9-5-18 Bell Work Collect your LAB-4 work sheet from graded work desk and the Bell-Work sheet

Chapter-2: Analyzing Data (measurements) Dr. Chirie Sumanasekera CHEMISTRY Notes_6 Dr. Chirie Sumanasekera 9/5/2018 TOPICS covered today: Dimensional Analysis (contd.) Uncertainty of data and why Sig-figs are important Error and Percent error calculations

Dimensional Analysis Dimensional Analysis (Unit Factor Method) is a problem-solving method that uses concept that any number (or factor) can be multiplied by 1 without changing its value. Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in. Ex: 1 inch = 2.54 cm There are exactly 2.540000000... cm in 1 inch. We can make two unit factors from this information:

Solving Problems with Dimensional Analysis Write down what you need to find with a question mark. Then set it equal to the information that you are given. The problem is solved by multiplying the given data and its units by the appropriate unit factors so that only the desired units are present at the end after the other units cancel out. (1) How many centimeters are in 6.00 inches? (2) Express 24.0 cm in inches.

Solving Problems with Dimensional Analysis You can also string many unit factors together. (3) How many seconds are in 2.0 years?  (4) Convert 50.0 mL to liters. (This is a very common conversion.)

Solving Problems with Dimensional Analysis (5) How many atoms of hydrogen can be found in 45 g of ammonia, NH3? We will need three unit factors to do this calculation, derived from the following information: 1 mole of NH3 has a mass of 17 grams. 1 mole of NH3 contains 6.02 x 1023 molecules of NH3. 1 molecule of NH3 has 3 atoms of hydrogen in it.

Measurements Chapter-2: ( 34 cm) Units Number Accuracy and Precision in data collection Scientific notation Graphical data Dimensional analysis Significant figures (Uncertainty in measurement) Error & Percent Error Base unit Prefixes Conversions between prefixes Dimensional analysis

What is the length of this pencil in cm? UNCERTAINTY of MEASUREMENT 21 22 24 26 23 27 29 cm 28 What is the length of this pencil in cm? 26.5 cm for sure + a bit more? 26.57 cm The part of the measurement we guessed is shown at the end (4) Significant figures are used to communicate the level of uncertainty in measurements

The last digit of a sig-fig shows the uncertainty of your data! Expressing UNCERTAINTY of MEASUREMENT with sig-figs (a) 30.0 (b) 30.00 (c) 30.00001 (a) 30.0 (b) 30.00 (c) 30.00001 = Certain up to 30. = Certain up to 30.0 = Certain up to 30.0000 The last digit of a sig-fig shows the uncertainty of your data!

Precision shown by significant figures Which of these is more precise? ANSWER: (c) Is most precise because there are more figures after (right of) decimal

Actual Length of the pencil is 26.56 cm Measured value is 26.54 cm Error Calculations 21 22 24 26 23 27 29 cm 28 Actual Length of the pencil is 26.56 cm Measured value is 26.54 cm Find error: (Absolute or positive value) ERROR = |Measured value – Actual value| Error: |26.56 – 26.54| = 0.02 cm

Percent Error Calculations 21 22 24 26 23 27 29 cm 28 Actual Length of the pencil is 26.56 cm Measured value is 26.54 cm Find % error: Percent ERROR = |Measured value – Actual value| x 100 Actual value % Error = |26.56 – 26.54| x 100 = 0.02 x 100 = 0.07530 % 26.56 26.56

Percent Error Calculations Smaller the percent error, the greater the accuracy Example: Comment which is more accurate: 0.07530 % vs. 23.05 % 0.07530% is smaller so it is more accurate

Today we examined how to perform and evaluate calculation using: Dimensional Analysis Significant figures 3. Error & Percent Error of data

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