1.2 Measurements
Measuring We have all measured things before, but how would you define it? Measurement: comparing an unknown quantity to a standard unit (known quantity)
How long is the arrow?
Any measurement can be accurately measured to only 1/10 of the smallest increment For this example, each increment is 1, and 1/10 of 1 is 0.1. So the measurement can only be accurate by 0.1. The most accurate measurement of the blue arrow would be 3.1, 3.2, or 3.3. We cannot say 3.21 or 3.205
How long is the arrow? The smallest increment is 0.5, so 1/10 of it is 0.05. So you can be accurate to 0.05 unit. 3.05, 3.10, 3.15, 3.20 can all be acceptable
How long is the red arrow? Each increment is 0.1 cm, so we can report measurements with an accuracy of 0.01 1.81, 1.82, 1.83 are acceptable. 1.824 is not. 1cm 2cm 3cm
Measurements can be described by accuracy and precision Accuracy describes how close a measurement was to the actual value Precision describes how close the measurements were to each other
Practice A student performed an experiment to extract carbon out of Cheetos. There was suppose to be 5.0 grams of carbon, but the student finds the following after multiple attempts: 3.4 g, 3.1 g, 3.2 g, 3.3 g. How would you describe the student s measurements? What if the student found the following? 1.4 g, 4.3 g, 0.23 g, 3.2 g What if the student found the following? 4.7 g, 4.2 g, 5.2 g, 5.5 g What if the student found the following? 5.1 g, 5.0 g, 5.1 g, 4.9 g
Percent Error Mistakes in measurements can occur The percent error is just one method to statistically determine how accurate results are It assumes we know what the measurement should be (accepted value)
You measure the mass of the product of a chemical reaction to be 3.80 grams. According to your theoretical calculations, the mass should have been 3.92 grams. What is the percent error of your experiment?
1. Individually measure the volume of the three different samples. Label the samples according to the max volume of each container. 2. Within your group, share your measurements. Discuss and come up with the most accurate measurements. 3. Which container is the most accurate device to use? Discuss and write down why you guys think so. 4. Design a simple experiment you can perform to actually test which container is the most accurate. 5. Place names and period.
Significant Figures The digits that can be reported accurately, plus one estimated digit, are called significant figures In chemistry, significant figures are important because accuracy is important
5 Rules of Sig Figs 1. All nonzero digits are significant A. 237 has three significant figures. B. 1.897 has four significant figures. What about 39,000?
2. Zeros between other nonzero digits are significant. A. 39,004 has five significant figures. B. 5.02 has three significant figures.
3. Zeros in front of all of the nonzero digits are not significant. A. 0.008 has one significant figure. B. 0.000416 has three significant figures. But what about 5.0000023?
4. Zeros after all nonzero digits are not significant. A. 140 has two significant figures. B. 75,210 has four significant figures. UNLESS.
5. Zeros with a decimal point are significant. This is true whether the zeros occur before or after the decimal point. A. 620.0 has four significant figures. B. 19,000. has five significant figures What about 0.000400? (Rule 3)
Practice. Determine number of SF A. 120,000 B. 0.00324 C. 0.002089 D. 12,005 E. 120,000. F. 120,000.00 G. 0.0039000
Exceptions to SF Exact quantities are numbers we know exactly A. Counter numbers, such as number of students B. Numbers in conversion factors, such as 1 feet/12 inches Exact numbers have infinite significant figures
Adding or Subtracting The answer is determined by the least number of significant figures to the right of the decimal points
ADDING 70.4312 + 5.3 75.7312 Answer: 75.7
SUBTRACTING 6,537.386-30.01 6,507.376 Answer: 6,507.37
Multiplying or dividing The answer is determined by the least number of significant figures
Multiplying (2.596) (1.4) = 3.6344 Answer: 3.6
Dividing (3.491)(580) = 5,338.202 (0.3793) Answer can have only 2 Sig Fig = 5,300
a. 8.7 g + 15.43 g + 19 g = 43.13 g b. 4.32 cm x 1.7 cm = 7.344 cm 2 c. 853.2 L - 627.443 L = 225.757 L d. 38.742 kg 0.421 = 92.023 75 kg e. 5.40 m x 3.21 m x 1.871 m = 32.432 914 m 3 f. 5.47 cm 3 + 11 cm 3 + 87.300 cm 3 = 103.770 cm