D. Harvey - Modern Analytical Chemistry (794078), страница 8
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Compare this with a complete instruction: “Transfer 1.5 g of yoursample to a 100-mL volumetric flask, and dilute to volume.” This is an instructionthat you can easily follow.Measurements usually consist of a unit and a number expressing the quantityof that unit. Unfortunately, many different units may be used to express the samephysical measurement. For example, the mass of a sample weighing 1.5 g also maybe expressed as 0.0033 lb or 0.053 oz. For consistency, and to avoid confusion, scientists use a common set of fundamental units, several of which are listed in Table2.1.
These units are called SI units after the Système International d’Unités. Othermeasurements are defined using these fundamental SI units. For example, we measure the quantity of heat produced during a chemical reaction in joules, (J), where1J =1scientific notationA shorthand method for expressing verylarge or very small numbers byindicating powers of ten; for example,1000 is 1 × 103.m2 kgs2Table 2.2 provides a list of other important derived SI units, as well as a few commonly used non-SI units.Chemists frequently work with measurements that are very large or very small.A mole, for example, contains 602,213,670,000,000,000,000,000 particles, and someanalytical techniques can detect as little as 0.000000000000001 g of a compound.For simplicity, we express these measurements using scientific notation; thus, amole contains 6.0221367 × 1023 particles, and the stated mass is 1 × 10–15 g.
Sometimes it is preferable to express measurements without the exponential term, replacing it with a prefix. A mass of 1 × 10–15 g is the same as 1 femtogram. Table 2.3 listsother common prefixes.Table 2.1Fundamental SI UnitsMeasurementmassvolumedistancetemperaturetimecurrentamount of substanceUnitkilogramlitermeterkelvinsecondamperemoleSymbolkgLmKsAmol1400-CH02 9/8/99 3:47 PM Page 13Chapter 2 Basic Tools of Analytical ChemistryTable 2.2Other SI and Non-SI UnitsMeasurementUnitlengthforcepressureenergy, work, heatpowerchargepotentialtemperatureTable 2.3Exponential101210910610310–110–210–310–610–910–1210–1510–18angstromnewtonpascalatmospherejoulewattcoulombvoltdegree Celsiusdegree FahrenheitSymbolEquivalent SI units1 Å = 1 × 10–10 m1 N = 1 m kg/s21 Pa = 1 N/m2 = 1 kg/(m s2)1 atm = 101,325 Pa1 J = 1 N m = 1 m2 kg/s21 W = 1 J/s = 1 m2 kg/s31C=1A s1 V = 1 W/A = 1 m2 kg/(s3 A)°C = K – 273.15°F = 1.8(K – 273.15) + 32⋅ÅNPaatmJWCV°C°F⋅⋅⋅⋅⋅⋅ ⋅Common Prefixes for ExponentialNotationPrefixteragigamegakilodecicentimillimicronanopicofemtoattoSymbolTGMkdcmµnpfa2A.2 Significant FiguresRecording a measurement provides information about both its magnitude and uncertainty.
For example, if we weigh a sample on a balance and record its mass as1.2637 g, we assume that all digits, except the last, are known exactly. We assumethat the last digit has an uncertainty of at least ±1, giving an absolute uncertainty ofat least ±0.0001 g, or a relative uncertainty of at least±0.0001 g× 100 = ±0.0079%1.2637 gSignificant figures are a reflection of a measurement’s uncertainty. The number of significant figures is equal to the number of digits in the measurement, withthe exception that a zero (0) used to fix the location of a decimal point is not considered significant. This definition can be ambiguous. For example, how many significant figures are in the number 100? If measured to the nearest hundred, thenthere is one significant figure.
If measured to the nearest ten, however, then twosignificant figuresThe digits in a measured quantity,including all digits known exactly andone digit (the last) whose quantity isuncertain.131400-CH02 9/8/99 3:48 PM Page 1414Modern Analytical Chemistrysignificant figures are included. To avoid ambiguity we use scientific notation. Thus,1 × 102 has one significant figure, whereas 1.0 × 102 has two significant figures.For measurements using logarithms, such as pH, the number of significantfigures is equal to the number of digits to the right of the decimal, including allzeros. Digits to the left of the decimal are not included as significant figures sincethey only indicate the power of 10. A pH of 2.45, therefore, contains two significant figures.Exact numbers, such as the stoichiometric coefficients in a chemical formula orreaction, and unit conversion factors, have an infinite number of significant figures.A mole of CaCl2, for example, contains exactly two moles of chloride and one moleof calcium.
