Chem. 31 – 9/6 Lecture

Announcements I Adding Turn in today If you received an add slip, turn it into the office soon (so I know status of lab sections) Turn in today Corrected diagnostic quiz Quiz 1 – Today (after announcements) Lab Procedures Quiz – Thursday and next Monday (sect. 5, 6, and 7 are now ahead)

Announcements II Websites Today’s Lecture Text homework solutions posted (class website) SacCT site is set up (only grading columns so far; but I will post the diagnostic quiz and quiz 1 solutions soon) Today’s Lecture Stoichiometry (Chapter 1) Error and Uncertainty (Chapter 3) Definitions Significant figures Accuracy and precision in measurements

Stoichiometry Stoichiometry refers to ratios between moles of reactants and products in chemical reactions The ratio of moles of reactants and products is equal to the ratio of their stoichiometric coefficients Example: aA + bB ↔ cC + dD Moles A/moles B = a/b

Stoichiometry Example problem: How many moles of H2O2 are needed to completely react with 25 mL of 0.80 M MnO4-? Reaction: 5H2O2(aq) + 2MnO4- +6H+ ↔ 2Mn2+ + 5O2(g) + 8H2O(l)

Stoichiometry Remember: there are two (common) ways to deliver a known amount (moles) of a reagent: Mass (using formula weight) Volume (if molarity is known)

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 7

Measures of Uncertainty Explicit Uncertainty: Measurement of CO2 in the air: 399 + 3 ppmv The + 3 ppm comes from statistics associated with making multiple measurements (Covered in Chapter 4) Implicit Uncertainty: Use of significant figures (399 has a different meaning than 400 and 399.32) 8

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 9

Significant Figures - Review Some Examples (give # of digits and place of last significant digit) 21.0 0.030 320 10.010 10

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 11

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 12

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) 13

Significant Figures More 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 = 2.029 107 = operand 3 sig fig results need 3 sig figs past decimal point = 2.51 x 10-12 = 3 x 10-12 1 sig fig past decimal point 14

Types of Errors Systematic Errors Random 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

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

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

Accuracy and Precision Both imprecise and inaccurate measurements can be improved Accounting for errors improves inaccurate measurements (if shot is above and right aim low + left) Averaging improves imprecise measurements rough ave of imprecise shots aim here