Jan 18, 2005 #3. Average (Ch. 4) Standard deviation Q-test Significant Figures (Ch 3) Error

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1 Jan 18, 2005 #3 Average (Ch. 4) Standard deviation Q-test Significant Figures (Ch 3) Error

2 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.

3 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

4 Quiz 1 from the last semester 1) A concentrated HCl solution contains 37.0 % wt HCl. The density of the solution is 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 = g/ml) if the apparent mass weighed in air is 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)?

5 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) ( Positions at UIC Chemistry and other departments (probably a good starting point)

7 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

8 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)

9 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 Q1. Is 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 = If Q calc > Q table the point should be discarded.

10 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? significant figures The value is within a range from to You can also write (9.25 ±0.01) significant figures significant figures significant figures significant figures significant figures

11 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 ( ±0.0200) 10 4 ( ± ) 10 4 ( ±0.0243) 10 4 ( ± ) 10 4

12 Problems

13 Quiz If the Fe 2 O 3 sample in Exp 3 weighs g on average. How many digits do you need in calculation of concentration of Ca 2+ in the original solution?

14 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 = g/ (120.2 g/mol)* = 2.30 mmol The weights for measurement 2 and 3 are g and 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 =

15 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) (3.111±0.001) ±

16 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 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

17 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)

18 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] = g / [mol/g] = = Is this correct?

19 Logarithms and Antilogarisms in Chemistry Q1. What is the ph for 0.10 M of HCl? ph = -Log[H + ] ph = -Log(0.10) = ? Q2. What is [H + ] when ph = 0.00? [H + ] = 10 -(ph) If ph = 0.00 [H + ] = M=?

Logarithms and antilogarithms (p48) Log: 12.6251065 What is mantissa? mantissa (e ) Log(4.

20 Logarithms and antilogarithms (p48) Log: What is mantissa? mantissa (e ) Log( ) = Answer the correct number of digits Cf. Log(a 10 b ) = Log(a) + b

21 Antilog: antilog(a) 10 a If y= antilog (x) x =log(y)

22 Which is a better graph? When drawing a graph, consider whether the graph is Intended to display qualitative behavior of the data.

23 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

25 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

26 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 But what is the uncertainty associated with this result?

27 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 (0.02) ml. The volume delivered is the difference: How much is e?

28 Multiplication and Division Ex. Convert absolute uncertainties to percent relative uncertainties %e 4 = 4.0 % corresponds to e 4 = = 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

29 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.

30 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

Chem 222 #3 Ch3 Aug 31, 2004

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