Chemical Formulas
Methane
CH4
MOLECULAR FORMULAS: representation of molecules in
terms of their constituent atoms -– H2, H2O
DIATOMIC - two atoms; example: H2, N2, CO (carbon monoxide)
TRIATOMIC - three atoms; example: CO2 (carbon dioxide),
O3(ozone)
POLYATOMIC - more than three atoms; examples: NH3
(ammonia), CH4 (methane), C2H6O2 (ethylene glycol)
What limits the “boundary” of a molecule?
Atoms in molecules are held together by strong interactions
called CHEMICAL BONDS
Interactions between neutral atoms in a molecule (e.g. H2,
H2O) is called a COVALENT bond, forming covalent
compounds
Interactions between charged elements (IONS) result in a
different kind of chemical bond, called an IONIC BOND
Compounds formed via interactions between ionic
(charged) elements are called ionic compounds.
In a crystal of NaCl a Na+ ion interacts with the neighboring
Cl- ion, hence a NaCl “molecule” does not exist.
However, if one counted the number of sodium ions and
the number of Cl- ions in a given volume we would find that
the ratio of Na+ : Cl- is 1:1.
A crystal of sodium chloride is electrically neutral and its
CHEMICAL FORMULA can be expressed as NaCl.
Chemical formulas indicate the constituent elements in a
compound (covalent or ionic)
The term molecular formula refers specifically to covalent
compounds.
How are chemical formulas determined?
ELEMENTAL ANALYSIS
Determination of the relative amounts of the elements in a
compound
Determines the EMPIRICAL FORMULA which is the simplest
possible formula and indicates the relative amounts of
constituent elements
For example, the molecular formula of hydrogen peroxide is
H2O2; its empirical formula is HO.
The empirical and the chemical formula can be the same, for
example, H2O.
For ionic compounds, the empirical formula is the same as
the chemical formula (NaCl)
Problem
An oxide of nitrogen is analyzed and found to contain 25.9%
N and 74.1% O. What is the empirical formula of the
compound?
In 100.0 g of compound:
# moles of N = 25.9 g N / (14.01 g/mol) = 1.85 mol
# moles of O = 74.1 g O / (16.00 g/mol) = 4.63 mol
Ratio of O: N :: 2.5:1
Must be whole numbers – N2O5
Combustion Analysis - elemental analysis of organic
compounds.
Organic compounds contain predominantly C and H.
Minor elements include O, N, S, Cl, P, etc.
In combustion analysis the organic compound is burnt in
the presence of oxygen (O2) to form carbon dioxide (CO2),
water (H2O) and other gases (nitrogen (N2), sulfur dioxide
(SO2))
A sample of a compound that is known to contain only
carbon, hydrogen, and oxygen is combusted, and the CO2
and H2O produced are trapped and weighed. The original
sample weighed 8.38 g and yielded 16.0 g CO2 and 9.5 g H2O.
What is the empirical formula?
Need to determine the number of moles of C and H in the
compound, and then determine the mass of O in the
compound.
Moles of C =
(16.0 g CO2 / 44.0 g/mol CO2) x (1 mol C/1 mol CO2)
= 0.364 mol C
Moles of H =
(9.80 g H2O / 18.0 g/mol H2O) x (2 mol H / 1 mol H2O)
= 1.09 mol H
Mass of C in compound = 0.364 mol C x 12.0 g/mol C
= 4.37 g C
Mass of H in compound = 1.09 mol H x 1.01 g/ mol H
= 1.10 g H
Mass of O in compound = 8.38 g - 4.37 g - 1.10 g = 2.91 g O
Moles of O in compound = (2.91 g O / 16.0 g/mol O)
= 0.182 mol O
Mole ratio of C : H : O is 0.364 : 1.09 : 0.182 or 2:6:1
Hence empirical formula is C2H6O
Determining Chemical Formulas
The empirical formula tells you the simplest ratio of the
individual elements in the compound.
