Calculating Percent Error

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Because nobody gets it perfectly right
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When an experiment is done, it is pretty much
certain that the answer is not going to be exactly
correct.
Many variables and actions go into an
experiment. A change or a misstep in any one
of them can result in an answer that is a bit
different from the actual value.
Actions such as mismeasurement, lack of purity
of reagents, and poor lab technique can all
result in error.
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There are several ways that error can be
described.
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SYSTEMATIC ERROR v. RANDOM ERROR
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POSITIVE PERCENT ERROR v.
NEGATIVE PERCENT ERROR
◦ Systematic Error is when the error is built into
the lab and there is nothing the experimenter
can do about it.
◦ Example: If you were given a sample of Iron to
determine its density and the sample wasn’t
pure iron, it would constantly and consistently
throw off your values.
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Random Error is when the lab mistake can
happen differently from lab to lab.
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Example: Let’s say you are making a solution
and it needs to be stirred and then put aside.
There can be solution lost by stirring and
splashing material out of the beaker. Some water
might evaporate out at different rates as the
solution is put aside.
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Positive Error is when the value the experimenter
gets is greater than the actual value. The actual
value is considered the ‘right answer’.
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Example: If you are determining the
concentration of a solution and you determine it to
be 2.5 M and it is only 2.2 M then you will record a
positive error.
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Negative Error is when the value the experimenter
gets is less than the actual value.
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In Chemistry, it is very common to get negative
percent errors in your work.
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Example: If you are determining the
concentration of a solution and you determine it to
be 1.5 M and it is 2.2 M then you will record a
negative error.
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We use the following formula.
◦ O  Observed Result (what you got)
◦ A  Actual Result (what you should get)
◦(( O – A) / A ) x 100 %
◦ You will use this often in Lab.
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A Lab group was working in a Lab to
determine the percent of Magnesium in a
sample of Magnesium Oxide. They
determined it to be 58.3 % They looked up
the actual value and found it to be 60.3 %
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What is their percent error ?
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Let’s start with the formula
 ((
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O – A) / A ) x 100 %
Substituting in gives us the following:
◦ ((58.3 – 60.3) / 60.3 ) x 100 %
◦ ( - 2 / 60.3)  - .00331
◦ - .00331 x 100 % = - 3.31 %
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A different group doing the same lab got a value of
68.6 % Mg. What is their percent error ?

Using the same formula

(( O – A) / A ) x 100 %
Substituting in gives us:
◦ ((68.6 – 60.3 ) / 60.3 ) x 100 %
◦ (8.3 / 60.3) x 100 %  .1376
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.1376 x 100 % = 13.76 %
The mass of the Magnesium Oxide
sample could have been measured
incorrectly.
 Product could have been lost while
performing the steps of the lab.
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There could have been impurities in the sample.
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The scale could be miscalibrated making the
mass readings consistently off.
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For your labs, you will have to complete an
error page.
It will include percent error if it is a numerical
lab.
It will always include “Sources of Error”
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Make sure that you don’t include errors that
didn’t happen.
◦ Don’t say you dropped your beaker if you didn’t
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You can include possible systematic errors
that might be present.
◦ An impure sample
◦ Miscalibrated lab equipment
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The class website has more detail if needed.
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