Balancing Chemical Equations: The Atom Conservation Approach

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Balancing Chemical Equations The Atom
Conservation Approach
Lecture 8

• Chemistry 142 B
• James B. Callis, Instructor
• Autumn Quarter, 2004

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Chemical Equations
Qualitative Information
Reactants
Products
States of Matter (s) solid (l)
liquid (g) gaseous (aq) aqueous
2 H2 (g) O2 (g) 2 H2O (g)
But also Quantitative Information!
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Information Contained in a Balanced Equation
Viewed in Reactants
Products terms of 2 C2H6 (g)
7 O2 (g) 4 CO2 (g) 6 H2O(g) Energy
Molecules Amount (mol) Mass (amu)
Mass (g) Total Mass (g)
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Balancing Chemical Equations by Explicit
Consideration of the Atom Conservation Equations
We start by considering the general algebraic
expression for a chemical equation
Where Cx, Cy, . represent the chemical formulas
of the reactants and Cu, Cv, represent the
chemical formula of the products.
The coefficients x, y, . represent the (sought
for) coefficients of the reactants and the
coefficients u, v, . represent the (sought for)
coefficients of the reactants
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We assume that the molecular formula for each of
the reactants and products is known and is
represented in the format
Where Cx is the reactant whose chemical balance
coefficient is x. The integers nxA are the number
of atoms of type A in the compound Cx.
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For each elemental specie in the reaction, there
must be the same number of atoms on both sides of
the chemical equation. We express this as a
series of atom conservation equations, one for
each element. For the element A
Similar equations are written for each one of the
atom types. All of these equations must be
simultaneously obeyed.
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There are N of the above equations, one for each
element (atom type) in the reaction. Generally
there are M coefficients to find using the N
equations. Unfortunately, in most chemical
equations, M gt N. Usually, we have the case that
M N1. Thus, we need to find one additional
equation.
One simple way to solve the problem is to
arbitrarily set one of the coefficients to one
and then solve the system of equations. We find
this approach works best when the coefficient of
the most complicated chemical species (the one
with the largest number of elements) is set to 1.
After all of the coefficients have been solved,
we then multiply the equation by the smallest
integer that will eliminate any fractions. Thus
our balanced equation contains the set of minimum
integers.
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Problem 8-1 Balance the following chemical
equation using the atom conservation method.
x XeF4 y H2O -gt u Xe v O2 w HF
Atom Conservation Equations Xe F H O
Solution
Final Result
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Balancing Chemical Equations- Example 2
Problem 8-2 The hydrocarbon hexane is a
component of Gasoline that
burns in an automobile engine to produce carbon
dioxide and water as well as
energy. Write the balanced chemical
equation for the combustion of hexane
(C6H14). Plan Write the skeleton equation from
the words into chemical compounds
with blanks before each compound. Assign
unknowns x, y, etc. to each blank
Skeleton equation
Assign unknowns
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Problem 8-2 Balance the following
x C6H14 (l) y O2 (g) -gt u CO2
(g) v H2O(g) Energy
Atom Conservation Equations C H O
Solution
Final Result C6H14 (l) O2 (g) -gt
CO2 (g) H2O(g) Energy
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Answers to Problems in Lecture 8

1. XeF4 2 H2O -gt Xe O2 4 HF
2. 2 C6H14 (l) 19 O2 (g) -gt 12 CO2 (g) 14
   H2O(g) Energy