of moles or grams, using
molar mass to interconvert between these units.
Ionic compounds do not form true molecules because of the way in which the oppositely charged ions
arrange themselves in the solid state. As solids, they can be considered as nearly infinite threedimensional
arrays of the charged particles that comprise the compound.
Solid NaCl is a coordinated lattice in which each of the Na ions
is surrounded by Cl ions and each of the Cl ions is surrounded by Na ions. This makes it rather
difficult to clearly define a sodium chloride molecule, and the term formula unit, representing the
empirical formula of the compound, is used instead. Because no molecule actually exists, molecular
weight becomes meaningless, and the term formula weight is used instead.
Remember that the term atomic weight is a misnomer because it is actually a weighted average of the
masses of the naturally occurring isotopes of an element, not their weights. The same applies here to
our discussion of molecular weight.
Molecular weight, then, is simply the sum of the atomic weights
of all the atoms in a molecule, and its units are atomic mass units (amu) per molecule. Similarly, the
formula weight of an ionic compound is found by adding up the atomic weights of the constituent ions
according to its empirical formula, and its units are also amu per molecule.
A mole is a quantity of any substance (atoms, molecules, dollar bills, kittens—anything) equal to the
number of particles that are found in 12 grams of carbon-12. This number of particles is defined
as Avogadro's number (N ), 6.022 × 10^23 mol.
One mole of a compound has a mass in grams
equal to the molecular or formula weight of the compound in amu. For example, one molecule of
(carbonic acid) has a mass of 62 amu; one mole of the compound has a mass of 62 grams. The
mass of one mole of a compound is called its molar mass and is usually expressed in g/mol. The formula for determining the number of moles of a substance sample is: mass of sample (g)/molar mass (g/mol)
This equation is often used in stoichiometry and titration problems.
KEY CONCEPT 1
Remember that Avogadro's number (and the mole) are just units of convenience, like the
dozen is a convenient unit for eggs.
Equivalent weight and the related concept of equivalents are a source of confusion for many
Part of the problem may be the context in which equivalents and equivalent weights are
usually discussed: acid-base reactions, oxidation-reduction reactions, and precipitation reactions, all
three of which can be sources of confusion and anxiety on their own.
Often, certain elements or compounds can act more potently than others in performing certain
reactions. For example, one mole of HCl has the ability to donate one mole of hydrogen ions (H ) in
solution, but one mole of H2SO4 has the ability to donate two moles of hydrogen ions, and one mole
of H3PO4 has the ability to donate three moles of hydrogen ions. To gather one mole of hydrogen ions
for a particular acid-base reaction, we could use one mole of HCl, a half-mole of H2SO4 , or onethird
of a mole of H3PO4.
Or, consider the difference between Na and Mg: One mole of sodium has
the ability to donate one mole of electrons, while one mole of magnesium has the ability to donate two
moles of electrons. This provides context for the concept of equivalents: How many moles of the
thing we are interested in (protons, hydroxide ions, electrons, or ions) will one mole of a given
compound produce? Sodium will donate one mole of electrons (one equivalent), but magnesium will
donate two moles of electrons (two equivalents).
So far, this discussion has been focused on the mole-to-mole relationship between, say, an acid
compound and the hydrogen ions it donates. However, sometimes we need to work in units of mass
rather than moles. Just as one mole of HCl will donate one mole of hydrogen ions, a certain mass of
HCl (about 36.5 g) will also donate one equivalent of hydrogen ions. This amount of a compound,
measured in grams, that produces one equivalent of the particle of interest is called the gram
equivalent weight and can be calculated from:
gram equivalent weight=Molar mass/n
where n is the number of particles of interest produced or consumed per molecule of the compound in
the reaction. For example, one would need 31 grams of H2CO3) to produce one equivalent of hydrogen ions because each molecule of H CO can donate two hydrogen ions (n =
2). Simply put, the equivalent weight of a compound is the mass that provides one mole of the particle
If the amount of a compound in a reaction is known and we need to determine how many equivalents
are present, use the equation:
equivalents=Mass of compound (g)/Gram of equivalent (g)
Finally, we can now introduce the measurement of normality. Normality (N) is a measure of
concentration, given in the units It is most commonly used for hydrogen ion concentration.
