Measurements and Calculations

I. Chemistry – the study of the composition of substances and the changes that they undergo on a small scale – the study of matter and energy. Remember, science is a process, not a list of facts. 1. Composition – what something is made of II. The Scientific Method – a way to explore the world around us; a logical approach to solving problems: See the diagram on page 31 of your text. 1. Define the problem – usually in the form of a question Research the problem – look things up, do interviews, observe, use your five senses Form a Hypothesis – develop an educated suggestion/answer to the problem/question, a testable if/then statement Experiment – make observations, take measurements and gather data as you test your hypothesis Must have only one variable – only one condition that is changing and, therefore, being tested. Must have controls – everything that is not changing or being tested Measurements are needed to reproduce experiments exactly the same way every time. Examples: rules in sports, cooking, designing automobiles. Qualitative Measurements – (quality) results are given in a descriptive non-numerical form. Remember: People do not always see things the same way. Quantitative Measurement – (quantity) results are in definite form, usually as numbers with units. 2. Draw a Conclusion – explain how your data either supports your hypothesis or does not, provide reasons for failure 3. Modify your hypothesis and/or retest if necessary Example: Flashlight A. Theory verses Law 1. Theory – explains why something is; repeatedly verified over a long period of time. It can never be proven; enables us to make predictions. 2. Scientific Law – description of what is happening, does NOT explain why, otherwise it is the same a as theory. Example: Balloon in hot sun expands… Theory – Increase heat (energy) of gas particles, increases speed, increases number and force of collisions, increases space (volume) if flexible. Scientific Law – the volume of a gas is directly proportional to the temperature if the pressure is kept constant. III. SI Measurement – International System of Units - metric system accepted worldwide – allows universal communication 1. Table 1 on page 34 of your text: Measurement Variable SI Unit Symbol Other Units Symbols length l meter m mass m kilogram kg time t second s Hour, Minute hr, min temperature T Kelvin K Celsius °C amount/count n mole mol volume v cubic meter m3 Liter L = dm3 energy E Joule J calorie cal pressure p Pascal Pa kilopascal kPa atmosphere atm millimeters of mmHg mercury density D grams/cubic g/cm3 grams/milliliter g/ml centimeter 2. Mass – the quantity of matter an object contains a. Mass does NOT change with gravity. Mass on Earth = Mass on the moon. b. SI Unit for Mass is kilogram – kg: kilo = 1000 so 1kg = 1000g 3. Weight - force – measure of pull on mass by gravity a. Weight changes with gravity. If x is the weight on the Earth then x/6 is he weight on the moon. 4. Length - metric unit is the meter 5. Volume - the space occupied by a sample of matter – volume changes with temperature – Table 3 page 36 of your text lists derived measurements which are combinations of SI units. a. Formula for a cube or rectangle: V = l x w x h 1. volume = length x width x height b. SI units for volume: 1L = 1dm3 c. Glassware for measuring the volume of a liquid: 1. beaker : like a cup 2. graduated cylinder: tall and skinny 3. Erlenmeyer flask: skinny neck and wide bottom 6. Density - the mass of an object in a given space, a physical property that varies with temperature: if the temperature goes up then usually the volume goes up and therefore the density will go down. a. If ↑T then ↑V so ↓D. The opposite is also true, if ↓T then ↓V so ↑D. 1. H2O is the exception. When the molecules freeze, they become crystals. The crystals create space within and between them, making them less dense than their liquid molecules which are constantly touching on all sides. b. Formula: Density = mass/volume 1. Units: g/ml or g/cm3 c. Different types of matter have different densities: 1. more mass in a smaller volume: more dense 2. less mass in a greater volume: less dense 3. more dense solid: sinks in its own liquid 4. less dense solid: floats in its own liquid Examples: Helium: He is less dense than air so balloon floats H2O: ice H2O(s) is less dense than water H2O(l) so it floats

IV. Prefixes to SI Measurements - are connected to the measurement (regardless of type) to express very large or very small numbers. Table 2 page 35 Kilo – 1000 times larger = x103 Ex: 1kg is 1000x larger than 1g Hecto – 100 times larger = x102 Deca – 10 times larger = x101 deci – 10 times smaller = x10-1 centi – 100 times smaller = x10-2 milli – 1 000 times smaller = x10-3 Ex: 1mg is 1000x smaller than 1g micro – 1 000 000 times smaller = x10-6 nano – 1 000 000 000 times smaller = x10-9 Note: Prefix maintains its meaning regardless of the type of measurement to which it is connected. Examples: Kilogram = 1000 grams Kilometer = 1000 meters Kiloliter = 1000 liters milligram = .001 grams = 1/1000 of a gram millimeter = .001 meters = 1/1000 of a meter milliliter = .001 liters = 1/1000 of a liter Note: Unit Measurement Gram = mass Meter = length Liter = volume = amount of matter in an area of space V. Calculations of Conversion 1. Conversion Factor - any fraction (ratio) in which the numerator equals the denominator - whenever two numbers are equal their ratio will be one Example: 1foot = 12inches can be written as 1foot/12inches or 12inches/1foot 2. Dimensional Analysis - using the conversion factor to change one unit into another unit. Example: Convert 36 inches into feet. a. Units that you want to cancel go in the denominator of the conversion factor. b. Always put the given number and units that you are changing over 1. c. If going from a larger unit to a smaller unit, the number will increase. If going from a smaller unit to a larger unit, the number will decrease. d. Always write the units along with the number in the problem and the conversion factor so you can see which units will cancel!!!!! 