2. Math Concepts Chemistry

3. Observations A large part of laboratory chemistry is making observations. A large part of laboratory chemistry is making observations. Two types of observations: Qualitative observations = descriptive observations, no numbers involved Quantitative observations = observations described by a numbered measurement.

4. Accuracy and Precision Chemists need to have to make exact and reproducible results. Chemists need to have to make exact and reproducible results. Accuracy = measurements that only have slight deviation from the true value. Accuracy = measurements that only have slight deviation from the true value. Depends on: Depends on: Equipment used Equipment used Precision = being able to reproduce a measured value through several experimental runs or trials. Precision = being able to reproduce a measured value through several experimental runs or trials. Depends on: Depends on: The person making the measurements The person making the measurements

5. Accuracy and Precision

6. Experimental results: Experimental results: Sean:2.56g Sean:2.56g2.37g 2.41g 2.41g Morgan: 3.12g Morgan: 3.12g 2.11g 2.11g 4.32g 4.32g Doug: 3.22g Doug: 3.22g 3.25g 3.25g 3.27g 3.27g If the true value of the mass is 3.10g, explain each students measurements in terms of the words accuracy and precision. If the true value of the mass is 3.10g, explain each students measurements in terms of the words accuracy and precision. Answer: Sean not accurate, but precise Morgan accurate, but not precise Doug: good accuracy and very precise.

7. Why is it so important to be accurate and precise as a chemist? Medicine – certain amounts can turn into lethal dosages Medicine – certain amounts can turn into lethal dosages Work with flammable products Work with flammable products To insure reproducible products (cosmetics, soap, hair products…) To insure reproducible products (cosmetics, soap, hair products…) To insure quality of our environments (air and water quality) To insure quality of our environments (air and water quality)

8. How can a chemist achieve exactness in measurements? Significant Digits/figures. Significant Digits/figures. Sig figs = the reliable numbers in a measurement and at least one estimated digit. Sig figs = the reliable numbers in a measurement and at least one estimated digit.

9. Make readings for the following measurements using significant figures. Make readings for the following measurements using significant figures.

10. Rules for significant figures 1. All non-zero numbers or digits are significant. Ex: 23 g 1. All non-zero numbers or digits are significant. Ex: 23 g 2. All zero in-between 2 non-zero numbers are significant. Ex: 2.002g 2. All zero in-between 2 non-zero numbers are significant. Ex: 2.002g 3. When working with a small decimal number, work your way over to the right until you get to your 1 st non-zero number - anything from there over is significant. Ex: 0.00250g 3. When working with a small decimal number, work your way over to the right until you get to your 1 st non-zero number - anything from there over is significant. Ex: 0.00250g 4. Final zeros 25.00g are significant. 4. Final zeros 25.00g are significant. 5. When working with large numbers (no decimals), look for your 1 st non-zero number – anything from there to the beginning of the number are significant. Ex: 240100g 5. When working with large numbers (no decimals), look for your 1 st non-zero number – anything from there to the beginning of the number are significant. Ex: 240100g 6. A line/bar over or under a zero designates it as significant. 6. A line/bar over or under a zero designates it as significant. 7. Exact numbers = numbers that you are use to working with are unlimited in terms of significant figs. Ex: there are 12 men on the football field. = unlimited. 7. Exact numbers = numbers that you are use to working with are unlimited in terms of significant figs. Ex: there are 12 men on the football field. = unlimited.

11. Significant Figures An easy way to count the number of significant figures in any number is: An easy way to count the number of significant figures in any number is: DOT LEFT – NOT RIGHT *If there is a visible decimal, look all the way to the left of the value and move to the right. Begin counting digits after your first non-zero digit. Any numbers that follow a non-zero digit are significant. EX: 2.500 = 4 sig figs 500.00 = 5 sig figs

12. *If there is no visible decimal, look all the way to the right of the value and move to the left. Begin counting digits after your first non-zero digit. Any numbers that precede a non-zero digit are significant. EX: 2500 = 2 sig figs 50000 = 1 sig figs 5001 = 4 sig figs

13. If an exponential number, look at coefficient only. If an exponential number, look at coefficient only. If decimal at end all numbers are significant. If decimal at end all numbers are significant. A line over a zero indicates that zero as the last significant digit. A line over a zero indicates that zero as the last significant digit. Use decimal or line, not both. Use decimal or line, not both. No lines over nonzero digits. No lines over nonzero digits.

