《基礎(chǔ)化學(xué)》英文教學(xué)課件：教學(xué)Chapter_1_2

1、Chapter 1_2 Physical Measurements,Units and Dimensional Analysis Apply dimensional analysis to solving numerical problems.,Learning Objectives,Measurement and Significant Figures Define and use the terms precision and accuracy when describing measured quantities. Learn the rules for determining sign

2、ificant figures in reported measurements. Apply the rules of significant figures to reporting calculated values. Use significant figures in calculations. SI Units Become familiar with the SI (metric) system of units, including the SI prefixes.,Physical Measurements,I. Measurement,Chemists characteri

3、ze and identify substances by their particular properties. To determine many of these properties requires physical measurements. Such as mass, volume, time, and so forth.,To report the measurement, both the measured number and the unit must be given.,1.75 m; 82 kg,物理量的測量值不可能與真實(shí)值絕對一致，測量值只能隨著人類對客觀世界認(rèn)識

4、能力的發(fā)展和儀器精確度的提高而無限接近于真實(shí)值。 同時(shí)，由于對試樣的分析測定通常由多個(gè)步驟和對多種物理量的測量而完成，加之受到費(fèi)用，時(shí)間等諸多因素的制約，因此測量或測定的結(jié)果總是存在或多或少的不可靠性和不確定性。,Physical Measurements,II. Errors (誤差),1. Determinate errors: They are systematic,Determinate errors(可測誤差): those that are determinable and that presumably can be either avoided or corrected. Su

5、ch measurable determinate errors are classed as systematic errors(系統(tǒng)誤差).,Determinate or systematic errors are nonrandom and occur when something is wrong with the measurement.,Physical Measurements,Instrumental errors(儀器誤差): These include faulty equipment, uncalibrated weights, and uncalibrated glas

6、sware. Operative errors(操作誤差): These include personal errors and can be reduced by experience and care of the analyst in the physical manipulations involved. Errors of the method(方法誤差). These include coprecipitation of impurities, side reactions, incomplete reactions, and impurities in reagents.,Sys

7、tematic errors,空白試驗(yàn): 在不加試樣的情況下，以樣品相同的條件、方法、步驟進(jìn)行分析，把所得結(jié)果作為空白值從樣品分析結(jié)果中減去。 空白試驗(yàn)可以消除由于試劑不純或容器不符合要求所帶進(jìn)的誤差。,分光光度法測定微量鐵,空白試驗(yàn)可以消除溶劑或其它物質(zhì)對入射光吸收等因素,對照試驗(yàn)：把含量已知的標(biāo)準(zhǔn)試樣或純物質(zhì)當(dāng)作樣品，以所用方法和條件進(jìn)行定量平行分析。由分析結(jié)果與其已知含量的差值，便可得出分析的誤差；用此誤差值對測定結(jié)果加以校正。 用純物質(zhì)做樣品進(jìn)行對照試驗(yàn)不如標(biāo)準(zhǔn)試樣好，因?yàn)榧兾镔|(zhì)中不存在樣品中的非被測成分，情況和實(shí)際不一致。,Physical Measurements,2. Indet

8、erminate errors: They are random,Indeterminate errors(不可測誤差): often called accidental errors(偶然誤差) or random errors(隨機(jī)誤差), which represent the experimental uncertainty that occurs in any measurement, for example, the fluctuation of temperature, humidity, and pressure etc. These errors will follow a

9、random distribution and cannot be predicted or estimated.,Indeterminate errors are random and can not be avoided.,偶然誤差造成測量值時(shí)大時(shí)小，時(shí)正時(shí)負(fù)，難以控制。 但在平行條件下進(jìn)行多次測定則可發(fā)現(xiàn)其統(tǒng)計(jì)規(guī)律：相同波動絕對值的正負(fù)誤差出現(xiàn)概率均等；小值誤差概率遠(yuǎn)多于大值誤差的概率，特別大的誤差概率非常小。因此，增加測定次數(shù)可使偶然誤差的算術(shù)平均值趨于零。 在消除系統(tǒng)誤差的前提下，通常可用多次測定結(jié)果的平均值代替真實(shí)值。,分析過程中也可能由于操作者粗心大意或違反操作要求等原因造成的加

