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High School Chemistry: Accuracy and Precision

Subject:

Science  

Grades:

10, 11, 12  

Summary:

This lesson provides an understanding of accuracy and precision. The topic is usually encountered within the first chapter and first days of a general chemistry course. Understanding this is important particularly in regards to any laboratory experience. Although there are numerous explanations provided in textbooks, they often use overly abstract analogies. The analogies often leave the students as much in the dark just as much as the central problem did.

The worksheet with the lesson provides a practical result from this topic. The practical aspect of the problem also provides the chance for students to be able to methodically express technical ideas in writing. It shows them the proper way to create a graph from a table of data. They will then give instructions on how to use the graph. Additionally they will gain experience in the proper way to present tables and graphs as the beginning of a cornerstone to express the mastery of chemical concepts.

Prepare The Student:

  • Start a discussion on the things we measure. How many of these need to be accurate? How many of these need to be precise?
  • Point out although these two words are interchangeable in ordinary English, these are not the same words in chemistry. Another example would be heat and temperature, (which fit in to this lesson nicely).
  • Read the textbook definition of what precision and accuracy mean. Ask the class what it means, and if it makes sense?

 

The Scenario:

There are three groups of lab students: John and Jane Smith, Smaug the Dragon, and John Q. Public.

They are given the simplest of experiments. The experiment is so simple in fact, even they can do it. They will boil water. Based on the data they collect, we will be able to decide how well they were able to boil water.

They will boil water four times and measure the temperature at which the water boils. The beaker of water is set up on a ring stand with a pot of water around it. It is heated with a Bunsen burner.

                                        

Figure 1: Experimental Apparatus

This is the experimental set up for boiling water to find its boiling point

 

At this point you may want to show them an overhead transparency or PowerPoint of the apparatus depicted above. The slide also includes the following table of results. It is also possible to show them with this example how to organize their work in terms of tables and to correctly label them. As an alternative you can set up the apparatus while you talk to the students.

 

Table 1:

Tabulated temperatures in ⁰C

Trial

The Smith’s

Smaug

John Q. Public

1

94.3

107.1

98.2

2

110.4

110.2

101.3

3

96.5

106.4

100.4

4

99.3

108.3

99.5

Average

100.1

108.0

99.9

 

If you compare the Smith’s results to John Q. Public’s results, the average looks very close. Yet when you look at the data that contribute to each average in each case, you see there is a difference. These two experiments were not in fact done with equal results.

In the case of the Smith’s, the average is 100.1ºC. This is very close to the known boiling point of water, by definition. If you judged their results based only on their average value on the known boiling point of water, you might be inclined to believe their results were accurate. The Smith’s however failed in their technique. The recorded values are wildly different from each other. You can have no real confidence in predicting what their next recorded value will be.

When some college students performed this exact lab, it turned out their lab station was near an open door. That meant at any given moment the flame from the Bunsen burner waned or the water bath assembly received a cold blast of air. Unfortunately despite the fact John and Jane Smith are happily in love, they did not learn how to use a Bunsen burner correctly.

Based on the data they collected, they introduced a random error. Their measurements are not accurate and are not precise.

Now you can look at Smaug’s data. He is normally a straight A student. He studies hard and one day wants to be accepted into “Elf Terrorizing” school. When you examine his data, the first thing that pops out at you is the average value for boiling water is 108.0ºC. You might be tempted to believe this experiment was done poorly. Don’t be too quick. Smaug’s recorded data points are reasonably close together. That means his results are reproducible. Within a narrow range of temperatures, you can successfully predict the next measured temperature.

The error came in when Smaug recognized the error the Smith’s introduced into their experimental method. Instead of using a Bunsen burner, Smaug decided to use his dragon breath to heat the beaker and water bath. What he did not know you will learn. Part of his dragon breath heated the sides of the thermometer making the liquid in the thermometer expand more than normal. The temperatures he read were not accurate for the boiling point of water.

He introduced a systematic error. His attention to detail though, made his data precise.

At last you come to John Q. Public. He came prepared for the lab and makes it looks easy. He is the kind of guy that shows up early and stays late, if that’s what it takes. Sometimes the other students see him gaze into space as he secretly wishes class was harder.

Just the type of person you are, no doubt.

He stayed up until 11:30 last night to study the correct use of a Bunsen burner and then promptly turned the light out. He would never dream of staying up past his bed time. When he turned on his Bunsen burner, he used his home economics textbook up in front of the experiment to prevent cold drafts of air.

John’s recorded temperatures are clustered around 100°C. This argues well for the fact they are reproducible. The average temperature is 99.9°C. This is very close to the actual value of 100°C for boiling water. John’s measurements are both accurate and precise.

 

Supplementary:

There are several teachable moments associated with completing the worksheets.

  • In writing a step-by-step procedure for finding the boiling point of water they will learn to organize their work and explain in simple terms how to do and understand a procedure in its simplest components.
  • They learn to create a graph from a table
  • Correctly label a graph with a correct number scale and x and y axes labeled. This should be done neatly on graph paper or a program designed for graphing like Excel.
  • Write a paragraph to go with the graph explaining what it shows and how it can be used.

 

 

Two PowerPoint slides have been included which can be printed out and passed out, printed onto transparencies and used as an overhead projection, or used as part of a PowerPoint presentation.

 

Snap Into Action!

 

Because John Q. Public has his act together and can boil water  just as well as anyone else, he is hired to manage Le Snob Bistro. He is in charge of boiling pasta.

The first task they must accomplish every morning is to find the boiling point of water so the bistro can cook the pasta until it is al dente.

The relationship between the temperature of boiling water and the length of the pasta cooking time is that for every 0.5°C that the boiling water does not boil at 100°C, it alters the cooking time by 1 minute. The table below summarizes the relationship.

bp°C

99.0

99.5

100

100.5

101.0

minutes

6

7

8

9

10

 

 

 

1)   

     Write an easy to follow . Explain when necessary how John Q. Public will evaluate the results when they hand in their data each morning.

2)   

     Prepare a graph and explain how they can use it so the bistro chefs will know how long to boil the pasta.

 

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Resources:

waterboiling point  [DOWNLOAD], 51b63467cabfd1.63624435_AccuracyPrecision  [DOWNLOAD]