Chem 222 #3 Ch3 Aug 31, 2004
Announcement Please work in the lab session you registered for. If you are found to work in any other lab without my permission, no points will be given for the lab. Please do not miss any labs. When you send me an e-mail, please identify your lab session with the name of your Lab TA. If you want to make up for your lab on 9/7, please send an e-mail to the following TA by tomorrow 10 AM. Because the space is limited (for 15 students for each session), choose only one. Tuesday 8am cjones26@uic.edu Tuesday 2pm mshaib1@uic.edu
Quiz on Thursday Memorize all the important equations (at least, equations highlighted by red in the text) Memorize definitions (molarity, molality, ppm/ppb, weight %,, units, buoyancy, significant figures, errors) Solve examples, problems, and home work (particularly ones covered in the class) 2 questions in 15 mins
Undergraduate Research Identify your area(s) Read general scientific journals and get some idea about the areas which will be hot 10 years after now. Choose what you will like for a long time. Do not choose topics because they are easy. It means you will be easily replaced. Multidisciplinary areas may be a good choice. Getting research experience will help Enhances your lab experience Enhances your career Research experience is a must for some career paths and awards Opportunities NSF Research Experience for Undergraduate Program (Locations all over the US including Chicago. This program will pay you during summer, but competitive) (http://www.nsf.gov/home/crssprgm/reu/start.htm) Positions at UIC Chemistry and other departments (probably a good starting point) We have a Chemistry undergraduate research seminar TODAY.
Ch. 3 Experimental Error 3-1 Significant Figures The number of significant figures is the minimum number of digits needed to write a given value of scientific notation without loss of accuracy. What does it mean? 9.25 10 4 3 significant figures The value is within a range from 9.24 10 4 to 9.26 10 4 You can also write (9.25 ±0.01) 10 4 9.250 10 4 4 significant figures 9.2500 10 4 5 significant figures 132 3 significant figures 0.002302 4 significant figures 2.302 10-3 4 significant figures
How many digits should we include? If the error is ±200, you can denote (9.25 ±0.02) 10 4 It is often allowed to add one extra digit as Ο (9.250 ±0.020) 10 4 Ο (9.252 ±0.024) 10 4 But it is not meaningful to add more than one digit as (9.2500 ±0.0200) 10 4 (9.25000 ±0.02000) 10 4 (9.2521 ±0.0243) 10 4 (9.25215 ±0.02436) 10 4 3-2 (a) Round 1.2367 to 4 significant figures. (b) Round 1.2384 to 4 significant figures. (c) Round 0.1352 to 3 significant figures.
Problems
3-2 Significant Number in Arithmetic Addition and Subtraction If the numbers to be added or subtracted have equal number of digits, the answer goes to the same decimal places (1.362±0.001) 10-4 + (3.111±0.001) 10-4 -------------------------------- 4.472±0.001 10-4
Addition and Subtraction #2 If the numbers to be added or subtracted does not have the same number of significant figures, we are limited by least certain one 121.80 (Q1. Why are the numbers insignificant?) Addition and Subtraction #2 In adding or subtracting numbers expressed in scientific notation, all the numbers should be expressed in the same exponent as
Quiz If the Fe 2 O 3 sample in Exp 3 weighs 3.254g and 3.3 g by an analytical balance and a normal balance, respectively, is it a good idea to average the two values in order to reduce the error?
Multiplication and Division In multiplication and division, we are normally limited to the numbers of digits contained in the number with fewest significant figures. The power of 10 Has no influence on the number of figures (a ± e a ) (b ± e b ) ~ ab ± be a ± ae b = ab(1 ± e a /a ± e b /b)
Logarithms and antilogarithms This is important for calculation of ph etc. 12.6251065 Log: What is mantissa? mantissa (e ) Log(4.218 10 14 ) = 14.6251065 Log(a 10 b ) = Log(a) + b Answer the correct number of digits
Antilog: antilog(a) 10 a If y= antilog (x) x =log(y) 242.129 6.02559 10-4
Which is a better graph? When drawing a graph, consider whether the graph is Intended to display qualitative behavior of the data.