10、錯(cuò)試劑，打翻容器，讀錯(cuò)數(shù)據(jù)，計(jì)算錯(cuò)誤等過失造成的測定錯(cuò)誤（或過失誤差）是沒有統(tǒng)計(jì)意義的。,Physical Measurements,Accuracy: the closeness of a single measurement to its true value. It is evaluated by using error.,Absolute errors (E, 絕對誤差): The difference between the true value (T) and the measured value (x), with regard to the sign, is the absol

11、ute errors, and it is reported in the same units as the measurement.,If a 2.62 g sample of material is analyzed to be 2.52 g, the absolute error:,3. Accuracy(準(zhǔn)確度),Physical Measurements,Relative error(Er , 相對誤差): The absolute error expressed as a percentage of the true value is the relative error.,Th

12、e above analysis has a relative error:,誤差可有正值和負(fù)值，分別表示測定結(jié)果偏高和偏低于真實(shí)值。,通常用相對誤差來表示分析結(jié)果的準(zhǔn)確度。,例題：,Physical Measurements,4. Precision(精密度): the closeness of the set of values obtained from identical measurements of a quantity. It is evaluated by using deviation(偏差).,xi: the individual measurement. : the me

13、an of a number of measurements.,偏差越小，則表明分析結(jié)果的精密度愈高，測定結(jié)果的再現(xiàn)性愈好。,常量分析： 試樣用量0.1g, 試液體積10mL半微量分析：試樣用量0.10.01g, 試液體積110mL微量分析： 試樣用量0.110mg, 試液體積0.011mL 超微量分析：試樣用量0.1mg, 試液體積0.01mL,常量分析成分時(shí)，分析結(jié)果的相對平均偏差一般應(yīng)小于0.2%。,Physical Measurements,Example 1-1: Calculate the mean and the standard deviation of the followi

14、ng set of analytical results: 15.67g, 15.69 g, and 16.03g.,Solution:,Accuracy versus precision,Physical Measurements,Accuracy is how close you get to the target. Precision is how close the repetitive shots are to one another. It is nearly impossible to have accuracy without good precision. However,

15、good precision does not guarantee accuracy.,精密度高而準(zhǔn)確度不高時(shí)，通常存在系統(tǒng)誤差。 精密度高并不一定意味著準(zhǔn)確度高，但分析結(jié)果的高準(zhǔn)確度，則一定要以高精密度為必備條件。,Physical Measurements,“To be sure of hitting the target, shoot first, and call whatever you hit the target.” Ashleigh Brilliant,“If reproducibility be a problem, conduct the test only once.”

16、Anonymous,“If a straight line fit is required, obtain only two data points.” Anonymous,Please do not do so !,Physical Measurements,III. Significant figures,1. Significant figures(有效數(shù)字),To indicate the precision of a measured number, we often use the concept of significant figures. Significant figure

17、s are those digits in a measured number (or result of a calculation with measured numbers) that include all certain digits plus a final one having some uncertainty.,9.12 cm,9.120 cm ?,可疑數(shù)字是根據(jù)測量儀器的最小分度值估計(jì)的，反映了儀器實(shí)際達(dá)到的精度。誤差為1. 例如：滴定管讀數(shù)24.02mL 實(shí)際體積為24.020.01mL 按照數(shù)字的精度也可以選擇合適的儀器。 例如：取樣品2.00mL, 2.0mL, 2mL

18、,Physical Measurements,2. Number of significant figures,Number of significant figures refers to the number of digits reported for the value of a measured or calculated quantity, indicating the precision of the value.,There are three significant figures in 9.12 cm, whereas 9.123 has four.,To count th

19、e number of significant figures in a given measured quantity, you observe the following rules:,Physical Measurements,All digits are significant except zeros at the beginning of the number and possible terminal zeros. Thus, 9.12 mm, 0.912 cm, 0.00912 m, all contain three significant figures. “1-9”均為有

