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Chem. 31 – 9/15 Lecture

Chem. 31 – 9/15 Lecture. Announcements. Last Week’s Quiz and Homework: scores generally high (although no pts lost for sig figs yet) problems will get harder First Lab Report Scheduled as due 9/22 (Next Monday), but may need to postpone Today’s Lecture Back titration example

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Chem. 31 – 9/15 Lecture

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  1. Chem. 31 – 9/15 Lecture

  2. Announcements • Last Week’s Quiz and Homework: • scores generally high (although no pts lost for sig figs yet) • problems will get harder • First Lab Report • Scheduled as due 9/22 (Next Monday), but may need to postpone • Today’s Lecture • Back titration example • Error and Uncertainty • Significant Figures • Definitions • Propagation of Uncertainty

  3. TitrationsBack Titration Example Sulfur dioxide (SO2) in air can be analyzed by trapping in excess aqueous NaOH (see 1). With addition of excess H2O2, it is converted to H2SO4 (see 2), using up additional OH- (see 3). SO2 (g) + OH- (aq) → HSO3- HSO3- + H2O2(aq) → HSO4- + H2O HSO4- + OH- (aq) → SO42- + H2O 208 L of air is trapped in 5.00 mL of1.00 M NaOH. After excess H2O2 is added to complete steps 1 to 3 (above), the remaining NaOH requires 21.0 mL of 0.0710 M HCl. What is the SO2 concentration in mmol/L?

  4. Chapter 3 – Error and Uncertainty Error is the difference between measured value and true value or error = measured value – true value Uncertainty Less precise definition The range of possible values that, within some probability, includes the true value

  5. Measures of Uncertainty Explicit Uncertainty: Measurement of CO2 in the air: 389 + 3 ppmv The + 3 ppm comes from statistics associated with making multiple measurements (Covered in Chapter 4) Implicit Uncertainty: Use of significant figures (389 has a different meaning than 400 and 389.32)

  6. Significant Figures(review of general chem.) Two important quantities to know: Number of significant figures Place of last significant figure Example: 13.06 4 significant figures and last place is hundredths Learn significant figures rules regarding zeros

  7. Significant Figures - Review Some Examples (give # of digits and place of last significant digit) 21.0 0.030 320 10.010

  8. Significant Figures in Mathematical Operations Addition and Subtraction: Place of last significant digit is important (NOT number of significant figures) Place of sum or difference is given by least well known place in numbers being added or subtracted Example: 12.03 + 3 = 15.03 = 15 Hundredths place ones place Least well known

  9. Significant Figures in Mathematical Operations Multiplication and Division Number of sig figs is important Number of sig figs in Product/quotient is given by the smallest # of sig figs in numbers being multiplied or divided Example: 3.2 x 163.02 = 521.664 = 520 = 5.2 x 102 2 places 5 places

  10. Significant Figures in Mathematical Operations Multi-step Calculations Follow rules for each step Keep track of # of and place of last significant digits, but retain more sig figs than needed until final step Example: (27.31 – 22.4)2.51 = ? Step 1 (subtraction): (4.91)2.51 Step 2 multiplication = 12.3241 = 12 Note: 4.91 only has 2 sig figs, more digits listed (and used in next step)

  11. Significant FiguresMore Rules Separate rules for logarithms and powers (Covering, know for homework, but not tests) logarithms: # sig figs in result to the right of decimal point = # sig figs in operand example: log(107) Powers: # sig figs in results = # sig figs in operand to the right of decimal point example: 10-11.6 = 2.02938 = 2.029 results need 3 sig figs past decimal point 107 = operand 3 sig fig = 2.51 x 10-12 = 3 x 10-12 1 sig fig past decimal point

  12. Significant FiguresMore Rules • When we cover explicit uncertainty, we get new rules that will supersede rules just covered!

  13. Types of Errors True Volume • Systematic Errors • Always off in one direction • Examples: using a “stretched” plastic ruler to make length measurements (true length is always greater than measured length); reading buret without moving eye to correct height • Random Errors • Equally likely in any direction • Present in any (continuously varying type) measurement • Examples: 1) fluctuation in readings of a balance with window open, 2) errors in interpolating (reading between markings) buret readings eye Meas. Volume

  14. Accuracy and Precision • Accuracy is a measure of how close a measured value is to a true value • Precision is a measure of the variability of measured values Precise, but not accurate Poor precision (Accuracy also not great) Precise and Accurate

  15. Accuracy and Precision • Accuracy is affected by systematic and random errors • Precision is affected mainly by random errors • Precision is easier to measure

  16. Propagation of Uncertainty Vinitial • What does propagation of uncertainty refer to? • It refers to situations when one or more variables are measured in order to calculate another variable • Examples: • Calculation of volume delivered by a buret: Vburet = Vfinal– Vintial • Note: uncertainty in Vburet can be calculated by uncertainty in Vinitial and Vfinal or by making multiple reading to get multiple values of Vburet (and then using the statistics covered in Chapter 4) • Calculation of the volume of a rectangular solid: Vobject = l·w·h • Calculation of the density of a liquid: Density = mliquid/Vliquid • Go to Board to go over examples Vfinal l h w

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