Conversion Factors

Let’s consider the use of conversion factors
in chemistry. There are a number of approaches to calculating
quantities in chemistry. The most common is the conversion factor approach. This is sometimes called the factor label
method, or dimensional analysis. The bottom line is that we will convert from
one quantity to another using what is called a conversion factor. Let’s try two examples that deal with measurements
you should be familiar with. For example, I’m six feet tall. What is my height in inches? You might just say multiply by 12 and get
the answer, but actually you did something more complex. You read the problem and saw it asked you
to convert from feet to inches. Then you took a standard measurement, one
foot, and asked what is in one foot. Then you did the algebra, starting with the
number given in the problem and multiplying by a conversion factor. The conversion factor was constructed from
the two equivalent amounts, placing feet in the denominator and inches in the numerator. Algebra on the numbers, six times 12 divided
by one, gives 72. Algebra on the units, feet times inches divided
by feet, shows feet canceling giving inches. The fraction 12 inches divided by one foot
is called a conversion factor. In any conversion factor, the numerator and
denominator are equivalent amounts; in this case, 12 inches and one foot are the same
length. Multiplying by a conversion factor changes
the number and the unit, but not the actual length. I did not get taller or shorter on going from
six feet to 72 inches! Here is another example that asks how many
liters are contained in 165 milliliters of liquid. We’ll use our three skills; reading, chemistry
and math. Reading the problem shows we need to convert
165 milliliters to liters. For the chemistry, we know a standard volume
measurement is one liter, so we ask what is in one liter. There is of course one liter, but also 1000
milliliters. For the math, we start with the number we
are given, 165 milliliters, and construct a conversion factor with milliliters on the
bottom so that they cancel out, and liters on the top. The answer is then 0.165 liters. In summary, using conversion factors is a
standard method in which we can express a measurement in more than one unit. To construct a conversion factor, we read
the problem to determine what units were being converted, we expressed equivalent amounts
in those two units based on a known standard, and we constructed the conversion factor such
that the original unit canceled. This three step process will be useful in
many applications in chemistry. When quantifying elements and compounds, the
standard amount will be one mole of that material.

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