Accelerated Chemistry Study Guide What is Chemistry? (Chapter 1) Conversion factor Density Uncertainty Significant digits/figures Precision Accuracy Percent error September 2017 Page 1 of 32
Scientific Method Steps (observation, question, hypothesis, experiment, conclusion) Natural law how nature behaves (not why) Theory (model) why nature behaves the way it does. Can be used to predict results of further experiments Units and Measurement SI units of mass, length, time, temperature, area, volume Metric prefixes (shown on page 20 and giga, G, 10 9 ) Scientific notation, how to convert a number into scientific notation and how to go from scientific notation back to a regular number. Know how to multiply and divide in scientific notation Significant Digits Significant digits certain AND estimated digits o Non-zero digits ALWAYS significant o Leading zeros NEVER significant o Trapped zeros ALWAYS significant o Trailing zeros ONLY significant when the number contains a decimal point o When using scientific notation, ALL significant digits are used Calculating with significant digits o Exact numbers (counting numbers, numbers in conversions) do NOT affect the number of significant digits in answer o Multiplication and division answer has the same number of significant digits as the measurement with the fewest number of significant digits o Addition and subtraction answer has the same uncertainty as the number with the largest uncertainty September 2017 Page 2 of 32
Conversions, Dimensional Analysis (converting from one unit to another) Start with unit equalities e. g. 1 L = 1000 ml, 1 ml = 1 cm 3 Make conversion factors from the unit equalities. A conversion factor always = 1. Using the unit equalities above, the conversion factors are: 1L 1000 ml 1 ml 1 cm 3 1000 ml 1 L 1 cm 3 1 ml Multiply the number you wish to convert by the conversion factor that results in canceling the first unit and leaving the correct unit for the answer. The correct conversion factor will have the unit to be canceled in the denominator and the unit for the answer in the numerator. Converting 350 ml to L: 350 ml x 1L = 0.35 L 1000 ml Converting 350 ml to cm 3 : 350 ml x 1 cm 3 = 350 cm 3 1 ml September 2017 Page 3 of 32
Scientific Notation Scientific Notation is a way of conveniently expressing very large or very small numbers. Numbers in scientific notation are the product of a number between 1 and 10 and a power of 10 or. some integer (number between 1 and 10) X 10 Example: 1.23 X 10 5 or 8.0 X 10 0 or 5 X 10 5 NEVER 0.800 X 10-2 and NEVER 45.09 X 10 2 When deciding what power of 10 to write, remember that moving the decimal point right decreases the power of 10 by 1 for every move, while moving the decimal point left increases the power of 10 by 1. Examples: 0.0821 in scientific notation is 8.21 X 10-2 because the decimal was moved right two places. 83100 in scientific notation is 8.31 X 10 4 because it was moved left four places. 0.800 X 10-2 is not written correctly in scientific notation. To write it correctly, we need to move the decimal point once to the right. This decreases the power of 10 by one to give 8.00 X 10-3. Similarly, 45.09 X 10 2 should have been written 4.509 X 10 1. Here are some of the base units we will use in this class Quantity being measured Unit Abbreviation time second s mass kilogram kg length meter m volume liter L quantity mole mol temperature kelvin K luminous intensity candela cd September 2017 Page 4 of 32
Prefixes Here is a complete list of prefixes that includes some not in your book. Memorize those in bold. Prefix symbol meaning Power of 10 for Scientific Notation Number in one meter Number of meters in one of this unit giga G 1,000,000,000 10 9 10-9 Gm = 1m 1 Gm = 10 9 m mega M 1,000,000 10 6 10-6 Mm = 1 m 1 Mm = 10 6 m kilo k 1,000 10 3 10-3 km = 1m 1 km = 10 3 m hecto h 100 10 2 10-2 hm = 1 m 1 hm = 10 2 m deka da 10 10 1 10-1 dam = 1 m 1 dam = 10 1 m - - - - - - deci d 0.1 10-1 10 dm = 1 m 1 dm = 10-1 m centi c 0.01 10-2 10 2 cm = 1 m 1 cm = 10-2 m milli m 0.001 10-3 10 3 mm = 1 m 1 mm = 10-3 m micro μ 0.000 001 10-6 10 6 μm = 1 m 1 μm = 10-6 m nano n 0.000 000 001 10-9 10 9 nm = 1 m 1 nm = 10-9 m pico p 0.000 000 000 001 10-12 10 12 pm = 1m 1 pm = 10-12 m Notice that the last two columns of this chart can be adapted to any unit (except for cubic or square units). Here are some examples: 10-6 ML = 1 L or 10 6 L = 1 ML 100 cs = 1 s or 10-2 s = 1 cs. Also, a few conversions: 1 cm 3 = 1 ml and 2.54 cm = 1 in Note: if 100 cm = 1 m then (10 2 cm) 3 = (1 m) 3 so 10 6 cm 3 = 1 m 3 September 2017 Page 5 of 32