20、效數(shù)字，而“0”做定位時(shí)是非有效數(shù)字；變換單位時(shí)，有效數(shù)字位數(shù)不變。,Terminal zeros ending at the right of the decimal point are significant. Each of the following has three significant figures: 9.00 cm, 9.10 cm, 90.0 cm.,Terminal zeros in number without an explicit decimal point (e.g., 93600) may or may not be significant. It is be

21、st to write only the significant figures and to locate the decimal point by scientific notation(科學(xué)計(jì) 記數(shù)法). 科學(xué)計(jì)數(shù)法用一位整數(shù)，若干位小數(shù)和 10的冪次方表示有效數(shù)字。 9.3600104, 9.360104, and 9.36104 have five, four, and three significant figures, respectively.,10100,一萬億億億億億億億億億億億億,1 googol =,Physical Measurements,Example 1-2:

22、List the proper number of significant figures in the following numbers and indicate which zeros are significant. 0.216; 90.7; 800.0; 0.0670,Solution:,0.216,three significant figures,90.7,800.0,0.0670,three significant figures; zero is significant,four significant figures; all zeros are significant,t

23、hree significant figures; only the last zero is significant,Physical Measurements,3. Significant figures in calculations,When adding or subtracting measured quantities, give the same number of decimal places (小數(shù)位) in the answer as there are in the measurement with the least number of decimal places.

24、, Addition and subtraction (加減),The most accurately known value for the formula weight of Ag2MoO4 is 375.68.,Ag2MoO4,Physical Measurements,When multiplying or dividing measured quantities, give as many significant figures in the answer as there are in the measurement with the least number of signifi

25、cant figures., Multiplication and division (乘除),Physical Measurements,In logarithms, it is the mantissa (尾數(shù)) that determines the numbers of significant figures.,The pH of a 2.010-3 molL-1 solution of HCl is:, Logarithm (對數(shù)),Physical Measurements,4. Exact numbers (確切數(shù)),Exact number is a number that a

26、rises when you count items or sometimes when you define a unit.,es,The conventions of significant figures do not apply to exact numbers.,An exact number has an infinite number of significant figures.,1b=0.45359237kg c=299 792 458 ms-1,Physical Measurements,5. Rounding (修約), If the leftmost digit to

27、be dropped is 5 or greater, add 1 to the last digit to be retained and drop all digits farther to the right. Thus, rounding 1.2151 to three significant figures gives 1.22.,Rounding is the procedure of dropping nonsignificant digits in a calculation result and adjusting the last digit reported.,Physi

28、cal Measurements, If this digit is less than 5, simply drop it and all digits farther to the right. Rounding 1.2143 to three significant figures gives 1.21., All nonsignificant digits should be rounded all at once. Rounding 1.2149 to three significant figures gives 1.21. It cannot be rounded first t

29、o 1.215 and then to 1.22.,“四舍五入”,“四舍五入” 見五就入，能引入明顯的舍入誤差，使修約后的數(shù)值偏高。,“四舍六入五留雙” 逢五有舍、有入，使由五的舍入引起的誤差可以自相抵消。,Physical Measurements,“四舍六入五留雙”, If the digit following the last significant figure is greater than 5, the number is rounded up to the next higher digit. If it is less than 5, the number is rounde

30、d to the present value of the last significant figure:, If the digit following the last significant figure is 5, the number is rounded off to the nearest even digit:,Physical Measurements,Solution:,Example 1-3: Perform the following calculations and round the answers to the correct number of signifi

31、cant figures. a. b. 5.41-0.398 c. 3.38-3.01d. 4.18-58.16(3.38-3.01),a.,The factor 5.8 has the fewest significant figures; therefore, the answer should be reported to two significant figures.,Physical Measurements,d.,Physical Measurements,Physical Measurements,In doing a calculation of two or more st