3. Problem Set-up a. Given Units/1 (Conversion Factor) = Wanted Units b. Conversion Factor = Units You Want/Units to Cancel VI. Good Measurements are accurate and precise – accuracy and precision are not the same. Page 44 Figure 8 1. Accurate- (correct) how close the measurement is to the true value 2. Precise - (reproducible) how close several measurements are to same # (measurement may be wrong) 3. Sources of Error - human (skill and knowledge of the person) and quality of the equipment a. Accepted Value - true (correct) value based on reliable references. You can look it up in a book. Often called the Theoretical Value. a. Experimental Value - measured value determined experimentally in the lab. b. Error - the difference between the accepted value and the experimental value 1. Formula: accepted value – experimental value = error 2. Units of error are the same as the measurements. 3. Note: The error can be positive (if the experimental value is less than the actual value) or negative (if the experimental value is greater than the actual value). b. Percent Error - the absolute value of the error (calculated above) divided by the accepted value and multiplied by 100 to get the percent 1. Formula: |error| /accepted value x 100 = % error 2. Units would only be the percent sign (%) as the units of measurement cancel. 3. Note: The lines on either side of the term “error” represent the absolute value of the error. The absolute value of a number is always a positive value. VII. Significant Figures - ones which are known to be reasonably reliable – includes all digits which are known precisely plus one last digit that is estimated. 1. Measurements – Rules are on page 47 of your text. a. every non-zero number is significant b. zeros between non-zeros are significant c. zeros in front of non-zeros are NOT significant - they are only place holders d. zeros at the end of non-zeros and to the right of the decimal are always significant e. zeros at the end of non-zeros and to the left of an invisible decimal are NOT significant – they are just place holders f. zeros at the end of non-zeros and to the left of a visible decimal are significant g. There are two instances in which the significant figures are unlimited in a number when counting (ex: people in a room) with exactly defined quantities (ex: 1hr = 60 min) h. In scientific notation only the coefficient is counted as significant or not (ignore the x10 to an exponent). 2. Calculations - A calculated number cannot be more precise than the least precise measurement from which it was calculated. a. Addition or Subtraction : round to the same number of decimal places as the measurement in the calculation (problem) with the least number of decimal places . Example: b. Multiplication and Division : round to the number of significant figures in the least precise term used in the calculation (problem). Example: c. Round off your answer: less than 5 – drop everything thereafter and 5 or more – round up by increasing the last digit by 1 d. Problem Solving Steps 1. Analyze - Identify the Unknown (A detective looks for a criminal.)  What are you looking for?  What units should your answer be in? 2. Identify the known (or given) information (A detective lists the known evidence.)  List the given numbers with units and variables  Variable – letter representing a measurement 3. Plan a solution (A detective asks questions, makes connections.)  Create drawings  List conversion factors  Look up known constants  Write down the formulas  Break the problem down into simple steps 4. Compute - Do the Calculation - do the math (A detective makes a deduction.)  Convert your units (if necessary)  Round off to appropriate # of significant figures  Adjust the decimal in scientific notation 5. Evaluate - Finish up (A detective checks her facts one last time before making the big arrest.)  Check for the correct significant figures  Check for the correct scientific notation  Check that you completely answered question  Check if you copied the given info correctly  Check if your answer is in the correct units  Check if your answer is rational (reasonable) VIII. Scientific Notation – A number is written the product of two numbers: a coefficient and a power of 10 1. Coefficient - number greater than or equal to 1 but less than 10 (only one number to the left of decimal, not zero). Example: 1.0 through 9.9 2. Exponent – is a whole number that indicates how many times the coefficient must be multiplied by 10 (if positive exp.) or by 1/10 (if negative exp.). a. Change a LARGE number by … moving the decimal to the LEFT – exponent will be a positive number. Example: 564 000 000 000 = 5.64 x 1011 b. Change a SMALL number by …moving the decimal to the RIGHT – exponent will be a negative number. Example: 0.000 000 087 = 8.7 x 10-8 c. A negative exponent does not make the whole number negative. 3. Multiplying numbers in scientific notation: multiply coefficients and ADD exponents. Example: 4. Dividing numbers in scientific notation: divide coefficients and SUBTRACT exponents (numerator minus denominator). Example: 5. Adding and Subtracting numbers in scientific notation: exponents must be made the same prior to doing any adding or subtracting of the coefficients. Example: 6. To do scientific notation on your calculator, input the following: coefficient (use +/- if necessary) EE or EXP (use 2nd or inv. if necessary) exponent (use +/- if necessary) IX. Directly verses Inversely Proportional 1. Directly Proportional a. If one variable increases or decreases, the second variable will do the same. b. Division of the two values would create a constant value c. Ratio remains constant d. Graph is a straight line through the origin (0,0) 2. Inversely Proportional a. If one variable increases or decreases, the second variable will do the opposite. b. Multiplication of the two values would create a constant value c. X and y increase by the same factor to keep product constant d. Graph is a curve (hyperbola)