P A Evaluating the number of significant figures in a number 1. All non-zero digits (1-9) are always significant. 2. There are three types of zeroes: leading, trapped, and trailing a. Leading zeroes occur before the first significant digit (in 0.00233 there are three leading zeroes in bold) Leading zeroes are NEVER significant b. Trapped zeroes occur between nonzero digits (in 0.02002 and 4003 the two bold zeroes are trapped zeroes). Trapped zeroes are ALWAYS significant. c. Trailing zeroes occur at the end of a measurement (40000 and 0.040000 each have four bold trailing zeroes) Trailing zeroes are significant if and only if a decimal point present. Notice that the presence of a decimal point anywhere in the number makes trailing zeroes significant no matter where they are. Example: 0.0030300 has five sig figs. Its trailing zeroes are significant because of the decimal point present. 300 has only one sig fig but 300. has three sig figs Note that if a number is in correct scientific notation, all of the digits in the mantissa (the front part) are significant. Ex: 6.022 x 10 23 has four significant digits and 9.0 x 10-8 has two significant digits. Using significant digits in calculations In multiplication and division the rules are different than they are for addition and subtraction. In multiplication and division, the answer must be rounded to have the same number of significant figures as the factor/divisor with the fewest number of significant figures Example: 4.05 X (6.022 X 10 23 ) X 0.002004 = 4.88758 X 10 21 on your calculator, but the final answer should be rounded to three significant figures because 4.05 has the fewest significant digits with three. (6.022 X 10 23 has four and 0.002004 has four) So the final answer should be 4.89 X 10 21. Notice that we round up because of the 7 in our initial answer. In addition and subtraction, we first line up our numbers to be added vertically. Then we draw a vertical line after the last digit that is known with certainty and round the value to the decimal place that is to the left of that line. Example: 0.900 + 40.20 + 0.2 + 0.0502 = 41.3502 on our calculator, but we must first line the numbers up vertically and draw a line between the tenths and hundredths place, since the hundredths place is unknown for the value 0.2. 0.900 0.9 00 40.200 40.2 0 0.2 0.2 + 0.0502 + 0.0 502 41.3502 41.3 502 We then round to 41.4 September 2017 Page 6 of 32
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ChemQuest 1 Name: Date: Hour: Information: Qualitative vs. Quantitative The following observations are qualitative. The building is really tall. It takes a long time for me to ride my bike to the store. I live really far away. The following observations are quantitative. The river is 31.5 m deep. The cheese costs $4.25 per pound. It is 75 o F outside today. Critical Thinking Questions 1. What is the difference between qualitative and quantitative observations? 2. Write an example of a quantitative observation that you may make at home or at school. 3. Why are instruments such as rulers, scales (balances), thermometers, etc. necessary? Information: Units The following tables contain common metric (SI) units and their prefixes. Table 1: metric base units Quantity Unit Unit Symbol Length meter m Mass kilogram kg Time second s Temperature Kelvin K Volume Liter L Amount of substance mole mol September 2017 Page 8 of 32
Table 2: prefixes for metric base units. Prefix Symbol Meaning Giga G billion Mega M million Kilo k thousand Centi c hundredth Milli m thousandth Micro millionth Nano n billionth Pico p trillionth Note the following examples: milli means thousandth so a milliliter (symbol: ml) is one thousandth of a Liter and it takes one thousand ml to make one L. Mega means million so Megagram (Mg) means one million grams NOT one millionth of a gram. One millionth of a gram would be represented by the microgram (g). It takes one million micrograms to equal one gram and it takes one million grams to equal one Megagram. One cm is equal to 0.01 m because one cm is one hundredth of a meter and 0.01 m is the expression for one hundredth of a meter Critical Thinking Questions 4. How many milligrams are there in one kilogram? 5. How many meters are in 21.5 km? 6. Is it possible to answer this question: How many mg are in one km? Explain. 7. What is the difference between a Mm and a mm? Which is larger one Mm or one mm? September 2017 Page 9 of 32