Thus, a 1 N solution of acid contains a concentration of hydrogen ions equal to 1 mole per liter; a 2 N
solution of acid contains a concentration of hydrogen ions equal to 2 moles per liter. The actual
concentration of the acidic compound may be the same or different from the normality because
different compounds are able to donate different numbers of hydrogen ions. In a 1 N HCl solution, the
molarity of HCl is 1 M because HCl is a monoprotic acid; in a 1 N H2CO3 solution, the molarity of
H2CO3 is 0.5 M because H2CO3 is a diprotic acid. Note that because normality calculations always
assume that a reaction will proceed to completion; while carbonic acid does not fully dissociate in
solution, it can be reacted with enough base for each molecule to give up both of its protons. The
conversion from normality to molarity of a given solute is:
where n is the number of protons, hydroxide ions, electrons, or ions produced or consumed by the
There is a real benefit to working with equivalents and normality because it allows a direct
comparison of the quantities of the entity we are most interested in. In an acid-base reaction, we care
about the hydrogen or hydroxide ions; where the ions come from is not really the primary concern.
is convenient to be able to say that one equivalent of acid (hydrogen ions) will neutralize one
equivalent of base (hydroxide ions), but the same could not necessarily be said if we were dealing
with moles of acidic compounds and moles of basic compounds. For example, one mole of HCl will
not completely neutralize one mole of Ca(OH) because one mole of HCl will donate one equivalent
of acid, but Ca(OH) will donate two equivalents of base.
KEY CONCEPT 2
In acid-base chemistry, the gram equivalent weight of an acid represents the mass that yields
one mole of protons, or one mole of hydroxide ions if a base.
There are different ways of representing compounds and their constituent atoms. In organic chemistry, it is common to encounter skeletal representations
of compounds, called structural formulas, that show the various bonds between the constituent atoms
of a compound. Inorganic (general) chemistry typically represents compounds by showing the
constituent atoms without representing the actual bond connectivity or atomic arrangement.
example, the formula C6H12O (glucose) tells us that this particular compound consists of six atoms of
carbon, twelve atoms of hydrogen, and six atoms of oxygen, but there is no indication of how the
different atoms are arranged or how many bonds exist between each of the atoms.
The law of constant composition states that any pure sample of a given compound will contain the
same elements in an identical mass ratio.
For example, every sample of water will contain two
hydrogen atoms for every one oxygen atom, or—in terms of mass—for every one gram of hydrogen,
there will be eight grams of oxygen.
There are two ways to express the formula of a compound. The empirical formula gives the simplest
whole-number ratio of the elements in the compound.
The molecular formula gives the exact number
of atoms of each element in the compound and is a multiple of the empirical formula.
The percent composition of an element (by mass) is the percent of a specific compound that is made
up of a given element. To determine the percent composition of an element in a compound, the
following formula is used:
One can calculate the percent composition of an element by using either the empirical or the
molecular formula. It is also possible to determine the molecular formula given both the percent
compositions and molar mass of a compound.
KEY CONCEPT 3
The molecular formula is either the same as the empirical formula or a multiple of it. To
calculate the molecular formula, you need to know the mole ratio (this will give you the
empirical formula) and the molar mass (molar mass divided by empirical formula weight will
give the multiplier for the empirical formula-to-molecular formula conversion).
A combination reaction has two or more reactants forming one product.
The formation of water by
burning hydrogen gas in air is an example of a combination reaction.
KEY CONCEPT 4
Combination reactions have more reactants than products: A + B → C
A decomposition reaction is the opposite of a combination reaction: a single reactant breaks down
into two or more products, usually as a result of heating, high-frequency radiation, or electrolysis.
example of decomposition is the breakdown of mercury(II) oxide. (The Δ [delta] sign over a reaction
arrow represents the addition of heat.)