For an ionic compound this information is enough.
For a molecular compound this may not be enough since the
empirical formula may not be the molecular formula.
Knowledge of the MOLAR MASS of the compound and its
empirical formula, allows the molecular formula to be
determined.
Elemental analysis of a sugar shows that it consists of 40.0%
carbon (C), 6.7% hydrogen (H), 53.3% oxygen (O). The molar
mass of the compound was found to be 180.0 g/mol. What is
the molecular formula of the compound?
moles of C in 100.0 g of compound
= (mass of C g)/(atomic mass g/mol)
= 40.0/12.01 = 3.33 mol C in 100.0 g of compound
moles of H in 100.0 g of compound
= (mass of H g)/(atomic mass g/mol)
= 6.7/1.01 = 6.7 mol H in 100.0 g of compound
moles of O in 100.0 g of compound
= (mass of O g)/(atomic mass g/mol)
= 53.3/16.00 = 3.33 mol O in 100.0 g of compound
Ratio of C:H:O :: 1:2:1; hence empirical formula is CH2O
Molar mass of empirical formula = 12.01 + 2(1.01) + 16.00 =
30.0 g/mol
Ratio of molar mass of compound : molar mass of empirical
formula
180.0/30.0 = 6.0
molecular formula is (CH2O) 6 or C6H12O6
Chemical Reactions & Equations
In a chemical reaction elements and/or compounds collide,
interact and react to form new compounds.
The compounds that come together are called the
REACTANTS and the new compounds formed are the
PRODUCTS.
An important aspect of a chemical reaction is that MASS IS
ALWAYS CONSERVED - i.e. the total mass of the reactants
must equal the total mass of the products.
To ensure that mass is conserved, we have to keep track of
the number of atoms of each element in the reactants and
number of atoms of each element in the products
Writing Chemical Equations
H2 + O2  H2O
reactants
products
Mass has not been conserved - equation is not BALANCED
Need to make sure that the number of atoms of a given
element is the same on either side.
H2 + O2  H2O
H is balanced, but O is not.
To balance O, multiply H2O by 2
H2 + O2  2 H2O
Now O is balanced but not H (4 H’s on right, 2 on left)
Multiply H2 by 2
2H2 + O2  2 H2O
2H2 + O2  2 H2O
Now the equation is balanced.
However, for a complete chemical equation the state of all
reactants and products must be included
2H2(g) + O2 (g)  2 H2O (g)
g - gas; l - liquid; s- solid
aq - denotes a solution of a solute in water (solvent)
Note: the subscripts in the molecular formula must never be
changed in balancing equations. Changing the subscript
corresponds to a different molecular formula, hence a
different molecule, with completely different properties
“Rules” to balance chemical equations
Consider the reaction of methane, CH4, burning in air to
produce CO2 and H2O (combustion reaction)
CH4 + O2  CO2 + H2O
It is usually best to first balance those elements that occur in
the fewest chemical formulas on each side of the equation.
So in this example balance C and H first
C is already balanced. However 4 H’s on the left and 2 on
the right
Hence,
CH4 + O2  CO2 + 2H2O
Now balance O
CH4 + 2O2  CO2 + 2H2O
Now specify the state of each reactant and product
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
Ag2S(s) + KCN(aq) + O2(g) + H2O(l) 
KAg(CN)2(aq) + S(s) + KOH(aq)
Sometimes it is hard to balance a chemical reaction by
“inspection”
Can the use algebraic expressions to balance equations
a Ag2S(s) + b KCN(aq) + c O2(g) + d H2O(l) 
1 KAg(CN)2(aq) + e S(s) + f KOH(aq)
Element
Reactant
Product
Ag
2a
1
S
a
e
K
b
1+f
C
b
2
N
b
2
O
2c + d
f
H
2d
f
2 a = 1 ; a = 0.5
b=2
a = e ; e = 0.5
b = 1 + f; f = 1
2d = f; d = 0.5
2c + d = f; c = 0.25
Divide all by 0.25
a = 2; b = 8; c = 1; d = 2; e = 2; f = 4
Hence
2 Ag2S(s) + 8 KCN(aq) + O2(g) + 2 H2O(l) 
4 KAg(CN)2(aq) + 2 S(s) + 4 KOH(aq)
Chemical Stoichiometry
Reactants are consumed and products are formed in
definite proportions.