In the equality1000 mL = 1 Lboth numbers have an infinite number of significant figures.Recording a measurement to the correct number of significant figures is important because it tells others about how precisely you made your measurement.For example, suppose you weigh an object on a balance capable of measuringmass to the nearest ±0.1 mg, but record its mass as 1.762 g instead of 1.7620 g.By failing to record the trailing zero, which is a significant figure, you suggest toothers that the mass was determined using a balance capable of weighing to onlythe nearest ±1 mg.
Similarly, a buret with scale markings every 0.1 mL can beread to the nearest ±0.01 mL. The digit in the hundredth’s place is the least significant figure since we must estimate its value. Reporting a volume of 12.241mL implies that your buret’s scale is more precise than it actually is, with divisions every 0.01 mL.Significant figures are also important because they guide us in reporting the result of an analysis. When using a measurement in a calculation, the result of thatcalculation can never be more certain than that measurement’s uncertainty. Simplyput, the result of an analysis can never be more certain than the least certain measurement included in the analysis.As a general rule, mathematical operations involving addition and subtractionare carried out to the last digit that is significant for all numbers included in the calculation.
Thus, the sum of 135.621, 0.33, and 21.2163 is 157.17 since the last digitthat is significant for all three numbers is in the hundredth’s place.135.621 + 0.33 + 21.2163 = 157.1673 = 157.17When multiplying and dividing, the general rule is that the answer contains thesame number of significant figures as that number in the calculation having thefewest significant figures. Thus,22.91 × 0.152= 0.21361 = 0.21416.302It is important to remember, however, that these rules are generalizations.What is conserved is not the number of significant figures, but absolute uncertaintywhen adding or subtracting, and relative uncertainty when multiplying or dividing.For example, the following calculation reports the answer to the correct number ofsignificant figures, even though it violates the general rules outlined earlier.101= 1.02991400-CH02 9/8/99 3:48 PM Page 15Chapter 2 Basic Tools of Analytical ChemistrySince the relative uncertainty in both measurements is roughly 1% (101 ±1, 99 ±1),the relative uncertainty in the final answer also must be roughly 1%.
Reporting theanswer to only two significant figures (1.0), as required by the general rules, impliesa relative uncertainty of 10%. The correct answer, with three significant figures,yields the expected relative uncertainty. Chapter 4 presents a more thorough treatment of uncertainty and its importance in reporting the results of an analysis.Finally, to avoid “round-off ” errors in calculations, it is a good idea to retain atleast one extra significant figure throughout the calculation. This is the practiceadopted in this textbook.
Better yet, invest in a good scientific calculator that allowsyou to perform lengthy calculations without recording intermediate values. Whenthe calculation is complete, the final answer can be rounded to the correct numberof significant figures using the following simple rules.1. Retain the least significant figure if it and the digits that follow are less thanhalfway to the next higher digit; thus, rounding 12.442 to the nearest tenthgives 12.4 since 0.442 is less than halfway between 0.400 and 0.500.2.
Increase the least significant figure by 1 if it and the digits that follow are morethan halfway to the next higher digit; thus, rounding 12.476 to the nearest tenthgives 12.5 since 0.476 is more than halfway between 0.400 and 0.500.3. If the least significant figure and the digits that follow are exactly halfway to thenext higher digit, then round the least significant figure to the nearest evennumber; thus, rounding 12.450 to the nearest tenth gives 12.4, but rounding12.550 to the nearest tenth gives 12.6. Rounding in this manner prevents usfrom introducing a bias by always rounding up or down.2B Units for Expressing ConcentrationConcentration is a general measurement unit stating the amount of solute presentin a known amount of solutionConcentration =amount of soluteamount of solution2.1concentrationAn expression stating the relativeamount of solute per unit volume orunit mass of solution.Although the terms “solute” and “solution” are often associated with liquid samples, they can be extended to gas-phase and solid-phase samples as well.
The actualunits for reporting concentration depend on how the amounts of solute and solution are measured. Table 2.4 lists the most common units of concentration.2B.1 Molarity and FormalityBoth molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. Molarityis the concentration of a particular chemical species in solution. Formality, on theother hand, is a substance’s total concentration in solution without regard to its specific chemical form. There is no difference between a substance’s molarity and formality if it dissolves without dissociating into ions.
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