14. Examples How many sig figs are in the following: How many sig figs are in the following: 20 kg 20 kg 1 sig fig 1 sig fig 0.0051 g 0.0051 g 2 sig figs 2 sig figs 11 m 11 m 2 sig figs 2 sig figs 0.010 s 0.010 s 2 sig figs 2 sig figs 90.4˚C 90.4˚C 3 sig figs 3 sig figs 0.004 cm 0.004 cm 1 sig fig 1 sig fig 0.089 kg 2 sig figs 0.00900 l 3 sig figs 100.0˚C 4 sig figs 20 cars unlimited 2.15000 cm 6 sig figs 5310 g 3 sig figs 12050 m 4 sig figs

15. Calculations using sig figs Adding or subtracting: Adding or subtracting: Look at the decimal places. Choose the given information that has the least number of decimal places. Make sure to put your answers in the least number of decimals. Your calculator does not do this! Your final measurement can not be more specific than your least specific measurement! Look at the decimal places. Choose the given information that has the least number of decimal places. Make sure to put your answers in the least number of decimals. Your calculator does not do this! Your final measurement can not be more specific than your least specific measurement! Multiplying or dividing: Multiplying or dividing: Identify sig figs for each number in your information. Your answer needs to be altered to the least number of sig figs used when solving the problem. (for the same reason) Identify sig figs for each number in your information. Your answer needs to be altered to the least number of sig figs used when solving the problem. (for the same reason)

16. Addition Division Multiplication Subtraction

17. Practice: 1. Give the correct number of significant figures for: 4500 4500. 0.00320.04050 2. 4503 + 34.90 + 550 = ? 3. 1.367 - 1.34 = ? 4. (1.3 x 103)(5.724 x 104) = ? 5. (6305)/(0.010) = ?

18. Scientific Notation Why is it that we use scientific notation in science? Why is it that we use scientific notation in science? because many of the numbers, amount, etc. that we use are either really big or very small. because many of the numbers, amount, etc. that we use are either really big or very small. Examples: Distance from the Earth to the Sun, size of an atom, the mass of an electron, proton, or even neutron….. Examples: Distance from the Earth to the Sun, size of an atom, the mass of an electron, proton, or even neutron…..

19. Scientific Notation If the number is large – you will have a positive exponent If the number is large – you will have a positive exponent If the number is very small – you will have a negative exponent. If the number is very small – you will have a negative exponent. Exponent decides which direction and how many spots you will move the decimal Exponent decides which direction and how many spots you will move the decimal EX: 10000 = 1 x 10 4 0.00044 = 4.4 x 10 -4 Must honor sig figs in original value Must honor sig figs in original value Root number or coefficient is the only number that is significant (exponent does not count) Root number or coefficient is the only number that is significant (exponent does not count) EX: 2.4327 x 10 4 5 sig figs 7.8 x 10 -3 2 sig figs 2 sig figs

20. Examples What is the correct scientific notation for: What is the correct scientific notation for: 25000.00000801 12.87 25000.00000801 12.87 What is the correct standard notation for: What is the correct standard notation for: 1.98 x 10 3 1.98 x 10 3 2.609 x 10 -2 2.609 x 10 -2 3.81 x 10 -5 3.81 x 10 -5 0.070 x 10 5 0.070 x 10 5 0.005 x 10 -3 0.005 x 10 -3

21. Calculations with scientific notation Multiplication: multiply the coefficients(roots) and add your exponents Multiplication: multiply the coefficients(roots) and add your exponents Division: divide the coefficients(roots) and subtract your exponents Division: divide the coefficients(roots) and subtract your exponents Add or subtract: Change your exponents to equal (largest one), then add and put back into correct scientific notation. OR put your numbers in standard notation +/- and then place back into scientific notation Add or subtract: Change your exponents to equal (largest one), then add and put back into correct scientific notation. OR put your numbers in standard notation +/- and then place back into scientific notation