These proportions are given by the coefficients in the
balanced equations for chemical reactions
The calculation of the quantities of reactants and products
is called STOICHIOMETRY.
Stoichiometry is the use of chemical equations to calculate
quantities of substances that take part in chemical
reactions.
To do a stoichiometric calculation, the chemical equation
for the calculation must be balanced.
Equations are read in terms of moles of reactants and
product
2H2(g) + O2 (g)  2H2O(g)
2 moles of H2 (g) reacts with 1 mole of O2 (g) to form 2
moles of H2O(g)
Or:
2No molecules of H2 (g) + No molecules of O2 (g)  2No
molecules of H2O(g)
Problem
Consider the reaction of 100 g of H2(g) with sufficient O2 (g)
to produce the stoichiometric quantity of H2O(g).
(stoichiometric quantities are the exact amounts of
reactants and products predicted by balanced equations).
Calculate the mass of H2O formed.
Need a balanced equation for this reaction
2H2(g) + O2 (g)  2H2O(g)
To find the mass of water formed, need to find the
number of moles of H2 that reacted:
(mass of H2)
(molar mass of H2)
= (100.g H2)/(2.02 g/mol) = 49.5 mol H2
2 moles of H2 reacts with 1 mole of O2 to form 2 moles of H2O
=> 49.5 moles of H2 will form 49.5 moles of H2O
Hence, the mass of H2O(g) formed
=(49.5 moles H2O) x (18.02 g/mol) = 892 g H2O
Problem: Diethyl ether (C4H10O) combusts in air, reacting
with O2 to form H2O and CO2. How many grams of CO2
would be produced if 350.0 mL of diethyl ether were
combusted in an unlimited amount of oxygen? The density
of diethyl ether is 0.713 g/mL.
First write a balanced equation
?C4H10O(l) + ?O2(g)  ?H2O(l) + ?CO2(g)
Then convert the volume of diethyl ether to mass
Next, determine the number of moles of diethyl ether
reacted
Determine the number of moles of CO2 formed based on
the stoichiometry of the reaction
Finally determine the mass of CO2 produced
Answer: 592 g CO2
For reactions occurring in solution, instead of using
moles as a unit of quantity, define moles/liter = MOLARITY
Molarity is defined as the number of moles of a solute per
liter of solution.
Note: the solute can be a solid, liquid, or gas dissolved in
a solvent.
Problem
For the reaction:
2 PbO2(s) + 4 HNO3(aq)  2 PbNO3(aq) + 2 H2O (l) + O2(g)
What volume of 7.91M solution of nitric acid, HNO3, is just
sufficient to react with 15.9 g of lead dioxide, PbO2?
Answer: 0.0168 L
Volume Relationship of Gases in Chemical Reactions
Gay Lussac’s law of combining volumes – states that the
volumes of gaseous reactants and products stand in ratios
of simple integers, as long as those volumes are measured
at the SAME temperature and pressure.
These integers are the same as the integers used to
balance the chemical equation.
A balanced chemical equation therefore provides a
relationship between the volumes of gases reacting.
Problem:
Gaseous H2 and N2 react according to the equation
3H2 (g) + N2 (g)  2 NH3(g)
If in a given reaction 5.00 L of NH3 are formed, what volume
of H2 reacted, assuming that the temperature and pressure
before and after the reaction are the same.