Information: Scientific Notation Scientific notation is used to make very large or very small numbers easier to handle. For example the number 45,000,000,000,000,000 can be written as 4.5 x 10 16. The 16 tells you that there are sixteen decimal places between the right side of the four and the end of the number. Another example: 2.641 x 10 12 = 2,641,000,000,000 the 12 tells you that there are 12 decimal places between the right side of the 2 and the end of the number. Very small numbers are written with negative exponents. For example, 0.00000000000000378 can be written as 3.78 x 10-15. The -15 tells you that there are 15 decimal places between the right side of the 3 and the end of the number. Another example: 7.45 x 10-8 = 0.0000000745 the -8 tells you that there are 8 decimal places between the right side of the 7 and the end of the number. In both very large and very small numbers, the exponent tells you how many decimal points are between the right side of the first digit and the end of the number. If the exponent is positive, the decimal places are to the right of the number. If the exponent is negative, the decimal places are to the left of the number. Critical Thinking Questions 8. Two of the following six numbers are written incorrectly. Circle the two that are incorrect. a) 3.57 x 10-8 d) 2.92 x 10 9 b) 4.23 x 10-2 e) 0.000354 x 10 4 c) 75.3 x 10 2 f) 9.1 x 10 4 What do you think is wrong about the two numbers you circled? 9. Write the following numbers in scientific notation: a) 25,310,000,000,000,000 = b) 0.000000003018 = 10.Write the following scientific numbers in regular notation: a) 8.41 x 10-7 = b) 3.215 x 10 8 = September 2017 Page 10 of 32
Information: Multiplying and Dividing Using Scientific Notation When you multiply two numbers in scientific notation, you must add their exponents. Here are two examples. Make sure you understand each step: (4.5x10 12 ) x (3.2x10 36 ) = (4.5)(3.2) x 10 12+36 = 14.4x10 48 1.44x10 49 (5.9x10 9 ) x (6.3x10-5 ) = (5.9)(6.3) x 10 9+(-5) = 37.17x10 4 3.717x10 5 When you divide two numbers, you must subtract denominator s exponent from the numerator s exponent. Here are two examples. Make sure you understand each step: 2.8x10 3.2x10 14 7 2.8 3.2 x10 14 7 0.875x10 7 8.75x10 6 5.7x10 3.1x10 19 9 5.7 3.1 x10 19 ( 9) 1.84x10 19 9 1.84x10 28 Critical Thinking Questions 11. Estimate the answer without using a calculator. a) (4.6x10 34 )(7.9x10-21 ) = b) (1.24x10 12 )(3.31x10 20 ) = 5 8.4x10 c) 17 4.1x10 32 5.4x10 d) 14 7.3x10 September 2017 Page 11 of 32
Information: Adding and Subtracting Using Scientific Notation Whenever you add or subtract two numbers in scientific notation, you must make sure that they have the same exponents. Your answer will them have the same exponent as the numbers you add or subtract. Here are some examples. Make sure you understand each step: 4.2x10 6 + 3.1x10 5 make exponents the same, either a 5 or 6 42x10 5 + 3.1x10 5 = 45.1x10 5 = 4.51x10 6 7.3x10-7 - 2.0x10-8 make exponents the same, either -7 or -8 73x10-8 2.0x10-8 = 71x10-8 = 7.1x10-7 Critical Thinking Questions 12. Solve the following problems. a) 4.25x10 13 + 2.10x10 14 = b) 6.4x10-18 3x10-19 = c) 3.1x10-34 + 2.2x10-33 = September 2017 Page 12 of 32
Skill Practice 1 Name: Date: Hour: For problems 1-3, please use these conversion factors: 1 pallet = 45 bundles 1 bundle = 32 cases 1 case = 12 cans 1 can = 218.4 ml 1. How many ml of apple juice does the company need to make to fulfill an order for 2.5 pallets? 2. If 46,680 ml of juice are produced, how many cases of juice can be made? 3. A certain store ordered 480 cases of juice. How many pallets were required to ship the order? 4. Please perform the following conversions; use conversion factors. a) 15.60 cm = m b) 41.0 kg = g c) 9.2 cl = L d) 9.16 x 10-5 m = nm September 2017 Page 13 of 32
