Jan 18, 2005 #3 Average (Ch. 4) Standard deviation Q-test Significant Figures (Ch 3) Error
Announcement When you send me an e- mail, please identify your full name and lab session. Jan 21 is the last day to drop the course without W grade or change the lab section. There is still some space in the M/W 11 AM-2 PM section.
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
Quiz 1 from the last semester 1) A concentrated HCl solution contains 37.0 % wt HCl. The density of the solution is 1.190 g/ml. What volume of this reagent should be diluted to 0.5 L to make 6 M HCl solution? (10 points) 2) Potassium hydrogen phthalate (KHP) is a primary standard used to measure of concentration of NaOH solutions. Find the true mass of KHP (density = 1.636 g/ml) if the apparent mass weighed in air is 3.1001 g (6 points). If you did not correct the mass for buoyancy, would the calculated molarity of NaOH be too high or too low (2 points)? By what percentage (approximately) (2 points)?
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. Getting research experience will help Enhances your lab experience Enhances your career Research experience is a must for some careers Opportunities NSF Research Experience for Undergraduate Program (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)
Mean or Average The arithmetic mean, also called the average is the sum of the x measured values divided by n, the number of measurements: The mean represents the best estimate of x on the basis of the measurements
Standard deviation (p63) The standard deviation, s, measures how closely the data are clustered about the mean. (Figure 4-2). _ X : Average n : The number of data points The quantity (n-1) in Equation 4-2 is called the degrees of freedom. When _ n x µ: True Mean S σ: True Standard Deviation Relative sd :s/ x or 100s/ x (%) (p51)
4-6 Q Test for Bad Data (p75) how to justify excluding an inconsistent data point Consider the five results 12.53, 12.56, 12.47, 12.67, and 12.48. Q1. Is 12.67 a bad point? Q test can tell you how to distinguish a bad point from good points Range: Max Min Gap: Difference between the questionable point and the nearest point Q calc = 0.11/0.20 = 0.55 0.94 3 If Q calc > Q table the point should be discarded.
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
Problems
Quiz If the Fe 2 O 3 sample in Exp 3 weighs 0.5003 g on average. How many digits do you need in calculation of concentration of Ca 2+ in the original solution?
Analysis Example X: Moles of CaC 2 O 4 H 2 O X = {Weight of CaC 2 O 4 H 2 O}/ {Mol weight of CaC 2 O 4 H 2 O} For measurement 1, X 1 = 0.502 g/ (120.2 g/mol)* = 2.30 mmol The weights for measurement 2 and 3 are 0.530 g and 0.350 g. Using these values, X 2 = 2.05 mmol & X 3 = 1.80 mmol. (* Note: the numbers are incorrect).. So molarity of Ca 2+ (y) is y = [Moles of CaC 2 O 4 H 2 O]/[? ] Using this, for measurement 1 y 1 =??? = Similarly, y 2 =?? & y 3 =
3-2 Significant Number in Arithmetic (p47) 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 for MW of KrF 2 (Q1. Why are the numbers not significant?) Addition and Subtraction #2 In adding or subtracting numbers expressed in scientific notation, all the numbers should be expressed in the same exponent as
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)
Quiz In Exp 2, we have to estimate # of moles. Sam tried the calculation in the following way. # of moles= weight [g]/mw [mol/g] = 0.503 g /120.092 [mol/g] = 0.004188455 = 4.188455 10-3 Is this correct?
Logarithms and Antilogarisms in Chemistry Q1. What is the ph for 0.10 M of HCl? ph = -Log[H + ] ph = -Log(0.10) = 1.0000? Q2. What is [H + ] when ph = 0.00? [H + ] = 10 -(ph) If ph = 0.00 [H + ] = 10-0.00 M=?
Logarithms and antilogarithms (p48) Log: 12.6251065 What is mantissa? mantissa (e ) Log(4.218 10 14 ) = 14.6251065 Answer the correct number of digits Cf. Log(a 10 b ) = Log(a) + b
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. (p52) 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 ) Read about Mixed Operation: See p53
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} Use Table 3-1.
Examples in P 52, P54 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