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Mathematics of Chemistry

Mathematics of Chemistry. Thursday, august 20, 2015 Ms. Bynum Chemistry. Objective: SWBAT… Write numbers in scientific notation Recognize how scientific methods are used to study living things. Do basic conversions needed for chemistry

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Mathematics of Chemistry

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  1. Mathematics of Chemistry Thursday, august 20, 2015 Ms. Bynum Chemistry

  2. Objective: SWBAT… • Write numbers in scientific notation • Recognize how scientific methods are used to study living things. • Do basic conversions needed for chemistry • Determine the number of significant figures in a number • Essential Questions: • Why does science often have standardize processes? • How do smaller parts combine to build larger substances in science? • Vocab you should know! • Chemistry Scientific Method Control Independent Variable Dependent Variable Data Significant Figure Scientific Notation

  3. What is science? Scientific Method: A systematic way of finding an answer to a problem • Purpose: State the question • Hypothesis: Research to help you predict the outcome to the problem • Experiment: Develop a procedure to test the hypothesis • Data : Record the results of the experiment and your observations • Analyze: Review the results • Conclusion:Compare the hypothesis to the experiment’s conclusion • Observations are the first step to doing science. Observations are made by using the five senses which are: • Smell • Taste • Seeing • Hearing • Touching • Observations gather clues, details, and information.

  4. What is science? Dependent Variable: Known as the responding variable. It is observed for change. Any changes in the dependent variable depends on changes made to the independent variable. • Independent Variable: Known as the manipulated variable. The condition in an experiment that is changed is the independent variable because it is the only variable that affects the outcome of the experiment. Control Group: The group in which all conditions are kept the same. The group that stays the same and is used for comparison. {Placebo} Experimental Group: The group in which all conditions are kept the same except for the single condition being tested. This group is the group that receives the independent variable.

  5. For each experiment below, specify the independent variable, dependent variable, and control group.

  6. Identify the controls and variables

  7. Identify the controls and variables

  8. Math of chemistry • Mathematics is used widely in chemistry as well as all other sciences. Mathematical calculations are absolutely necessary to explore important concepts in chemistry. • There are three very important things you’ll use throughout the semester. • Significant Figures • Scientific Notation • Unit Conversions (prefixes on Units) • Practice makes perfect, so the more we do now – the less it will feel like a chore later.

  9. Significant figures • Significant figures are critical when reporting scientific data. Before looking at examples, lets summarize the rules for significant figures. • ALL non-zero numbers (1, 2, 3, 4, 5, 6, 7, 8, & 9) are ALWAYSsignificant. • ALLzeros between non-zero numbers are ALWAYS significant. EXAMPLE: 202 (0 is significant) 20002 (all 3 zeros are significant) • ALL zeros which are SIMULTANEOUSLY to the right of the decimal point & at the end of the number are always significant. A final zero or trailing zeros. EXAMPLE: 7.3000 (all zeros are significant because they are at the end of a number and to the right of the decimal) ** 3 & 4 is to write the number in scientific notation. If you can/must get rid of the zeroes , then they are not significant

  10. Significant figures How many significant figures in each number below?

  11. Significant figures • Examples: How many significant figures are in each number listed below? Underling the significant figures. • 3.14159 350.670 0.00340 • 320,001 107.854 • 1,000 1,000.0 • 0.00035 0.000350 • 0.678 14.600 700,000

  12. Significant figures • Significant figures are also used in completing math operations such as adding, subtracting, multiplying, and dividing. • Addition and Subtraction • The answers is reported in such a way that it reflects the reliability of the least precise operation. Look at the decimal portion of the numbers only. • Count the number of significant figures in the decimal portion of each number in the problem. • Add of subtract in the normal fashion. • Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

  13. Significant figures • WITHOUT a calculator solve the following problems with the appropriate amount of significant figures in your answer.

