PROPAGATION OF

ERROR

We tend to use these words interchangeably, but in science they are different

Accuracy vs. Precision

Accuracy Versus Precision

Pin the electron on the halogen …

Periodic Table

An electronic balance is used to measure the mass of a salt (NaCl). The balance displays 0.53 g. What is range in values for the mass of the salt within the precision of the electronic balance?

Example

An electronic balance is used to measure the mass of a salt (NaCl). The balance displays 0.53 g. What is range in values for the mass of the salt within the precision of the electronic balance?

0.53 ±0.01 g

The values will range from 0.52 to 0.54 g

Random Error

random error

Table 1 – Temperature of Solutions

NOTE: the uncertainty appears in the heading for the column.

Sample Data Collection

Sample Temperature ( 0.2°C)

Solution A 15.8Solution B 20.4

errors in measurements because of limitations in the experimental design or procedure

these errors always affect a result in a particular direction i.e. the recorded value will consistently be either too high or too low.

reduce the accuracy of a measurement

Systematic Errors

Example - A piece of Cu wire is weighed on the electronic balance. The measurement would be recorded as 2.89 g 0.01g.

The absolute error = ± 0.01 g

% error = 0.01/2.89 x 100% = 0.35%

Absolute and Percentage Error

% error = absolute error / measurement x 100 %

The tracking of the error in each piece of equipment through all calculations

 Addition and Subtraction – Add the absolute

errors

Multiplication and Division – Add the % errors

NOTE: Report all final calculated values with an absolute error.

Error Propagation

If a literature can be found, then calculate the % experimental error as part of the Data Processing in your report.

A reference must be cited for a literature value

Report % experimental error as a positive value

Percent Experimental Error

% experimental error = literature value - value obtained in an experiment X 100% literature value

Example – Ms Delvecchio’s awesome chemistry students measured the amount of Fe in a vitamin tablet. They determined that the a table contained 25 mg of Fe. The label on the bottle indicated that the table contained 28 mg. What is the % experimental error?

Percent Experimental Error

Example – Ms Delvecchio’s awesome chemistry students measured the amount of Fe in a vitamin tablet. They determined that the a table contained 25 mg of Fe. The label on the bottle indicated that the table contained 28 mg. What is the % experimental error?

% experimental error = (28-25) / 28 x 100% = 10%

Percent Experimental Error

If the % experimental error is GREATER than the % equipment error, then the error from the equipment does NOT account for all the error in the value from the experiment. Therefore, there are significant systematic errors (experimental design flaws) that must be identified.

A statement like this must appear in the Conclusion section of your lab report.

These other sources of error must be discussed in the Evaluation section of your lab report.

So what all this tell us?

1. ± 0.01 g2. ± 0.05 mL3.

The Activity

Trial Density (g/mL)

1 2.72

2 2.69

3 2.65

Trial 1 on board …..

Question 4

Question 4

Trial 3 D = 2.65 g/mL

Trial 2 D = 2.69 g/mL

Absolute error = 1.44/100 x 2.69 = 0.04D = 2.69 g/mL ± 1.44% OR 2.69 ± 0.04 g/mL

D = 2.65 g/mL ± 1.42% OR2.65 ± 0.04 g/mL

average density = (2.72 + 2.69 + 2.65) / 3 = 2.69 g/ mL

Absolute error = 0.04 + 0.04 + 0.04 = 0.12

% error = 0.12/2.69 x 100 = 4.46 %

Question 5

% experimental error = (2.70 – 2.69)/2.70 X 100 = 0.37%

Since the % experimental error is SMALLER than the % equipment error, there are NO significant systematic

errors in this experiment.

i.e., the equipment error accounts for the difference btwn the average experimental value and the literature value.

Question 6

Question 7

% error = 2.81 % compared to the value for Trial 1 of 1.46%absolute error = 2.81/100 x 2.72 = 0.08 compared to 0.04 for Trial 1

The equipment error accumulates with each measurement taken. A design that involves fewer measurements will have less equipment (random) error.

What does this mean?

This experiment is accurate as the average experimental value differs from the literature value by 0.37 %.

The three trials are equally precise as the absolute error is the same for each trial (i.e., 0.04 g/mL).

The alternative method proposed in Question 7 gives a less precise value (i.e., 0.08 g/mL)

Question 8

In this experiment, the mass and volume of aluminum were measured in order to determine the density of the metal. Three trials were completed which produced equally precise results. The experimental density values were found to be 2.72 g/mL, 2.69 g/mL and 2.65 g/mL. The first two values were the most accurate because they were closest to the literature value of 2.70 g/mL1. The average density was found to be 2.72 g/mL. The total equipment error was found to be 4.46 %. The experimental error was found to be 0.37 %. Since this value was smaller than the equipment error, 1.42%, systematic errors were not significant.

1 Winter, M. (2012). Web elements. Retrieved on April 1, 2012 from http://www.webelements.com/aluminium/physics.html .

Question #9