Measurement and Calculations

1. Chapter 2 Measurement and Calculations

2. Scientific Method Observing and Collecting data Uses of senses to obtain information Qualitative and/or Quantitative Formulating Hypotheses Make generalizations Testing Hypotheses Controls variables Formulating Theories Model-explanation of how phenomena occur and how data or events are related Theory-broad generalization that explains a body of facts or phenomena

3. Using and Expressing Measurements A measurement is a quantity that has both a number and a unit A quantity is something that has magnitude, size, or amount. measurement ? quantity the teaspoon is a unit of measurement volume is a quantity The choice of unit depends on the quantity being measured.

4. Density Is the ratio of the mass of an object to its volume Is an intensive property that depends only on the composition of a substance, not on the size of the sample. The density of a sample generally decreases as its temperature increase

5. Density A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum.

6. Conversion Factors A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other.

7. Conversion Factors How many nickels are in 4 dollars and 35 cents?

8. Dimensional Analysis

9. Dimensional Analysis You're throwing a pizza party for 15 and figure each person might eat 4 slices. You call up the pizza place and learn that each pizza will cost you $14.78 and will be cut into 12 slices. How much is the pizza going to cost you? Write all conversion factors and solve

10. Accuracy, Precision, and Error Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

11. Accuracy and Precision

12. These values were recorded as the mass of products when a chemical reaction was carried out three separate times: 8.83 g; 8.84 g; 8.82 g. The mass of products from that reaction is 8.60 g. The values are a. accurate, but not precise. b. precise, but not accurate. c. both accurate and precise. d. neither accurate nor precise.

13. Determining Error Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. % error = experimental value-accepted value accepted value

14. Practice Problem A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?

15. Significant Figures Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. The term significant does not mean certain.

16. “Sig Figs”

17. “Sig Figs” How many significant figures are in each of the following measurements? 28.623 g 3440 cm 910.0 m 201 000 L 0.006 300 kg

18. The number of significant figures in the measurement 0.000 305 kg is a. 2. c. 6. b. 3. d. 7.

19. How many significant figures are in the measurement 811.40 grams? a. two c. four b. three d. five

20. Which of these measurements has been expressed to three significant figures? a. 0.052 g c. 3.065 g b. 0.202 g d. 500 g

21. “sig Figs” Rounding

22. What is the measurement 111.009 mm rounded off to four significant digits? a. 111 mm c. 111.01 mm b. 111.0 mm d. 110 mm

23. What is the measurement 1042 L rounded off to two significant digits? a. 1.0 x 103 L c. 1050 L b. 1040 L d. 1.1 x103 L

24. The measurement 0.035550 g rounded off to two significant figures would be a. 0.03 g. c. 0.036 g. b. 0.35 g. d. 3.5 x 102 g.

25. “sig Figs” w/ addition/subtraction When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. 3.461728 + 14.91 + 0.980001 + 5.2631 23.1 + 4.77 + 125.39 + 3.581 22.101 - 0.9307 564,321 - 264,321

26. “sig Figs” w/ Multiplication/Division For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. 13.7 x 2.5 = 200 x 3.58 = 5000 / 55 = 0.00003 x 727 = 8.5/0.356 =

27. How many significant digits should be shown in the product of 1.6 cm and 2.4 cm? a. 1 c. 3 b. 2 d. 4

28. Express the sum of 7.68 m and 5.0 m using the correct number of significant digits. a. 12.68 m c. 13 m b. 12.7 m d. 10 m

29. Scientific notation

30. Scientific Notation If you moved the decimal to the left, n is positive. If you moved it to the right, n is negative. Example: 1 320 000 000

31. How would 0.00930 m be expressed in scientific notation? a. 93 x 10–4 m c. 9.30 x 10–3 m b. 9.3 x 10–4 m d. 9.30 x 10–5 m

32. Express in Scientific Notation 61,500   0.0000568   64,960,000   Express in Standard Form 4.22715 x 108 3.078 x 10-4 9.004 x 10-2

33. Direct vs. Inverse Two quantities are directly proportional to each other if dividing one by the other gives a constant value y= k x Two quantities are inversely proportional to each other if their product is constant xy = K