Chemistry: Matter and Change
1st Edition
ISBN:9780078746376
Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Publisher:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Chapter9: Chemical Reactions
Section: Chapter Questions
Problem 64A
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Question
![Application A typical application of linear systems to chemistry is balancing a chemical
equation. The rationale behind this is the Law of conservation of mass which states the
following:
"mass is neither created nor destroyed in any chemical reaction. Therefore balancing of
equations requires the same number of atoms on both sides of a chemical reaction. The
mass of all the reactants (the substances going into a reaction) must equal the mass of the
products (the substances produced by the reaction)."
As an example consider the following chemical equation
CH + O → CO, + H,O.
Balancing this chemical reaction means finding values of x, y, z and w so that the number of
atoms of each element is the same on both sides of the equation:
xC₂H6+ YO2 → ZCO2+ wH₂0.
This gives the following linear system:
(2x = z
6x = 2w
2y = 2z+w
The general solution of the above system is
X=
y =
Z=
WE
7w
2w
XAN 3
y
W
"C"
"H"
"0"
= W
[1/3]
7/6
2/3
choosing w = 6 gives
ہو"
y
N 3
W
27
4
6
Since we are looking for whole values of the variables x, y z, and w, choose x=2 and get y-7, z=
4 and w-6. The balanced equation is then:
2C2H 6+ 702 4CO2+ 6H₂O.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F510b87f1-1062-4180-bcf7-c90378c42705%2F912835cb-0332-46d3-8451-7ca4d78e0d18%2Fm1t8v7h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Application A typical application of linear systems to chemistry is balancing a chemical
equation. The rationale behind this is the Law of conservation of mass which states the
following:
"mass is neither created nor destroyed in any chemical reaction. Therefore balancing of
equations requires the same number of atoms on both sides of a chemical reaction. The
mass of all the reactants (the substances going into a reaction) must equal the mass of the
products (the substances produced by the reaction)."
As an example consider the following chemical equation
CH + O → CO, + H,O.
Balancing this chemical reaction means finding values of x, y, z and w so that the number of
atoms of each element is the same on both sides of the equation:
xC₂H6+ YO2 → ZCO2+ wH₂0.
This gives the following linear system:
(2x = z
6x = 2w
2y = 2z+w
The general solution of the above system is
X=
y =
Z=
WE
7w
2w
XAN 3
y
W
"C"
"H"
"0"
= W
[1/3]
7/6
2/3
choosing w = 6 gives
ہو"
y
N 3
W
27
4
6
Since we are looking for whole values of the variables x, y z, and w, choose x=2 and get y-7, z=
4 and w-6. The balanced equation is then:
2C2H 6+ 702 4CO2+ 6H₂O.
Transcribed Image Text:Balance the following chemical equation.
Na₂S O6 + H₂O2 → Na₂SO4 + H₂O + H₂SO4
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