Problem Solving. How to handle numbers.

Transcription

1 Problem Solving How to handle numbers. 1

2 Problem Solving Chemistry is a quantitative science. The only way to get good at solving quantitative problems is to practice. 2

3 Practice The key math in chemistry involves algebra and conversion factors. Try some algebra first. 1. Solve PV = nrt for T 2. Solve X = M YZ for Z Practice: Problem set #1a & 1c 3

4 Conversion Factors The most important math technique in chemistry. Used in regular life: Currency (euros to dollars) Measuring length, mass, volume (English to metric) Speed limits in other countries Cooking, carpentry, etc. 4

5 Conversion Factors A conversion factor is made from two equal quantities. Example: 1 cm = m (see Table C) 1 x 10-2 Practice: Write equalities for: minutes to hours micrograms to grams Problem set #2b & 2f 5

6 Conversion Factors Anything divided by itself equals one. 1 hr = 1 hr thus: 1hr 1hr = 1 60 min = 1 hr 60 min 1 hr = 1 Conversion factor and 1 hr 60 min = 1 6

7 Conversion Factor: Definition a ratio of two equal quantities, with units. It equals one. 1 cm = 10-2 m, thus 10-2 m 1 cm = 1 and 1 cm 10-2 m = 1 7

8 More Conversion Factors Baby sitter costs $5 per hour $5 = 1 hr Thus for this job, $5 1 hr = 1 and 1 hr $5 = 1 8

9 Using Conversion Factors to Solve Real Problems I ll do one, then it s your turn! How many kilometers are there in 475 m? 9

10 Solving Real Problems Try it using conversion factors: If apples cost 5 for a dollar, how many apples can you buy for $4.40? Don t use ratios or proportions! Practice: Problem set #3a & 3d 10

11 Multiple Conversion Factors I ll do one: How many micrograms is 45.2 kilograms? Try one: How many centimeters is 3.43 nanometers? Try problem 4f. 11

12 They Get Tougher! I ll do one. The speed of light is 3.0 x 10 8 m/s. How fast is this in km/hr? You try one. How fast is 60. miles per hour in m/s? (1609 m = 1 mile) miles/hr 12

13 Density is a Conversion Factor! The density of aluminum is 2.7 g/cm 3 D Al = 2.7 g/cm 3 Thus for aluminum, 2.7 g = 1 cm g 1 cm 3 1 cm 3 = 1 and = g What is the volume of 6.45 g aluminum? 13

14 Regents Table C 1 cg = 10-2 g c = 10-2 Never put the number from Table C next to the letter on Table C in a conversion factor. 14

15 Area & Volume Conversion Factors How many cm is 4.5 m? How many cm 2 is 4.5 m 2? How many cm 3 is 4.5 m 3? 15

16 Ratios 4 The sides of this rectangle are in a ratio of 4:3. 3 In science we divide the 1 st number by the 2 nd number & express as a decimal: 4/3 = 1.33 A recipe call for 3 cups of water for every 2 cups of flour. What is the ratio of water to flour? 16

17 Graphing A way to visualize data. 17

18 Graphing Example A bicycle trip: Distance from home (km) Time (hr)

19 Graphing Steps 1. Select the x and y axes: X = horizontal axis = independent variable y Y = vertical axis x = dependent variable 19

20 Select x and y Axes time 20

21 Graphing Steps 2. Scale the axes on the paper count squares leave room to label the axes use full sheet of paper start at 0 if reasonable multiple of 1, 2, 5 units / square don t break the axis. 21

22 Scale Axes on the Paper time 22

23 Graphing Steps 3. Label the graph name the x & y variables don t forget units select a meaningful title 23

24 Label the Graph Bicycle Trip time (hr) 24

25 Graphing Steps 4. Enter data and show trend line use bold dots for data is 0,0 a valid point? draw smooth curve (line) don t connect the dots 25

26 Enter Data & Show Trend Line Bicycle Trip time (hr) 26

27 Graphing Steps 5. Analyze the graph direct vs. inverse relationship calculate the slope use line, not data points Slope = change in y change in x = D y D x 27

28 Analyze the Graph Bicycle Trip Slope = 14. km/hr 28 km 2.0 hr time (hr) 28

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30 Warm-up What is the volume of a sample of cough syrup that has a mass of 51 g? Density of cough syrup is g/cm 3. 30

31 1. Solve for A XY = Warm-up B A + D 2. Express as conversion factor: micrograms and grams 3. How many cm is 67 m? 31

32 Warm-up How many mg is 1.23 ng? How fast is 60. miles per hour in m/s? (1609 m = 1 mile) miles/hr 32

33 Warm-up How many meters is 27 nanometers? How many seconds are there in 1.0 yr? 33

34 Warm-up Convert 27 kg to ng. An orange weighs 217 g. How many oranges are in 5.21 kg of oranges? The density of iron is 7.87 g/ml. What is the volume of 2.1 kg of Fe? 34

35 Graphing Practice Plot the density data from your lab! 35

36 Warm-up Convert 14.7 deciliters to microliters. A room measures 5.0 m x 3.0 m x 8.0 m. What is the room s volume in L? 36

37 Warm-up How many kg is 3.4 x 10-2 ng? Covert 42 dm 2 to m 2. The speed limit in Nepal is 105 km/hr. At this rate, how many miles could you travel in 2.52 days? (given 1609 m = 1.00 mi) 37