Measurements must have a number and a unit Measurements are fundamental to the experimental sciences. It is important that you are able to make measurements and decide if a measurement is correct Large and small numbers can be written in scientific notation so that they are easier to work with When a number is written as a product of two numbers: a coefficient and 10 raised to a power Ex. 602,000,000,000,000 can be written 6.02x10 14 It is necessary to make good, reliable measurements in the lab Precision- how close a series of measurements are to each other The more sig figs a measurement has the more precise it is Accuracy-how close a measurement comes to the actual true value of what is being measured Neither accurate nor precise Precise, but not accurate Precise AND accurate Accepted value = the correct value based on reliable references (Density Table page 90) Experimental value = the value measured in the lab Include digits that are known, plus a last digit that is estimated Measurements must be reported to the correct number of significant figures. Figure 3.5 Significant Figures - Page 67 Which measurement is the best? What is the measured value? Non-zeros always count as significant figures: 3456 has 4 significant figures Zeros Leading zeroes do not count as significant figures: has 3 significant figures Zeros Captive zeroes always count as significant figures: has 4 significant figures Zeros Trailing zeros are significant only if the number contains a written decimal point: has 4 significant figures Two special situations have an unlimited number of significant figures: 1.Counted items a)23 people, or 425 thumbtacks 2.Exactly defined quantities b)60 minutes = 1 hour How many significant figures in the following? m 5 sig figs kg 4 sig figs 100,890 L 5 sig figs 3.29 x 10 3 s 3 sig figs cm 2 sig figs 3,200,000 mL 2 sig figs 5 dogs unlimited These all come from some measurements This is a counted value In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Rounding Decide how many significant figures are needed Round to that many digits, counting from the left Is the next digit less than 5? Drop it. Next digit 5 or greater? Increase by 1 - Page 69 Be sure to answer the question completely! Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem. = 18.7 (3 sig figs) - Page 70 3.24 m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L lb lb lb lb mL mL 0.16 mL mL *Note the zero that has been added. Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem. 6.38 x 2.0 = 13 (2 sig figs) - Page 71 3.24 m x 7.0 m CalculationCalculator says:Answer m 2 23 m g 23.7 cm g/cm g/cm cm x cm cm cm m 3.0 s m/s240 m/s lb x 3.23 ft lbft 5870 lbft g x 2.87 mL g/mL2.96 g/mL SI The standard of measurement used in science is the metric system Metric system is now revised and named as the International System of Units (SI), as of 1960 It has simplicity, and is based on 10 or multiples of 10 7 base units, but only five commonly used in chemistry: meter, kilogram, kelvin, second, and mole. Part 1 number Part 2 - scale (unit) Examples: 20 grams 6.63 x Joule seconds Measurement - quantitative observation consisting of 2 parts: Sometimes, non-SI units are used Liter, Celsius, calorie Some are derived units They are made by joining other units Speed = miles/hour (distance/time) Density = grams/mL (mass/volume) In SI, the basic unit of length is the meter (m) Length is the distance between two objects measured with ruler The space occupied by any sample of matter. Calculated for a solid by multiplying the length x width x height; thus derived from units of length. SI unit = cubic meter (m 3 ) Everyday unit = Liter (L), which is non-SI. (Note: 1mL = 1cm 3 ) Graduated cylinders Pipets Burets Volumetric Flasks Syringes Volumes of a solid, liquid, or gas will generally increase with temperature Much more prominent for GASES Therefore, measuring instruments are calibrated for a specific temperature, usually 20 o C, which is about room temperature Mass is a measure of the quantity of matter present Weight is a force that measures the pull by gravity- it changes with location Mass is constant, regardless of location The SI unit of mass is the kilogram (kg), even though a more convenient everyday unit is the gram Measuring instrument is the balance scale PrefixMeaning Mega (M)1 =1,000,000 base unit Kilo (k)1 = 1000 base unit Deci (d)10 = 1 base unit Centi (c)100 = 1 base unit Milli (m)1000 = 1 base unit Micro ()1,000,000 = 1 base unit Nano (n)1,000,000,000 = 1 base unit Pico (p)1,000,000,000,000 = 1 base unit UnitRelationship Kilometer (km)1 km =1000 m Meter (m)Base unit Decimeter (dm)10 dm = 1 m Centimeter (cm)100 cm = 1m Millimeter (mm)1000 mm =1 m Micrometer (m)10 6 m = 1 m Nanometer (nm)10 9 nm = 1m UnitRelationship Liter (L)Base unit Milliliter (mL)10 3 mL = 1L Cubic centimeter (cm 3 )1 cm 3 = 1 mL Microliter (L)10 6 L =1 L UnitRelationship Kilogram (kg)Base unit Gram (g)1 g = kg Milligram (mg)10 3 mg = 1g Microgram (g)10 6 g = 1g Temperature is a measure of how hot or cold an object is. Heat moves from the object at the higher temperature to the object at the lower temperature. We use two units of temperature: Celsius named after Anders Celsius Kelvin named after Lord Kelvin Fahrenheit Scale Freezing Point of water= 32F Boiling Point of water= 212F Celsius scale defined by two readily determined temperatures: Freezing point of water = 0 o C Boiling point of water = 100 o C Kelvin scale does not use the degree sign, but is just represented by K absolute zero = 0 K (thus no negative values) C=(F-32)(5/9) F=(9/5)(C)+32 K=C+273 C=K-273 Energy is the capacity to do work, or to produce heat. Energy can also be measured, and two common units are: 1) Joule (J) = the SI unit of energy, named after James Prescott Joule 2) calorie (cal) = the heat needed to raise 1 gram of water by 1 o C Conversions between joules and calories can be carried out by using the following relationship: 1 cal = J Conversion factors are a way to express the one quantity in different ways Ex. 1 dollar = 4 quarters= 10 dimes= 20 nickels =100 pennies Ex. 1 meter= 10 decimeters= 100 centimeters = 1000 millimeters Ratio of equivalent measurements 2 dollars = 20 dimes = 1 2 dollars 2 dollars 1 meter = 100 centimeters = 1 1 meter 1 meter How many seconds are in a workday that lasts exactly eight hours? What is 0.073cm in micrometers? Ratio of the mass of an object to its volume Density = mass/volume Density depends on what the substance is made of not how much of the substance you have Ex 10.0 cm 3 piece of lead has a mass of 114 g. What is the density? As temperature increases, the volume of a substance increases Since volume increases, then the density will decrease as the temperature increases Volume = mass/density Mass = density X volume A copper penny has a mass of 3.1g and a volume of 0.35 cm 3. What is the density of copper? What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5g/cm 3.