Unformatted text preview: Chemistry 106 Lecture 3 Topic: Measurement Chapter 1.4 – 1.6 Announcements Ø། If you have not already done so, pick up a syllabus aEer class. Ø། Register for MasteringChemistry Ø། Reminder: First Homework and Tutorial sets are due on the MasteringChemistry website on Friday, September 9th by midnight. Measurement and Signiﬁcant Figures • Measurement is the comparison of a physical quanOty to be measured with a unit of measurement   that is, with a ﬁxed standard of measurement. – Length (meters, kilometers, etc.) – Mass (milligrams, kilograms, etc.) – Time (seconds, hours, etc.) Precision and Accuracy Precision: • The term precision refers to the closeness of the set of values obtained from idenOcal measurements of a quanOty. Accuracy: • Accuracy is a related term; it refers to the closeness of a single measurement to its true value. Precision and Accuracy Precision of Measurement With a CenOmeter Ruler • What is the length of this steel rod? • From the ruler markings, we know it is between 9.1 and 9.2 cenOmeters (cm). • Reasonable guesses are 9.11, 9.12, 9,13 Measurement and Signiﬁcant Figures • To indicate the precision of a measured number (or result of calculaOons on measured numbers), we oEen use the concept of signiﬁcant ﬁgures. – Signiﬁcant ﬁgures are those digits in a measured number (or result of the calculaOon with a measured number) that include all certain digits plus a ﬁnal one having some uncertainty. Precision and Uncertainty of Measurement With a CenOmeter Ruler • What is the length of this steel rod? • From the ruler markings, we know “9” and “0.1” in the measurement exactly (certain). • The guesses of 9.11, 9.12, 9,13 have uncertainty in the last digit. Measurement and Signiﬁcant Figures • An exact number is a number that arises when you count items or when you deﬁne a unit. – For example, when you say you have nine coins in a bo\le, you mean exactly nine. – When you say there are twelve inches in a foot, you mean exactly twelve. – Note that exact numbers have no eﬀect on signiﬁcant ﬁgures in a calcula9on. Measurement and Signiﬁcant Figures • To count the number of signiﬁcant ﬁgures in a measurement, observe the following rules: – All nonzero digits are signiﬁcant. • 1.234 (4 signiﬁcant ﬁgures) – Zeros between signiﬁcant ﬁgures are signiﬁcant. • 10.234 (5 signiﬁcant ﬁgures) – Zeros preceding the ﬁrst nonzero digit are not signiﬁcant. • 0.00123 (3 signiﬁcant ﬁgures) – Zeros to the right of the decimal aEer a nonzero digit are signiﬁcant. • 123.000 (6 signiﬁcant ﬁgures) Measurement and Signiﬁcant Figures • Zeros at the end of a non decimal number may or may not be signiﬁcant. (Use scienOﬁc notaOon to ﬁx this.) – Just wriOng “900” could mean 1, 2, or 3 signiﬁcant digits. – WriOng 9.00 x 102 indicates a precision of 3 signiﬁcant digits. – WriOng 9.0 x 102 indicates a precision of 2 signiﬁcant digits. Measurement and Signiﬁcant Figures • Number of signiﬁcant ﬁgures refers to the number of digits reported for the value of a measured or calculated quanOty, indicaOng the precision of the value. • So what happens when using mathemaOcal funcOons? – When mul5plying and dividing measured quanOOes, give as many signiﬁcant ﬁgures as the least found in the measurements used. – When adding or subtrac5ng measured quanOOes, give the same number of decimals as the least found in the measurements used. Measurement and Signiﬁcant Figures • 14.0 g /102.4 mL = 0.13671875 g/mL XXX
– only three signiﬁcant ﬁgures – correct answer is 0.137 g/mL • 184.2 g + 2.324 g = 186.524 g X
– only one decimal – correct answer is 186.5 g Measurement and Signiﬁcant Figures Example 320.5 – (6104.5/2.3) = ? Order of mathemaOcal operaOons: 1) Evaluate anything in parentheses 2) Then mulOplicaOon and division 3) Finally, addiOon and subtracOon Only 2 signiﬁcant digits 320.5 – (6104.5/2.3) = ? used in 2654.130… 320.5 – (6104.5/2.3) =  2.3 x 103 Carry all digits through a calculaOon to the very end and then use signiﬁcant digits to round the answer. Signiﬁcant Figures and Calculators • Not all of the ﬁgures on a calculator display are signiﬁcant. • On a typical calculator, 100.0 x 0.0634 ÷ 25.31 = 0.2504938 • However the answer with the correct number of signiﬁcant ﬁgures is 0.250. Rounding • This is the procedure for dropping non signiﬁcant digits in a calculaOon and adjusOng the last reported digit. • Look at the leEmost digit to be dropped. – If this digit is 5 or greater, add 1 to the last digit to be retained and drop all digits farther to the right. • 1.2151 rounded to three signiﬁcant ﬁgures = 1.22 – If this digit is less than 5, simply drop it and all digits farther to the right. • 1.2143 rounded to three signiﬁcant ﬁgures = 1.21 SI Units and SI Preﬁxes • In 1960, the General Conference of Weights and Measures adopted the Interna9onal System of Units (or SI), which is a parOcular choice of metric units. – This system has seven SI base units, the SI units from which all others can be derived. Table 1.4 SI Base Units Time Standard: Atomic Clocks • NaOonal InsOtute of Standards and Technology (NIST) F 1 Cesium Fountain Clock • Method was developed by Steve Jeﬀerts and Dawn Meekhof. • h\p://o.nist.gov/cesium/