Types of error What is systematic error? Systematic error, also called determinate error, arises from a [Q1] in equipment or the design of an experiment. If you conduct the experiment again in exactly the same manner, the error is [Q2]. What is random error? Random error, also called indeterminate error, arises from the effects of [Q3] (and maybe uncontrollable) variables in the measurement. Random error has an equal chance of being positive or negative. It is always present and cannot be corrected. Q. Tell the difference between accuracy and precision Accuracy Precision
Definitions Precision Reproducibility of experiments: <{(y) - <y>} 2 > Accuracy Nearness to the true value: {<y> - y true } 2 <A> denotes the average in measurements of A Absolute Uncertainty the margin of uncertainty associated with a measurement. Relative Uncertainty = absolute uncertainty/magnitude of measurement Percent Relative Uncertainty = 100 Relative Uncertainty
Propagation of Uncertainty Suppose you wish to perform the following arithmetic, in which the experimental uncertainties, designated e 1, e 2, and e 3, are given in parentheses. The arithmetic answer is 3.06. But what is the uncertainty associated with this result?
Uncertainty in addition and subtraction (a + δ 1 ) + (b + δ 2 ) = (a+b) + δ 1 + δ 2 < δ SUM > = {<(δ 1 ± δ 2 ) 2 >} 1/2 = {< (δ 12 ± 2 δ 1 δ 2 + δ 22 )>} 1/2 = {< δ 12 > ± 2 < δ 1 > < δ 2 > + < δ 22 > } 1/2 = {< δ 12 > + < δ 22 > } 1/2 where δ 1 and δ 2 are measurement errors for Measurement 1 and 2, respectively, and < δ 1 > = < δ 2 > = 0 and e k = <δ k2 > 1/2 (k =1,2) Ex. Suppose that the initial reading is 0.05 (0.02) ml and the final Reading is 17.88 (0.02) ml. The volume delivered is the difference: How much is e?
Multiplication and Division Ex. Convert absolute uncertainties to percent relative uncertainties %e 4 = 4.0 % corresponds to e 4 = 0.040 5.64 = 0.23 (a + δ a )(b + δ b ) ~ ab + a δ b + b δ a = ab + ab(δ b /b) + ab(δ a /a) e ab = { (ab) 2 (e a /a) 2 + (ab) 2 (e b /b) 2 } 1/2 = ab {(e a /a) 2 + (e b /b) 2 } 1/2 %e ab = 100 e ab / ab = 100{(e a /a) 2 + (e b /b) 2 } 1/2 = {(%e a ) 2 + (%e b ) 2 ) Mixed Operation: See p53
P54 Ex. Significant Figures in Lab You prepared a 0.250 M NH 3 solution by diluting 8.45 (±0.04) ml of 28.0 (± 0.5) wt % NH 3 [density 0.899 (± 0.003) g/ml] up to 500.0 (± 0.2) ml. The uncertainty in molecular mass of NH 3, 17.030 6 g/mol, is negligible. Find the uncertainty in 0.250 M. First convert wt % to the molarity y for the concentrated NH 3. y = (0.899 ± 0.003) 1000 [g/l] (0.280± 0.005)/17.0306 [g/mol] %e y = 100{(0.003/[Q1]) 2 + (0.005/[Q2]) 2 } 1/2 = Use the dilution equation (1-3) M conc V conc = M dil V dil M dil = y (8.45±0.004 ml)/(500±0.2 ml) =
Exponents and Logarithms y = x a y+ δ y = (x+ δ X ) a ~ x a {1 +a(δ X /x)} So δ y /x a = a(δ X /x) In general, Y + δ Y = f(x + δ X ) = f(x)+δ X df(x)/dx e Y = e x {df(x)/dx} Memorize Table 3-1.
Ch: 3-6, 3-7, 3-9, 3-10, 3-13, 3-14a, 3-14b, 3-14d, 3-15g Ch4: 4-A, 4-1, 4-3, 4-11, 4-16, 4-22 Read Ch4, 5