22. Practice: (2.68 x 10 -5 ) x (4.40 x 10 -8 ) (2.68 x 10 -5 ) x (4.40 x 10 -8 ) (2.95 x 10 7 ) ÷ (6.28 x 10 15 ) (2.95 x 10 7 ) ÷ (6.28 x 10 15 ) (8.41 x 10 6 ) x (5.02 x 10 12 ) (8.41 x 10 6 ) x (5.02 x 10 12 ) (9.21 x 10 -4 ) ÷ (7.60 x 10 5 ) (9.21 x 10 -4 ) ÷ (7.60 x 10 5 ) (4.52 x 10 -5 ) + (1.24 x 10 -2 ) + (3.70 x 10 -4 ) + (1.74 x 10 -3 ) (4.52 x 10 -5 ) + (1.24 x 10 -2 ) + (3.70 x 10 -4 ) + (1.74 x 10 -3 ) (2.71 x 10 6 ) - (5.00 x 10 4 ) (2.71 x 10 6 ) - (5.00 x 10 4 ) (4.56 x 10 6 ) + (2.98 x 10 5 ) + (3.65 x 10 4 ) + (7.21 x 10 3 ) (4.56 x 10 6 ) + (2.98 x 10 5 ) + (3.65 x 10 4 ) + (7.21 x 10 3 ) (3.05 x 10 6 ) x (4.55 x 10 -10 ) (3.05 x 10 6 ) x (4.55 x 10 -10 )

23. How can you decide if your experiments are accurate/precise? Percent error = calculations that will give you a percent deviation from the true value. Percent error = calculations that will give you a percent deviation from the true value. Formula: l True – experimental l x 100 Formula: l True – experimental l x 100 True True

24. Example A student measured the density of an object to be 2.889 g/ml, the true density of the object is 2.699g/ml. What is the percent error of the experiment? Is the student accurate? A student measured the density of an object to be 2.889 g/ml, the true density of the object is 2.699g/ml. What is the percent error of the experiment? Is the student accurate? ANSWER: 7.000% error, anything below 10% is acceptable as accurate. The closer to 0% the better! ANSWER: 7.000% error, anything below 10% is acceptable as accurate. The closer to 0% the better!

25. Metric System The Metric system was developed in France during the Napoleonic reign of France in the 1790's. The Metric system was developed in France during the Napoleonic reign of France in the 1790's. The metric system has several advantages over the English system which is still in place in the U.S. The metric system has several advantages over the English system which is still in place in the U.S. However the scientific community has adopted the metric system almost from its inception. However the scientific community has adopted the metric system almost from its inception.

26. The advantages of the Metric system are: The advantages of the Metric system are: 1. It is based on a decimal system (powers of ten). 2. It simplifies calculations by using a set of prefixes. 3. In order to move from one prefix to another you simply move the decimal. 4. It provides a standard measurement system that is used by the scientific community. (SI Base Units)

27. Prefix Decimal equivalent Exponent Pico 0.000000000001 10 -12 Nano 0.000000001 10 -9 Micro 0.000001 10 -6 Milli 0.001 10 -3 Centi 0.01 10 -2 Deci 0.1 10 -1 no prefix 1.0 10 0 Deka 10.0 10 1 Hecto 100.0 10 2 Kilo 1000.0 10 3 Mega 1,000,000. 10 6 Giga 1,000,000,000. 10 9

28. SI Base Units Table 1. Table 1. Base quantityNameSymbol SI base units Base quantityNameSymbol SI base units Lengthmeterm Masskilogramkg Timeseconds electric currentampereA temperature kelvinK amount of substance molemol

29. Common Base Units The SI Base Units are standard for Scientific Reports. The SI Base Units are standard for Scientific Reports. During your chemistry experience, you will use these common base units: During your chemistry experience, you will use these common base units: -temperature  Celcius°C -length  centimetercm -mass  gramg

30. Common Prefixes

31. Converting Between Units of Metric EX: Convert 500.0 mm  m Step 1: Identify the prefixes in the given values. Step 2: Refer to the order of prefixes: K h D m(base unit) d c m Step 3: Find the direction that you will need to move the decimal to achieve your new prefix. Step 4: Move the decimal in that direction, the same number of times. Step 5: Express new value with correct unit and sig fig.

