Chem. 31 – 2/4 Lecture

Announcements Due Today –Corrected diagnostic quiz –Additional Problem 1.1 Quiz After Announcements Today’s Lecture –Sig figs (continuing) –Definitions (types of errors/accuracy and precision) –Propagation of Uncertainty

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 Note: 4.91 only has 2 sig figs, more digits listed (and used in next step)

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: = operand 3 sig fig = results need 3 sig figs past decimal point = = 2.51 x = 3 x sig fig past decimal point

Significant Figures More Rules When we cover explicit uncertainty, we get new rules that will supersede rules just covered!

Types of Errors 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 True Volume Meas. Volume eye

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 and Accurate Precise, but not accurate Poor precision (Accuracy also not great)

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 aim here rough ave of imprecise shots

Propagation of Uncertainty 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: V buret = V final – V intial –Note: uncertainty in V buret can be calculated by uncertainty in V initial and V final or by making multiple reading to get multiple values of V buret (and then using the statistics covered in Chapter 4) –Calculation of the volume of a rectangular solid: V object = l · w · h –Calculation of the density of a liquid: Density = m liquid /V liquid Go to Board to go over examples V initial V final l h w