KEY CONCEPT 5
Decomposition reactions generally have more products than reactants. A → B + C
A combustion reaction is a special type of reaction that involves a fuel—usually a hydrocarbon—
and an oxidant (normally oxygen).
In its most common form, these reactants form the two products of
carbon dioxide and water.
KEY CONCEPT 6
Combustion involves oxidation (using O or similar) of a fuel (typically a hydrocarbon).
A single-displacement reaction occurs when an atom or ion in a compound is replaced by an atom
or ion of another element. For example, solid copper metal will displace silver ions in a clear
solution of silver nitrate to form a blue copper sulfate solution and solid silver metal.
Single-displacement reactions are often further classified as oxidation-reduction reactions. For example,
Ag in AgNO3 has an oxidation state of +1, but when it leaves the compound, it gains one electron (the
Ag^+ is reduced to Ag). On the other hand, copper loses an electron (oxidation) when it joins the
In double-displacement reactions, also called metathesis reactions, elements from two different
compounds swap places with each other to form two new compounds. This type of reaction occurs
when one of the products is removed from the solution as a precipitate or gas or when two of the
original species combine to form a weak electrolyte that remains undissociated in solution.
example, when solutions of calcium chloride and silver nitrate are combined, insoluble silver
chloride forms in a solution of calcium nitrate.
Neutralization reactions are a specific type of double-displacement reaction in which an acid reacts
with a base to produce a salt (and, usually, water).
Because chemical equations express how much and what types of reactants must be used to obtain a
given quantity of product, it is of utmost importance that the reaction be balanced so as to reflect the
laws of conservation of mass and charge. The mass of the reactants consumed must equal the mass
of products generated.
More specifically, one must ensure that the number of atoms of each element
on the reactant side equals the number of atoms of that element on the product side. Stoichiometric
coefficients, which are the numbers placed in front of each compound, are used to indicate the
relative number of moles of a given species involved in the reaction. In general, stoichiometric coefficients
are given as whole numbers.
KEY CONCEPT 7
When balancing equations, focus on the least represented elements first and work your way to
the most represented element of the reaction (usually oxygen or hydrogen). If you,re stuck,
take a guess for the coefficient of the first reactant and balance the remainder appropriately.
Perhaps the most useful information to glean from a balanced reaction is the mole ratio of reactants
consumed to products generated. One can also generate the mole ratio of one reactant to another or
one product to another. All of these ratios can be generated using the stoichiometric coefficients.
the formation of water (2 H2 + O2 → 2 H O), for example, one can determine that, for every one mole
of hydrogen gas consumed, one mole of water can be produced; for every one mole of oxygen gas
consumed, two moles of water can be produced. Furthermore, mole-to-mole, hydrogen gas is being
consumed at a rate twice that of oxygen gas.
KEY CONCEPT 8
Stoichiometry, an application of dimensional analysis, is often simplified to a series of three
fractions. These fractions demonstrate an underlying three-step process:
-Convert from the given units to moles
-Use the mole ratio
-Convert from moles to the desired units
Rarely are reactants added in the exact stoichiometric proportions shown in the balanced equation of
a reaction. As a result, in most reactions, one reactant will be used up or consumed first. This reactant
is known as the limiting reagent (or reactant) because it limits the amount of product that can be
formed in the reaction. The reactants that remain after all the limiting reagent is used up are called
excess reagents (or reactants).
For problems involving the determination of the limiting reagent, keep in mind two principles:
1. All comparisons of reactants must be done in units of moles. Gram-to-gram comparisons will
be useless and may even be misleading.
2. It is not the absolute mole quantities of the reactants that determine which reactant is the
limiting reagent. Rather, the rate at which the reactants are consumed (the stoichiometric ratios
of the reactants), combined with the absolute mole quantities determines which reactant is the
The yield of a reaction can refer to either the amount of product predicted (theoretical yield) or
actually obtained (raw or actual yield) when a reaction is carried out. Theoretical yield is the
maximum amount of product that can be generated as predicted from the balanced equation, assuming
that all of the limiting reactant is consumed, no side reactions have occurred, and the entire product
has been collected. Theoretical yield is rarely ever attained through the actual chemical reaction.