32. 500.0 mm  m Step 1: (milli) (base unit of meter so no prefix) Step 2: K h D Base Unit d c m Step 3: Step 4: 500.0 Step 5: 0.5000 m

33. EX: Convert 7.500 L  cL Step 1: (liters is (centi) base unit) base unit) Step 2: K h D Base Unit d c m Step 3: Step 4: 7.500 Step 5: 750.0 cL

34. Practice: Practice: 5000 mg  g 5000 mg  g 0.0076 km  m 0.0076 km  m 1.000 hL  L 1.000 hL  L 250000 mm  km 250000 mm  km 50.0 cg  mg 50.0 cg  mg 3.0 cm  dm 3.0 cm  dm 1.0 kg  mg 1.0 kg  mg

35. Density and Temperature Density and Temperature

36. Mass Mass = amount of matter that an object contains. This is a physical property of matter Mass = amount of matter that an object contains. This is a physical property of matter Golf ball or tennis ball? Golf ball is solid therefore has more mass, tennis ball is made of empty space. Lab instrument and unit? Scale and grams (g)

37. Volume Volume = The amount of space an object occupies. This is also a physical property of matter Volume = The amount of space an object occupies. This is also a physical property of matter 1. Volume of a regular shaped object like a cube, uses the formula: 1. Volume of a regular shaped object like a cube, uses the formula: V = L x W x H V = L x W x H What lab instrument would be used to find and its unit? What lab instrument would be used to find and its unit? Ruler and cubic centimeters (cm 3 ) Ruler and cubic centimeters (cm 3 )

38. Volume 2. Volume by displacement 2. Volume by displacement Used when you have an irregular shaped object. Ex: Marble or rock Used when you have an irregular shaped object. Ex: Marble or rock Lab instrument and unit? Lab instrument and unit? Graduated cylinder and milliliters (mL) Graduated cylinder and milliliters (mL) How do you perform? How do you perform?

40. Density Both mass and volume make up density, it is the relationship between the two. Both mass and volume make up density, it is the relationship between the two. Density is also a physical property of matter Density is also a physical property of matter Formula = D = m/v Formula = D = m/v M= mass M= mass V = volume V = volume

41. Density Units for density are: Units for density are: 1. g/mL 1. g/mL 2. g/cm 3 2. g/cm 3 Question: A piece of metal has a mass of 40 grams and a volume of 80 milliliters, what is its density? Question: A piece of metal has a mass of 40 grams and a volume of 80 milliliters, what is its density? D= m = 40g = v 80 ml 0.5g/mL D= m = 40g = v 80 ml 0.5g/mL

42. Density A piece of wood has a density of 45 g/cm 3, its mass is 5.0 grams. What is its volume? A piece of wood has a density of 45 g/cm 3, its mass is 5.0 grams. What is its volume? New formula: m/D = v New formula: m/D = v 5.0 grams = 0.11 cm 3 5.0 grams = 0.11 cm 3 45g/cm 3 45g/cm 3

43. Temperature A measurement which describes the hotness or coldness of a substance. A measurement which describes the hotness or coldness of a substance. Instrument used = thermometer Instrument used = thermometer We will commonly use ˚C in labs, but SI unit is K = Kelvins We will commonly use ˚C in labs, but SI unit is K = Kelvins Formulas: Formulas: ˚F = (˚c x 1.8) + 32 ˚F = (˚c x 1.8) + 32 ˚C = (˚F – 32) ÷ 1.8 ˚C = (˚F – 32) ÷ 1.8 ˚C = K – 273 ˚C = K – 273 K = ˚C + 273 K = ˚C + 273