Chapter 2a. Measurements and Calculations

Transcription

1 Chapter 2a Measurements and Calculations

2 Chapter 2 Table of Contents 2.1 Scientific Notation 2.2 Units 2.3 Measurements of Length, Volume, and Mass 2.4 Uncertainty in Measurement 2.5 Significant Figures

3 Section 2.1 Scientific Notation Measurement Quantitative observation. Has 2 parts number and unit. Number tells comparison. Unit tells scale.

4 Section 2.1 Scientific Notation Technique used to express very large or very small numbers. Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

5 Section 2.1 Scientific Notation Using Scientific Notation Any number can be represented as the product of a number between 1 and 10 and a power of 10 (either positive or negative). The power of 10 depends on the number of places the decimal point is moved and in which direction.

6 Section 2.1 Scientific Notation Using Scientific Notation The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.

7 Section 2.1 Scientific Notation Using Scientific Notation If the decimal point is moved to the left, the power of 10 is positive. 345 = very large number If the decimal point is moved to the right, the power of 10 is negative = very small number In Webassign homework use format: 345 = 3.45e = 6.71e-02

8 Section 2.1 Scientific Notation Concept Check Which of the following correctly expresses 7,882 in scientific notation? a) b) c) d)

9 Section 2.1 Scientific Notation Concept Check Which of the following correctly expresses in scientific notation? a) b) c) d)

10 Section 2.1 Scientific Notation Precision vs. Accuracy good precision poor precision good precision poor accuracy good accuracy good accuracy

11 Section 2.1 Scientific Notation Measurement Accuracy How long is this line? There is no such thing as a totally accurate measurement!

12 Section 2.2 Units Nature of Measurement Measurement Quantitative observation consisting of two parts. number scale (unit) Examples 20 grams joule seconds If a CHP asks you what do you have and you answer I have 3 kilos, you may go to jail. You should have said I have 3 kg of doughnuts for my chemistry instructor.

13 British SI System Section 2.1 Scientific lll Notation Measurement in Chemistry Length Mass Volume Time meter gram Liter second Km=1000m Kg=1000g KL=1000L 1min=60sec 100cm=1m 1000mm=1m 1000mg=1 g 1000mL=1L 60min=1hr Foot pound gallon second 12in=1ft 16oz=1 lb 4qt=1gal (same) 3ft=1yd 5280ft=1mile lb=1 ton 2pts=1qt

14 Section 2.1 Scientific Notation Conversion between British and SI Units 2.54 cm = 1 in 454 g = 1 lb 1 (cm) 3 = 1 cc = 1 ml = 1 g water 1.06 qt = 1 L

15 Section 2.2 Units Prefixes Used in the SI System Prefixes are used to change the size of the unit.

16 Section 2.3 Measurements of Length, Volume, and Mass Length Fundamental SI unit of length is the meter.

17 Section 2.3 Measurements of Length, Volume, and Mass Volume Measure of the amount of 3-D space occupied by a substance. SI unit = cubic meter (m 3 ) Commonly measure solid volume in cm 3. 1 ml = 1 cm 3 1 L = 1 dm 3

18 Section 2.3 Measurements of Length, Volume, and Mass Mass Measure of the amount of matter present in an object. SI unit = kilogram (kg) 1 kg = lbs 1 lb = g

19 Section 2.3 Measurements of Length, Volume, and Mass Concept Check Choose the statement(s) that contain improper use(s) of commonly used units (doesn t make sense)? A gallon of milk is equal to about 4 L of milk. A 200-lb man has a mass of about 90 kg. A basketball player has a height of 7 m tall. A nickel is 6.5 cm thick. Copyright Cengage Learning. All rights reserved

20 Section 2.4 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Record the certain digits and the first uncertain digit (the estimated number).