Actual yield is the amount of product one actually obtains during the reaction. The ratio of the actual
yield to the theoretical yield, multiplied by 100 percent, gives the percent yield:
ionic compounds are made up
of positively charged cations, usually metals, and negatively charged anions, usually nonmetals. This
rule does not always hold true for elements like
hydrogen, which can act like an anion or cation but is
still classified as a nonmetal. Ionic compounds are held together by ionic
bonds, which rely on the force of electrostatic attraction between oppositely charged particles.
Ionic species, by definition, have charge. Cations have positive charge, and anions have negative
charge. Some elements are only found naturally in their charged forms, while others may exist
naturally in the charged or uncharged state. Some elements can even have several different charges or
oxidation states, depending on the other atoms in a compound.
Some of the charged atoms or molecules that are on the MCAT include the active metals—the alkali
metals (Group IA or Group 1) and the alkaline earth metals (Group IIA or Group 2), which have
charges of +1 and +2, respectively, in the natural state.
Nonmetals, which are found on the right side of the Periodic Table, generally form anions. For
example, all the halogens (Group VIIA or Group 17) form monatomic anions with a charge of -1
because they already have 7 electrons and aim to fill an octet.
In summary, all elements in a given group tend to form monatomic ions with the same charge (for
example, all Group IA elements have a charge of +1 in their ionic state). Note that there are anionic
species that contain metallic elements (for example, MnO [permanganate] and CrO [chromate]);
even so, the metals have positive oxidation states. Also note that in the oxyanions of the halogens,
such as ClO and ClO , the halogen is assigned a positive oxidation state.
For nonrepresentative elements like many of the transition metals, such as copper, iron, and
chromium, there are numerous positively charged states. These states need not be memorized.
Experimentally, the color of a solution can be indicative of the oxidation state of a given element in
the solution. The same element in different oxidation states can undergo different electron transitions
and therefore absorb different frequencies of light.
The trends of ionicity, as we've described here, are helpful but are complicated by the fact that many
elements have intermediate electronegativity and are consequently less likely to form ionic
compounds, and by the left-to-right transition from metallic to nonmetallic character
In spite of the fact that ionic compounds are composed of ions, solid ionic compounds tend to be poor
conductors of electricity because the charged particles are rigidly set in place by the lattice
arrangement of the crystalline solid. In aqueous solutions, however, the lattice arrangement is
disrupted by the ion-dipole interactions between the ionic components and the water molecules. The
cations and anions are now free to move, and as a result, the solution of ions is able to conduct
Solutes that enable solutions to carry currents are called electrolytes. The electrical conductivity of
aqueous solutions is governed by the presence and concentration of ions in the solution. Subsequently,
the number of electron equivalents being transferred in such a system, such as in electrochemical
cells, varies. Pure water, which has no ions other than the very few hydrogen ions and hydroxide ions
that result from water's low-level autodissociation, is a very poor conductor.
The tendency of an ionic solute to dissolve, or solvate, into its constituent ions in water may be high
or low. A solute is considered a strong electrolyte if it dissociates completely into its constituent
ions. Examples of strong electrolytes include certain ionic compounds, such as NaCl and KI, and
molecular compounds with highly polar covalent bonds that dissociate into ions when dissolved, such
as HCl in water.
A weak electrolyte, on the other hand, ionizes or hydrolyzes incompletely in aqueous solution, and
only some of the solute is dissolved into its ionic constituents. Examples include Hg2I2 (Ksp = 4.5 ×
10^-29), acetic acid and other weak acids, and ammonia and other weak bases. Many compounds do
not ionize at all in aqueous solution, retaining their molecular structure in solution, which may also
limit their solubility. These compounds are called nonelectrolytes and include many nonpolar gases
and organic compounds, such as O2(g), CO2(g), and glucose.
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