General Chemistry II
General Chemistry II CHEM 1120
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This 24 page Class Notes was uploaded by Justus Shields on Wednesday September 23, 2015. The Class Notes belongs to CHEM 1120 at Middle Tennessee State University taught by Gary White in Fall. Since its upload, it has received 38 views. For similar materials see /class/213194/chem-1120-middle-tennessee-state-university in Chemistry at Middle Tennessee State University.
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Date Created: 09/23/15
Uncertainties Linearizing nonlinear data Activity 4 Also Test 1 26 Jan 2011 125 Today Test 1 Uncertainties Linearizing NonLinear Data Activity 4 Free Fall 225 Test 1 Test 1 is next week gt BAS 102 starting at 410 pm gt Time allowed is 1 hour 25 minutes Format for tests gt 10 multiple choice questions worth 3 points each gt 3 word questions with a combined value of 70 points usually 25 pts 25 pts and 20 pts Test 1 Allowed materials gt pencil and eraser gt calculator Not allowed gt cell phones you cannot use the calculator on your cell phone gt notes of any kind gt extra scratch paper Provided An equation sheet a copy of the inside back cover of your lab manual will be provided Test 1 Answers and Solutions gt An answer only with no work shown will receive very little credit gt To receive full credit you must show all your working This will usually include Drawing and correctly labeling a sketch of the problem 0 Writing all known quantities symbol and value 0 Writing the relevant equations in symbols before using itthem Test 1 What s on the test gt Questions will cover all material in lectures 1 through 4 with a smattering from lecture 5 gt Word questions will be similar to the homework problems and whiteboard problems from lab gt See the previous tests on D2L From lecture 5 gt Definition of momentum conservation of momentum gt Types of collision inelastic and elastic gt There will be at least one possibly two multiple choice questions on lecture 5 There will be no word problems 625 Discussion Quiz 1 Material gt Will cover lectures 1 5 gt 5 conceptual or simple number plugging multiple choice problems gt One or two more difficult problems that will require some working to obtain an answer still multiple choice Availability gt Available on D2L under Quizzes for 24 hours starting at 9 am tomorrow morning gt Once started you will have 60 minutes to complete the quiz gt One attempt only How many decimal places In textbook problems gt Textbook problems include things like your homework problems and test and exam problems gt Your final answers to textbook problems should be rounded to the same number of significant figures as the quantity with the least number of significant figures that is given in the problem statement In laboratory reports We will spend a large portion of today39s lecture talking about how to report results of your lab experiments Uncertainties Why do we care gt GPS gt Speedometers and police speed guns 925 Rules for Dealing With Uncertainties 1 If you make a direct measurement of a quantity X you should estimate the uncertainty in that quantity 6X 2 The fractional uncertainty FU of a calculated value is equal to the largest fractional uncertainty of the measured quantities used in the calculation 3 All uncertainties should be reported to 1 significant figure sf or sig fig See also Appendices B and D in your lab manual Rule 1 Direct Measurements gt For direct measurements you must estimate the uncertainty in the measurement gt In Phys 2011 most direct measurements you make will consist of lengths times angles and masses gt The uncertainty in a quantity X is written as 6X Examples The height h of a coffee filter above the ground is 186 i 2 cm In this case we say 6h 2 cm The time t it takes for the coffee filter to fall to the ground is 12 i 03 s so that we have 61 03 s Rule 2 Fractional Uncertainties The definition of the fractional uncertainty FU in a quantity X is 7 uncertainty in X 7 6X 7 X 7 X Thus if we know FUX we can calculate 6X by FUX 6X FUX x X Example If h 186 cm and 6h 2 cm then 20m m 39 FUh 1125 Rule 3 Significant Figures gt Also called significant digits How tail is the man in the p etc 5 ft 55264983 ft m2 Rules for Significant Figures 1 All digits between and including the first and last nonzero digits are significant 2 Leading zeros are not significant 3 Trailing zeros after a decimal point are significant Examples 1425 Rules for Significant Figures gt Numbers without a decimal place can be ambiguous Example Census worker 1 says Australia39s population is 19387235 people while Census worker 2 says Australia39s population is 19000000 people What is the meaning the significance of these numbers gt In this course we will treat the trailing zeros in numbers without a decimal point as not significant gt To show that you want the 0quot in 630 to be treated as significant use scientific notation 630 x 10 1525 Example 6 Calculating Uncertainties Calculate the density p and its uncertainty for a sample of liquid for which you measured the volume to be V 147 i 04 cm3 and the mass to be m 76 i 4 g Ans p 52 i 03 gcm3 Note that the final answer is rounded to the same digit position as the position of the nonzero digit in the uncertainty Linear Graphs Review The equation of a straight line y mX b or y slopeX b Generic Straight Line Graph 1725 What does the slope of a graph really mean A typical equation for the bestfit straight line from Activity 2 y 897 cmst 941 cm where y height of the coffee filter 1 time taken for the filter to fall 1825 What does the slope of a graph really mean The slope of 897 cms tells us that for each change in time of 1 second the coffee filter fell a distance of 897 s Typical Data for Falling Coffee Filter Experiment y 897 cmst 941 cm Height ycm 0 02 04 06 08 1 12 14 Time t s 1925 What does the slope of a graph really mean In general the slope of a linear graph tells us how much the y quantity changes for each unit change in the x quantity 2025 A Closer Look at the Form of the StraightLine Equation y slopex b y and X represent numbers that change slope and b are numbers that are constant variable quantity constantvariabe quantity constant 239125 A Closer Look at the Form of the StraightLine Equation gt Often the relationship between two quantities say A and B that we measure is nonlinear which simply means that the graph of A vs B is not a straight line gt However it is often the case that by carefully choosing a function of A or B or both we can linearizethe data and the resulting graph will be linear a straight line gt Lets see how this works with an example See also Appendices C and E in your lab manual 2225 Some Background gt From lecture 4 g 98 ms2 is the magnitude of the acceleration due to gravity at the Earth39s surface gt It gravity is the only force acting on an object in particular air resistance is negligible all objects will accelerate towards the center of the Earth at 98 ms2 32 tts2 Note NEVER write g 798 ms2 This is WRONG Activity 4 Free Fall gt The aim of Activity 4 is to experimentally measure the acceleration due to gravity and compare the experimental value to the accepted value of 98 ms2 gt The experiment is very similar to the terminal velocity experiment except tha 0 ball bearings will be dropped instead of coffee filters 0 air resistance is negligible freefall motion very accurate electronic timing equipment will be used gt When you plot your hvs I data you should find that your graph is nonlinear 2425
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