21 Section 2.4 Uncertainty in Measurement Measurement of Length Using a Ruler The length of the pin occurs at about 2.85 cm. Certain digits: 2.85 Uncertain digit: 2.85 Estimate between smallest division! Copyright Cengage Learning. All rights reserved

22 Section 2.4 Uncertainty in Measurement Significant Figures Numbers that measure or contribute to our accuracy. The more significant figures we have the more accurate our measurement. Significant figures are determined by our measurement device or technique. Copyright Cengage Learning. All rights reserved

23 Section 2.4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 1. All non-zero digits are significant. 234 = 3 sig figs = 4 sig figs 1,234.2 = 5 sig figs 2. All zeros between non-zero digits are significant. 203 = 3 sig figs = 4 sig figs 1,030.2 = 5 sig figs

24 Section 2.4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 3. All zeros to the right of the decimal and to the right of the last non-zero digit are significant = 3 sig figs = 4 sig figs = 5 sig figs 4. All zeros to the left of the first non-zero digit are NOT significant = 3 sig figs = 4 sig figs = 5 sig figs

25 Section 2.4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 5. Zeros to the right of the first non-zero digit and to the left of the decimal may or may not be significant. They must be written in scientific notation = 2.3 x 10 3 or 2.30 x 10 3 or x sig figs 3 sig figs 4 sig figs

26 Section 2.4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 6. Some numbers have infinite significant figures or are exact numbers. 233 people 14 cats (unless in biology lab) 7 cars on the highway 36 schools in town

27 Section 2.4 Uncertainty in Measurement How many significant figures are in each of the following? 1) significant figures 2) ) ) 210 5) 200 students 6) significant figures 4 significant figures 2 or 3 significant figures infinite significant figures 1, 2, 3, or 4 significant figures

28 Section 2.4 Uncertainty in Measurement Chapter 2b Measurements and Calculations

29 Section 2.4 Uncertainty in Measurement 2.5 Significant Figures 2.6 Problem Solving and Dimensional Analysis 2.7 Temperature Conversions: An Approach to Problem Solving 2.8 Density

30 Section 2.4 Uncertainty in Measurement Using Significant Figures in Calculations Addition and Subtraction 1. Line up the decimals. 2. Add or subtract. 3. Round off to first full column =? = 38.4 or three significant figures

31 Section 2.4 Uncertainty in Measurement Using Significant Figures in Calculations Multiplication and Division 1. Do the multiplication or division. 2. Round answer off to the same number of significant figures as the least number in the data. (23.345)(14.5)(0.523) =? = 177 or three significant figures

32 Section 2.5 Significant Figures Rules for Rounding Off 1. If the digit to be removed is less than 5, the preceding digit stays the same rounds to 5.6 (if final result to 2 sig figs)

33 Section 2.5 Significant Figures Rules for Rounding Off 1. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by rounds to 5.6 (if final result to 2 sig figs) rounds to 3.9 (if final result to 2 sig figs)

34 Section 2.5 Significant Figures Rules for Rounding Off 2. In a series of calculations, do within the parenthesis first and determine the significant figures and use that answer to calculate and find the significant figures after the multiplication and/or division.

35 Section 2.5 Significant Figures Concept Check You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred). How would you write the number describing the total volume? 3.08 ml What limits the precision of the total volume? st graduated cylinder nd graduated cylinder or 3.08 ml

36 Section 2.6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? To convert from one unit to another, use the equivalence statement that relates the two units. 1 ft = 12 in The two unit factors are: 1 ft 12 in and 12 in 1 ft

37 Section 2.6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel). 6.8 ft 12 in in 1 ft Copyright Cengage Learning. All rights reserved

38 Section 2.6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. 6.8 ft 12 in 1 ft 82 in Correct sig figs? Does my answer make sense? Copyright Cengage Learning. All rights reserved

39 Section 2.6 Problem Solving and Dimensional Analysis Example #2 An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams? (1 kg = lbs; 1 kg = 1000 g) 4.50 lbs 1 kg lbs 1000 g 1 kg 3 = g 454 g OR 4.50 lbs x lb = 2043g = 2.04x10 3 g