From the balanced reaction above, assuming the same
temperature and pressure before and after the reaction,
2 volumes of NH3 are formed from 3 volumes of H2
Hence, 5.00 L of NH3 are formed from (3/2)x5.00 L = 7.5 L
of H2
Limiting Reactants and Product Yields
If everything went perfectly in the reaction :
Fe(s) + S (s)  FeS (s)
55.8 g (1 mole) of iron will react with 32.1 g (1 mole) of S to
form 87.9 g (1 mole) of FeS.
If stoichiometric amounts of reactants were used, and
assuming that there are no competing factors to limit the
amount of products being formed, then a stoichiometric
amount of product is formed
If we were to mix reactants together in non-stoichiometric
amounts then what determines the amount of product
formed?
The reactant which is first used up determines the amount of
product formed.
This reactants is called the LIMITING REACTANT.
The other reactants are in EXCESS when the reaction stops.
If additional amounts of the limiting reactant is added the
reaction starts again.
Problem:
Calcium carbonate CaCO3(s) is decomposed by HCl(aq) to
give CaCl2 (aq), CO2(g) and H2O(l). If 10.0g of CaCO3 are
treated with 10.0 g of HCl, how many grams of CO2 are
generated?
First write a balanced equation for the reaction:
CaCO3 (s) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g)
1 mole of CaCO3 reacts with 2 moles of HCl to form 1 mole
of CO2
Moles of CaCO3 = (10.0 g)/(100.0g/mol) = 0.100 mole CaCO3
Moles of HCl = (10.0 g)/(36.5 g/mol) = 0.274 mol HCl
Hence 0.1 mole of CaCO3 reacts with 0.2 moles of HCl.
Since the amount of HCl present is greater that 0.2, HCl is
in excess and CaCO3 is the limiting reactant.
Hence, 0.1 mole of CO2 formed.
Mass of CO2 formed = 0.1 mol x 44.01 g/mol = 4.40 g CO2
Product Yields
In the previous calculation 4.40 g is the amount of CO2 we
would expect to be formed
4.40 g CO2 is the CALCULATED or the THEORETICAL
PRODUCT YIELD.
This assumes that the reaction goes to completion, and that
there are no competing factors that may reduce the amount
of CO2 formed.
The measured amount of product formed is called the
ACTUAL YIELD which is often smaller than the theoretical
yield.
Percentage Yield = (actual yield) x 100 %
(theoretical yield)
The larger the % yield the more cost effective is the process
and hence a more likely candidate for industrial scale
processes
(other factors are also important: the nature of the byproducts - are they environmentally safe -, the cost of the
starting materials, etc.)
Problem:
The principle step in the recovery of elemental iron (Fe)
from iron oxide (FeO) is a process known as reduction. In
this reaction hydrogen (H2) at elevated temperatures is
used as the reducing agent. Calculate the percent yield of
Fe if 1.00 g of H2 reacts with 30.0 g of FeO and produces
19.5 g of Fe. The reaction between FeO and H2 is:
FeO(s) + H2 (g)  Fe(s) + H2O(g)
First we need to determine the limiting reactant
Moles of H2 in reaction mixture = 1.00 g / (2.02g/mol)
= 0.500 mol
Moles of FeO reaction mixture = 30.0 g / (71.85 g/mol)
= 0.418 mol
From the stoichiometry of the equation FeO and H2 react in
a 1:1 ratio.
Hence, FeO is the limiting reactant
The number of moles of Fe that should be formed = 0.418
moles
Mass of Fe that should be formed
= 0.418 mole x 55.85g.mol = 23.3 g of Fe.
The actual yield of FeO is 19.5 g
% yield = (19.5)x100 = 83.7%
23.3
Ideally for an industrial process, the % yield should be
large.
Performing stoichiometric calculations, determining %
yields, are important in analyzing the “success” of a
chemical reaction.
Sometime, a reaction performed on a lab-scale may have
good product yields but when the reaction is scaled up to
an industrial process, the yield may be lower.