32、eps, it is desirable to retain nonsignificant digits for intermediate answers. This ensures that accumulated small errors from rounding do not appear in the final result.,運(yùn)算過程中，為了減小舍入誤差，可多保留一位有效數(shù)字（不修約），在算出結(jié)果后，再按運(yùn)算法則，將結(jié)果修約至應(yīng)有的有效數(shù)字位數(shù)。特別在運(yùn)算步驟長，涉及數(shù)據(jù)多的情況尤其重要。,真實(shí)，自有萬鈞之力,三十斤為一鈞,千鈞一發(fā)：出自于“其危如一發(fā)引千鈞（韓愈）”,Physi

33、cal Measurements,IV. SI units,In 1960 the General Conference of Weights and Measures (CGPM, 國際計(jì)量大會) adopted the International System (or SI, after the French le systme International dUnits，國際單位制), Which is a particular choice of metric system (米式制).,This system has SI base units (SI 基本單位) and SI Der

34、ived units (SI 導(dǎo)出單位).,This system has seven SI base units (SI 基本單位), the SI units from which all others can de derived.,Physical Measurements,One advantage of any metric system is that it is a decimal system (十進(jìn)制). In SI, a larger or smaller unit for a physical quantity is indicated by an SI prefix,

35、 which is a prefix used in the international system to indicate a power of ten.,10-15 femto f,兆 百萬倍 千 千倍 分 十倍 厘 百分之 毫 千分之 微 百萬分之 納 十億分之 皮 萬億分之 飛 千萬分之,Ahmed H. Zewail Nobel prize in Chemistry 1999,The total time of the reaction was 700 fs (10-15 s).,Femtochemistry (飛秒化學(xué)),Two possible potential-energy

36、 curves for the decomposition of cyclobutane to ethylene.,Physical Measurements,1. Length, The meter (m) is the SI base unit of length.,1 kilometer (km) = 103 m; 1 millimeter (mm) = 10-3 m; 1 micrometer (m) = 10-6 m; 1 nanometer (nm) = 10-9 m.,KULeuven Afdeling Fotochemie en Spectroscopie Prof. Dr.

37、F.C. De Schryver,The meter was originally defined in terms of a standard platinum-iridium(鉑-銥合金) bar kept at Svres, France. In 1983, the meter was defined as the distance traveled by light in a vacuum in 1/299,792,458 seconds.,Physical Measurements, A non-SI unit of length traditionally used by chem

38、ists is the angstrom (, 埃), which equals 10-10 m. An oxygen atom has a diameter of about 1.3 .,If you could place oxygen atoms adjacent to one another, you could line up over 75 million of then in 1 cm.,Physical Measurements,The Celsius scale (攝氏溫標(biāo)): C; Absolute scale (絕對溫標(biāo)): kelvin (K), SI unit; Fa

39、hrenheit scale (華氏溫標(biāo)): F.,2. Temperature,The Fahrenheit scale is at present the common temperature scale in the United States.,Physical Measurements,Comparison of temperature scales,KULeuven Afdeling Fotochemie en Spectroscopie Prof. Dr. F.C. De Schryver,The hottest place on record in North America

40、is Death Valley in California. It reached a temperature of 134F in 1913. What is this temperature reading in degrees Celsius? In Kelvins?,Physical Measurements,V. Derived units,Once base units have been defined, you can derive other unit from them.,Physical Measurements,1. Volume (體積),Volume has the

41、 SI unit of cubic meter (m3). Chemists often use the liter (L), which equals a cubic decimeter, and milliliter (mL), which equals a cubic centimeter.,Physical Measurements,2. Density (密度),The density of an object is its mass per unit volume.,An object has a mass of 15.9 g and a volume of 10.0 dm3 (L), then its density is:,Water has a density of 1.000 gL-1 at 4 C. The density of solid materials on earth ranges from 1 gL-1 to 22.5 gL-1 (osmium metal).,Physical Measurements,基礎(chǔ)化學(xué)中涉及大量的定量化學(xué)計(jì)算?；瘜W(xué)計(jì)算的方程式往往是量的方程式，量的方程式計(jì)算的每一個(gè)步驟中，用于計(jì)算的物理量數(shù)據(jù)都應(yīng)該帶單位。由于單位代表量綱，所以這樣的計(jì)算方法稱為量綱分析。,Physical Measurements,3. D