Measurement In this course we will be measuring using the “metric system” Really called the SI system. We need to be both accurate and precise in our measurements. Precision is the degree of being able to produce the same results over and over again. Some people like to think of this as being a property of the tool being used. They might say that one ruler is more precise than another. Accuracy is the degree to which a measurement agrees with other people’s measurement. It is possible to have a precision instrument that is not accurate (a very good ruler that has the first .3 cm broken off). We need to extent this reasoning to include SIGNIFICENCE of measurement (Chapter 3 of your text book) The two basic rules of doing math with significant figures are: Rule #1: KNOW! When adding and subtracting you must “line up” the decimals and report the digits that you Rule #2: When multiplying and dividing your answer can not contain more significant figures than the lowest number of significant figures used in the calculation. (Remember that WHOLE numbers are exact and unlimited significance) The seven basic quantities included in SI system of measurement are: 1. Length 2. Mass 3. Time 4. Current 5. Temperature 6. Amount of substance (mole) 7. Luminous intensity The corresponding seven basic units with their symbols are defined here (as officially defined): 1: meter (m): It is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. 2: kilogram (kg): It is equal to the mass of the international prototype of the kilogram. The prototype is a platinum-iridium cylinder kept at International Bureau of Weights and Measures, at Severes, near Paris, France. 3: time (t): It is the duration of 9, 192, 631, 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. 4: ampere (A) : It is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2x10 −7 newton per meter of length. 5: kelvin (K): It is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 6: mole (mol): It is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 7: candela (cd): It is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540x1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian (measure of solid angle). MKS system of units vs. CGS system of units (physics or chemistry) MKS is an abbreviation of Meter, Kilogram and Second. These three quantities form the basic set of units in MKS system. Clearly, it is a subset of SI system of units. As we can realize, mechanics - a branch of physics involves only length, mass and time. Therefore, MKS system is adequate to represent quantities used in mechanics. CGS is an abbreviation of Centimeter, Gram and Second. These are the units most often used in chemistry and it is imperative that simple conversions like these are made easily. This distinction between mechanics and rest of physics is hardly made in recent time. We can, therefore, completely do away with MKS nomenclature in favor of SI system. Si prefixes below are the 20 currently accepted System International (SI) prefixes and their meanings A list of the 7 base units is on page 33 of the Chemistry text on page 33 is a partial list of the prefixes prefix symbol value yotta Y 1024 zetta Z 1021 exa E 1018 peta tera giga mega kilo hecto deca P T G M k h da 1015 1012 109 106 103 102 101 100 deci centi milli micro nano d c m u n 10-1 10-2 10-3 10-6 10-9 pico p 10-12 femto f 10-15 atto a 10-18 zepto z 10-21 yocto y 10-24 expanded value English name U.S. septillion; U.K. 1 000 000 000 000 000 000 000 000 quadrillion 1 000 000 000 000 000 000 000 U.S. sextillion U.S. quintillion; U.K. 1 000 000 000 000 000 000 trillion 1 000 000 000 000 000 U.S. quadrillion 1 000 000 000 000 U.S. trillion; U.K. billion 1 000 000 000 U.S. billion 1 000 000 million 1 000 thousand 100 hundred 10 Ten (Not usually used) Base unit of meter, gram, watt, liter, one etc.1 0.1 tenth 0.01 hundredth 0.001 thousandth 0.000 001 millionth 0.000 000 001 U.S. billionth U.S. trillionth; U.K. 0.000 000 000 001 billionth 0.000 000 000 000 001 U.S. quadrillionth U.S. quintillionth; U.K. 0.000 000 000 000 000 001 trillionth 0.000 000 000 000 000 000 001 U.S. sextillionth U.S. septillionth; U.K. 0.000 000 000 000 000 000 000 001 quadrillionth Highlighted information is more commonly used; know these!!! (also listed on page 33 of text) Temperature and Pressure conversions In your everyday life and in your study of Chemistry, you are likely to encounter three different temperature scales and several units for measuring pressure. When you watch the weather report on the news, they will report the temperature on one scale, yet you measure temperature in the laboratory on a different scale. Many Chemistry equations must be done using yet another temperature scale. Clearly, you can see the importance of the use of units when reporting temperature and pressure. You can also see the need, for a student of Science, to be able to convert temperatures from one scale to another and one pressure to another.. This page is designed to help you do just that. The Fahrenheit Scale - The Fahrenheit scale is the scale that is used when they report the weather on the news each night. It is probably the temperature scale that you are most familiar with, if you live in the United States. The Celsius Scale - The Celsius scale is commonly used for scientific work and most countries of the world. The thermometers that we use in our laboratory are marked with the Celsius scale. The Celsius scale is also called the Centigrade scale because it was designed in such a way that there are 100 units or degrees between the freezing point and boiling point of water. One of the limitations of the Celsius scale is that negative temperatures are