40 Section 2.6 Problem Solving and Dimensional Analysis Concept Check What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation. Sample Answer: Distance between New York and Los Angeles: 2500 miles Average gas mileage: 25 miles per gallon Average cost of gasoline: $3.25 per gallon 1 gal $ mi = $325 = $(3.3x10 2 ) 25 mi 1 gal

41 Section 2.7 Temperature Conversions: An Approach to Problem Solving Three Systems for Measuring Temperature Fahrenheit Celsius Kelvin Gabriel Fahrenheit Lord Kelvin Copyright Cengage Learning. All rights reserved

42 Section 2.7 Temperature Conversions: An Approach to Problem Solving The Three Major Temperature Scales F = 1.8C + 32 C = (F-32)/1.8 K = C What is 35 o C in o F? 95 o F What is 90 o F in o C? 32 o C What is 100K in o C? -173 o C

43 Section 2.7 Temperature Conversions: An Approach to Problem Solving Exercise The normal body temperature for a dog is approximately 102 o F. What is this equivalent to on the Kelvin temperature scale? a) 373 K b) 312 K c) 289 K d) 202 K C = (F-32)/1.8 = (102-32)/1.80 = 38.9 o C K = C = = 312 K

44 Section 2.7 Temperature Conversions: An Approach to Problem Solving Exercise At what temperature does C = F? Copyright Cengage Learning. All rights reserved

45 Section 2.7 Temperature Conversions: An Approach to Problem Solving Solution Since C equals F, they both should be the same value (designated as variable x). Use one of the conversion equations such as: T C T F Substitute in the value of x for both T C and T F. Solve for x. Copyright Cengage Learning. All rights reserved

46 Section 2.7 Temperature Conversions: An Approach to Problem Solving Solution T C T F x x x = x x = -32 x = -32/0.80 x 40 So 40 C = 40 F Copyright Cengage Learning. All rights reserved

47 Section 2.8 Density Mass of substance per unit volume of the substance. Common units are g/cm 3 or g/ml. mass Density = volume Copyright Cengage Learning. All rights reserved

48 Section 2.8 Density Measuring the Volume of a Solid Object by Water Displacement

49 Section 2.8 Density Example #1 A certain mineral has a mass of 17.8 g and a volume of 2.35 cm 3. What is the density of this mineral? mass Density = volume 17.8 g Density = 2.35 cm 3 Density = g/cm Copyright Cengage Learning. All rights reserved

50 Section 2.8 Density Example #2 What is the mass of a 49.6 ml sample of a liquid, which has a density of 0.85 g/ml? mass Density = volume x 0.85 g/ml = 49.6 ml mass = x = 42 g OR 49.6 ml 0.85 g/ml = 42 ml g

51 Section 2.8 Density Exercise If an object has a mass of g and occupies a volume of L, what is the density of this object in g/cm 3? a) b) 1.95 c) 30.5 d) g 1L 1mL 3 = 1.95g/ L 1000mL 1cm cm 3

52 Section 2.8 Density Using Density as a Conversion Factor How many lbs of sugar is in 945 gallons of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is g/ml? 945 gal 4 qt 1 gal 1 L 1.06qt 1000 ml 1 L g T 1 ml 60.0 g S 100 g T 1 lb s 454g S = lbs = 6.06 x 10 3 lbs sugar lbs of what? Coffee? Cocaine?

53 Section 2.8 Density Using Density as a Conversion Factor Using the Formula How many lbs of sugar is in 256 L of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is g/ml? D = M V Solve for Mass ( g/ml)(256,000 ml) = g T DV = M = 3.29 x 10 5 g T 3.29 x 10 5 g T 1 lb T 454 g T 60.0 lbs S 100 lbs T = lbs S = 4.35 x 10 2 lbs S = 435 lbs S

54 Section 2.8 Density Concept Check Copper has a density of 8.96 g/cm 3. If 75.0 g of copper is added to 50.0 ml of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise? a) 8.4 ml b) 41.6 ml c) 58.4 ml d) 83.7 ml 1 1mL 75.0g = 8.37mL Cu g 1cm 3 cm 8.37 ml Cu ml water = 58.4 ml