5. Solve the following problems. Write answers in scientific notation. a) (7.430 x 10 4 )(3.0 x 10 2 ) = b) 8.03 x 10 6 + 4.0 x 10 4 = c) (2.22 x 10-12 ) / (4.10x10-33 ) = d) (35,020)(321.0) = 6. Convert the following numbers to scientific notation: a) 23,000,210,000 = b) 0.00000000351 = 7. Convert the following numbers to "regular" notation: a) 2.354 x 10 5 = b) 3.400 x 10 9 = September 2017 Page 14 of 32
ChemQuest 2 Name: Date: Hour: Information: Significant Figures We saw in the last ChemQuest that scientific notation can be a very nice way of getting rid of unnecessary zeros in a number. For example, consider how convenient it is to write the following numbers: 32,450,000,000,000,000,000,000,000,000,000,000 = 3.245 x 10 34 0.000000000000000127 = 1.27 x 10-16 There are a whole lot of zeros in the above numbers that are not really needed. As another example, consider the affect of changing units: 21,500 meters = 21.5 kilometers 0.00582 meters = 5.82 millimeters Notice that the zeros in 21,500 meters and in 0.00582 meters are not really needed when the units change. Taking these examples into account, we can introduce three general rules: 1. Zeros at the beginning of a number are never significant (important). 2. Zeros at the end of a number are not significant unless (you ll find out later) 3. Zeros that are between two nonzero numbers are always significant. Therefore, the number 21,500 has three significant figures: only three of the digits are important the two, the one, and the five. The number 10,210 has four significant figures because only the zero at the end is considered not significant. All of the digits in the number 10,005 are significant because the zeros are in between two nonzero numbers (Rule #3). Critical Thinking Questions 1. Verify that each of the following numbers contains four significant figures. Circle the digits that are significant. a) 0.00004182 b) 494,100,000 c) 32,010,000,000 d) 0.00003002 2. How many significant figures are in each of the following numbers? a) 0.000015045 b) 4,600,000 c) 2406 d) 0.000005 e) 0.0300001 f) 12,000 September 2017 Page 15 of 32
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Skill Practice 2 Name: Date: Hour: Perform the following operations and give the answers in the correct number of significant figures. If the question is in scientific notation, then please use scientific notation in your answer. 1. 200.00 + 125.2 = 2. 12,020 + 6000 = 3. 0.003450 + 0.0140 = 4. 0.820 0.030 = 5. (240,900)(120.0) = 6. 340/12.5 = 7. (2.450 x 10 6 )(2.0 x 10 6 ) = 8. (5.369 x 10 12 )/(2.89 x 10 7 ) = September 2017 Page 19 of 32
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Name Period Date Accelerated Chemistry 2017-2018 Practice Quiz Chapter 1 (43 points) Identifying the Number of Sig Figs in a Number (1 point each) Write the number of significant figures in each of the following. 1. 0.020 g 2. 0.08 km 3. 3.910 x 10 5 m 4. 460. cm 3 5. 21,040 m 6. 23,010 s 7. 1,080 g Metric Prefixes (2 points each) Complete each of the following conversions. 8. 2.0 km = m 9. 4 Mg = mg 10. 740 cm = Gm 11. 80.0 cm 3 = ml September 2017 Page 30 of 32 Page 1 of 3.
Name Free Response Date MASS OF SAMPLE Team 1 Team 2 Team 3 Team 4 Reading 1 42 g 41.04 g 31.33 g 42.34 g Reading 2 42.158 g 39.77 g 31.30 g 41.12 g Reading 3 42.07 g 43.15 g 31.36 g 41.21 g Average 42.1 g 41.32 g 31.33 g 41.55 g Accepted measure from issuing lab: 41.33 g Percent error 1.9% 0.02% 24.2% 0.53% 12. For each team select one of the following to describe their data: accurate and precise, accurate but not precise, precise but not accurate, and neither precise nor accurate. (2 points each team, 8 total) 13. The label on a lemon Snapple bottle lists the following information: an 8.00 oz serving size contains 100. Calories. The bottle is 20.0 oz, which is the same as 591 ml. How many Calories are present in 2.50 L? (8 points) September 2017 Page 31 of 32 Page 2 of 3.
Name Date cm 3 14. Read the image to record the volume of the liquid to the appropriate number of significant figures. (2 points) 15. The mass of the liquid of the liquid. ( 4points) is 28.00 g, determine the density 16. Using the information from 14 & 15, the percent errorr was 12.2%. What is the accepted value for the density of the liquid? (4 points) 17. A metal cube, density 3.94 g/ml, measuring 0.50 cm on each side is added to the liquid in the graduated cylinder above. Will the metal cube sink or float? Explain. (2 points) Page 3 of 3. September 2017 Page 32 of 32