When you are asked to determine the
percentage composition of a compound, it should be understood that this refers to the
percentage by mass. In other words, the percentage composition of water shows what
percentage of the mass of a water molecule is made up of hydrogen and what percentage of
the mass is made up of oxygen. Percentage composition by mass does not tell us the
relative rate by which the atoms combine, or what portion of the volume is made up by an
individual element. Percentage composition, as shown here, refers to mass.
Finding the percentage composition of a
compound should be very simple. You know how to determine the percentage composition
of other things by number, and the process used here is just the same. Look at two
examples of word problems.
Example 1. Homer has a box of assorted doughnuts. 3
of these doughnuts are chocolate. What percentage of Homer's doughnuts are
chocolate? (note, we are talking about total number, not mass, in this case.)
number of chocolate doughnuts
% of doughnuts that are chocolate =
--------------------------------- x 100
Total number of doughnuts
3
% of doughnuts that are chocolate = ----------- x 100
12
% of doughnuts that are chocolate = 25%
Example 2. Jim goes to a school that has 258 total
students. If 94 of the students are girls, what percentage of the student body is
made up of girls?
number of girls
% of the student body that is made up by girls = -------------------------- x 100
Total number of students
94
% of the student body that is made up by girls = -------------------------- x 100
258
% of the student body that is made up by girls = 36.4%
In both
cases, you found the percent composition by putting dividing one part by the total and
multiplying by 100.
part
percent composition = --------------------- x 100
whole
Finding the percentage composition by
mass works the same way. You divide the mass that one element contributes to the
compound by the mass of the entire compound. Let's look at the formula and two
examples.
partial mass from element
% of the mass of the compound that is made up by an element = -------------------------- x
100
total mass of the compound
Example 1. What percentage of the mass of carbon dioxide
(CO2) is made up by the carbon?
Solution:
first find the mass of the total compound.
C = 12.0 u x 1 atom = 12.0 u
O = 16.0 u x 2 atoms = 32.0 u
--------
44.0 u
next use the formula:
partial mass from carbon
% of the mass of CO2 that is made up by carbon =
-------------------------- x 100
total mass of the CO2
12.0 u
% of the mass of CO2 that is made up by carbon =
------------------------- x 100
44.0 u
% of the mass of CO2 that is made up by
carbon = 27.3%
Answer = 27.3%
Now, it is more typical to be asked what
the percentage composition of the entire compound is. In the example above, you can
assume that if carbon makes up approximately 27% of the mass of carbon dioxide then oxygen
makes up about 73%, for the total must be 100%. Example 2, below, shows the typical
wording for this type of problem. The solution will follow.
Example 2. What is the percentage composition of glucose (C6H12O6)
?
solution:
find the mass of the entire molecule,
C = 12.0 u x 6 atoms = 72.0 u
H = 1.01 u x 12 atoms = 12.1 u
O = 16.0 u x 6 atoms = 96.0 u
----------
180 u
Then use the formula for each element in the compound:
partial mass from element
% of the mass of the compound that is made up by an element = -------------------------- x
100
total mass of the compound
72.0 u
% for Carbon = ---------------- x 100 = 40.0%
180 u
12.1 u
% for Hydrogen = ---------------- x 100 = 6.7 %
180 u
96.0 u
% for Oxygen = ---------------- x 100 = 53.3%
180 u
One way to check your answer is to make sure that all of the
percentages add up to approximately 100%. (i.e. 40.0% + 6.7% + 53.3% = 100%)
Your total may be off by a few tenths of a percent, due to rounding.
Now you should be ready to try some on your own.
Percentage
Composition Quizzes |
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Please forward all questions, comments and criticisms to Gregory L. Curran.
© Copyright 2004 Fordham Preparatory School, All Rights Reserved.
Last Modified February 07, 2008 |