very common. Since we know that temperature is a measure of the kinetic energy of molecules, this would almost suggest that it is possible to have less than zero energy. This is why the Kelvin scale was necessary. The Kelvin Scale - The International System of Measurements (SI) uses the Kelvin scale for measuring temperature. This scale makes more sense in light of the way that temperature is defined. The Kelvin scale is based on the concept of absolute zero, the theoretical temperature at which molecules would have zero kinetic energy. Absolute zero, which is about -273.15 oC, is set at zero on the Kelvin scale. This means that there is no temperature lower than zero Kelvin, so there are no negative numbers on the Kelvin scale. For certain calculations, like the gas laws, which you will be learning soon, the Kelvin scale must be used. Comparison of Temperature Scales at Normal Pressure Comparison Points Fahrenheit Celsius Kelvin water boils 212 100 373 body temperature 98.6 37 310 water freezes 32 0 273 absolute zero -460 -273 0 There will be times when you need to be able to convert a temperature from one scale to another. In real life, you might be in a country where temperature is reported in Celsius and you will want to convert that into Fahrenheit, in order to figure out if you need to wear a sweater. In your laboratory work, you may need to change from Celsius to Kelvin in order to calculate the volume that a gas might occupy at standard temperature and pressure. The table below will show you the formulas that you can use to change from one scale to another. Temperature Conversion Formulas Conversion Celsius to Kelvin Formula K = C + 273 Example 21oC = 294 K Kelvin to Celsius C = K - 273 313 K = 40 oC Fahrenheit to Celsius C = (F - 32) x 5/9 89 oF = 31.7 oC Celsius to Fahrenheit F = (C x 9/5) + 32 50 oC = 122 oF * Note, to change back and forth between Fahrenheit and Kelvin is a two step process. Practice these conversions. 0oF = ____________ oC -150 oC = ____________oF 50 oC = ___________ K 300 K = ____________ oC -40 oC = ____________oF -10 oC = ____________oF 105 K = ____________ oC 212oF = ____________ 25 oC = ____________oF 68oF = ____________ oC Is 37oC a good day to go swimming or a good day to go snow skiing? Pressure is defined as force divided by area. Pressure = Force / Area Pressure Affects the Boiling point of liquids. If there is less pressure above a liquid it is easier for a molecule to escape the liquid as a gas. LOWERING THE ATMOSPHERIC PRESSURE LOWERS THE BOILING POINT. As a liquid warms more and more of the liquid evaporates and its vapor pressure increases. The standard unit of pressure is the Pascal. One Pascal is the pressure exerted by one Newton of force acting on one square meter of area (it is a very small unit of pressure and often units of Kilopascals are reported (kPa). The average atmospheric pressure is “1 atm” but it can be described in several other units. 1 atm = 101.3 kPa = 760 mm Hg = 760 torr 1 atm = about 32 ft H2O = 29.9 in. Hg= 14.7 p.s.i. or lbs/in2 The news caster in the twin cities have become lazy and often say the barometric pressure is 29.5 and falling (they leave off the 29.5 “inches of mercury” and falling). Convert the following units of pressure: 5 atm = __________ mmHg 560 mm Hg = _________ atm 30.3 in. Hg = __________ atm 250 kPa = __________ mm Hg 26.5 in. Hg = ___________ kPa Simple metric conversions Name: _______________________ period: ______ The SI (or System International) units of measurement are often referred to as the metric system in the United States. The SI is the preferred method of measurement in the scientific community for a variety of reasons. You must be able to convert units of measure quickly and accurately to be a competent science student. Remember: The prefix Milli means 1/1000 Centi means 1/100 The basic unit are GRAM, METER, and in America LITER Kilo mean 1,000 There are many other prefixes you should know but the three listed above are by far the most common. In other parts of the world the unit dm3 (or cubic decimeter) is used rather than liter. 1. 25 mm = _________ meters 11. 25 cm = __________ km * 2. 2 liters = ________ ml 12. 17.3 g = __________mg 3. 500 meters = _________ km 13. 29.3 mg = _______ cg * 4. 10 km = __________meters 14. 500 km = __________ cm * 5. 140 cm = ________ m 15. 2.73 liters = ________ ml 6. 35 m = __________ cm 16. 25.5 mg = __________ grams 7. 200 mg = __________g 17. 25 cm = __________ km * 8. 2.5 grams = __________ mg 18. 50.5 grams = __________ cg 9. 2.5 g = __________ cg 19. 100 km = _______________ mm * 10. 750 ml = __________ l 20. 50.5 gm = __________ kg indicates the problem may be a 2 step conversion Convert 53 000 000 to scientific notation ___________________________ 0.000 000 000 25 is _____________________________ in scientific notation. 1 783 002 000 000 is _____________________________ in scientific notation. 134.68 is _____________________________ in scientific notation. 8 675 309 000 000 000 000 000 is _____________________________ in scientific notation. 6.5001 x 10-10 is the same as _______________________________ 1.37505 x 10 13 is the same as _______________________________ Now try a few of these harder ones (probably have to look up a few of the prefixes). 21. 25 micrometers = _____________ meters 22. 1.25 milligrams = ________ kg 23. 500 mega bits = _______________ bits 24. 10.3 picometers = _____________nanometers 25. 140 cg = ________ kg 26. 355.7 mega bits = __________ kilo bits 27. 20.701 micrograms per liter = __________milligrams per liter 28. 2.5 decagrams = _____________ mg 29. 2.5 x10 10 meters = _____________ km 30. 2.5 x10 15 millimeters = _____________ km