  14. Significant figures • Significant figures are also used in completing math operations such as adding, subtracting, multiplying, and dividing. • Multiplication & Division • The answer is reported in such a way that it reflects the reliability of the least precise operation. The leastnumber of significant figures in any number of the problem determines the number of significant figures in the answer. EXAMPLE: 2.5 x 3.42 The answer would be 8.6. Why? 2.5 has two significant figures whole 3.42 has three. Two significant figures is less precise than three so the answer has two significant figures. EXAMPLE: 2.33 X 6.085 X 2.1. How many significant figures in the answer? Which number decides this? Answer- two. Number- 2.1

  15. Scientific notation • Scientific notation is the way that scientist easily handle very large numbers or very small numbers. For example: Instead of writing 0.0000000056 we write 5.6 x 10-9 • A positive exponent shows that the decimal point is shifted that number of places to the left. • A negative exponent shows that the decimal point is shifted that number of places to the right.

  16. Scientific notation Examples: write each number in standard notation 1.71 x 107 0.9 x 10-3 7.5 x 10-5 8.4 x 105 4 x 100 • Examples: write each number in scientific notation • 0.0000006 • 6.7 • 20000000 • 0.0045 • 0.000984

  17. Units & Dimensions • When measuring a quantity, the units we use are just as important as the numerical value we obtain. Stating that the mass of an object is one (1) says very little … “One what?!” • To be complete, every measurement should be expressed with the appropriate units. If you fail to mention the unit at the end of an answer it can be counted as wrong • So, What are the basic units of measurement? You may measure length, mass, time, and temperature. Each of these quantities has a variety of units to use. ** Units in bold are the base units used in the SI system of units.

  18. Prefixes on units • With base units, there are times when you will have to represent the units as a very large multiple of that unit or as a very small fraction of the unit. Prefixes allow us to show these representations. Kilo is a prefix that is used to represent a multiple of a thousand. You can use the prefix kilo if you wanted to denote 1000 seconds, 1000 meters, or 1000 grams by writing kilosecond, kilometer, or kilogram. You could also give the abbreviated form of the prefix and unit ks, km, or kg. 1000 seconds = 1 kilosecond = 1ks

  19. Need to remember  • Examples: • 0.002 meters = _____ millimeters = ________ mm • 300 grams = ______ hectograms = ________ dag • 4,556,563 seconds = _______ megaseconds = _______Ms • 0.01 meters = _______ centimeters = ______ cm

  20. Unit Conversions • Changing between units is easy if we have a conversion equation. For example: • 1 kg = 1000 g • 1 mg = 0.001 g • 1000 mg = 1 g • 5 kg = 5000 g • You move the decimal 3 places to the right to go from kg to g. • You move the decimal 3 places to the left to go from mg to g. • As the unit gets larger the number should get smaller and vice-versa

  21. Find the prefix the original measurement starts with (ex. Milligrams). If there is no prefix start with the base unit. Find the step you wish to make the conversion to (ex. Decigram). Count the number of steps you moved, and determine in which direction you move (left or right) The decimal in your original measurement moves the same number of places as steps you moved and in the same direction (ex. Milligram to decigram is 2 steps to the left, so 40 milligrams = .40 decigrams). If the number of steps you move is larger than the number you have, you will have to add zeros to hold the places (ex. Kilometers to meters is three steps to the right, so 10 kilometers = 10,000 meters).

  22. Unit Conversions One cereal bar has a mass of 37g. What is the mass of 6 cereal bars? Is that more than or less than 1 kg? Explain your answer Wanda needs to move 110 kg of rocks. She can carry 10 hg each trip. How many trips can she make? • Examples: Write the equivalent measurement • 5 dm = _________ m • 4 mL = _________ L • 9 mg = _________ g • 6035 mm = ________ cm • 0.32 m = __________ cm • 12 mg = __________ g • 0.3 hg = _________ dg • 8 g = _________ mg • 67.89 kg = _____________ dg • 23.4 L = __________ mL • 40.0 μL = ___________ L • 0.04 L = ____________ GL

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