fountain.htm Cesium “Fountain” Clock • Six lasers bring cesium gas to almost a complete standsOll (near absolute zero in temperature). • The cesium atoms are accurately and precisely probed to measure their natural resonance frequency . • The natural resonance frequency of the cesium atom (9,192,631,770 Hz) is the frequency used to deﬁne the second. Hz = Hertz = cycles per second Cesium ball Amazing Precision of Atomic Clocks • The NIST F 1 clock neither gains nor loses a second in more than 60 million years! 2005 version SI Units and SI Preﬁxes • The advantage of the metric system is that it is a decimal system. – A larger or smaller unit is indicated by an SI preﬁx   that is, a preﬁx used in the InternaOonal System to indicate a power of 10. – Table 1.5 lists the SI preﬁxes. The next slide shows those most commonly used. Table 1.5 Common SI Preﬁxes Table 1.4 SI Base Units By deﬁniOon, temperature is a measure of the average kineOc energy of the parOcles in a sample. Temperature • The Celsius scale (formerly the CenOgrade scale) is the temperature scale in general scienOﬁc use. – However, the SI base unit of temperature is the kelvin (K), a unit based on the absolute temperature scale. – The conversion from Celsius to Kelvin is simple since the two scales are simply oﬀset by 273.15°. o K = C + 273.15 Temperature • The Fahrenheit scale is at present the common temperature scale in the United States. – The conversion of Fahrenheit to Celsius, and vice versa, can be accomplished with the following formulas. o o F − 32
C=
1.8 o o F = 1.8 ( C) + 32 Temperature Figure 1.18: Comparison of temperature scales. Derived Units • The SI unit for speed is meters per second, or m/s. – This is an example of an SI derived unit, created by combining SI base units. • Volume is deﬁned as length cubed and has an SI unit of cubic meters (m3). – TradiOonally, chemists have used the liter (L), which is a unit of volume equal to one cubic decimeter. 3 1 L = 1 dm and 1 mL = 1 cm 3 Volume • The most commonly used metric units for volume are the liter (L) and the milliliter (mL). – A liter is a cube 1 dm long on each side. – A milliliter is a cube 1 cm long on each side. Derived Units • The density of an object is its mass per unit volume, m
d=
V where d is the density, m is the mass, and V
is the volume.
• Generally the unit of mass is the gram.
• The unit of volume is the mL for liquids;
cm3 for solids; and L for gases. A Density Example • A sample of the mineral galena (lead sulﬁde) weighs 12.4 g and has a volume of 1.64 cm3. What is the density of galena? mass 12.4 g = 7.5609 = 7.56 g/cm3 Density = = volume 1.64 cm3 Common Derived Units Units: Dimensional Analysis • In performing numerical calculaOons, it is good pracOce to associate units with each quanOty. – The advantage of this approach is that the units for the answer will come out of the calculaOon. – And, if you make an error in arranging factors in the calculaOon, it will be apparent because the ﬁnal units will be nonsense. Units: Dimensional Analysis • Dimensional analysis (or the factor label method) is the method of calculaOon in which one carries along the units for quanOOes. – Suppose you simply wish to convert 20
yards to feet. 3 feet
20 yards ×
= 60 feet
1 yard – Note that the units have cancelled properly
to give the final unit of feet. Units: Dimensional Analysis • The raOo (3 feet/1 yard) is called a conversion factor. – The conversion factor method may be used to convert any unit to another, provided a conversion equaOon exists. – RelaOonships between certain U.S. units and metric units are given in your book on the inside back cover. RelaOonships of Some U.S. and Metric Units Length Mass 1 in = 2.54 cm 1 lb = 0.4536 kg 1 qt = 0.9464 L 1 yd = 0.9144 m 1 lb = 16 oz 4 qt = 1 gal 1 mi = 1.609 km 1 oz = 28.35 g 1 mi = 5280 ft Volume Unit Conversion • Sodium hydrogen carbonate (baking soda) reacts with acidic materials such as vinegar to release carbon dioxide gas. Given an experiment calling for 0.348 kg of sodium hydrogen carbonate, express this mass in milligrams. 103 g 103 mg 0.348 kg x = 3.48 x 105 mg x 1 kg 1 g Unit Conversion • Suppose you wish to convert 0.547 lb to grams. – From your book, note that 1 lb = 453.59 g, so the conversion factor from pounds to grams is 453.59 g/1 lb. Therefore, 453.59 g
0.547 lb ×
= 248 g
1 lb Next Lecture • Topics: Atomic Theory, Periodic Table • Text Reading: 2.1 2.5 ...
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 Fall '08
 Freedman
 Chemistry, Kilogram

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