Chem 110A week one notes
Chem 110A week one notes CHEM 110
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This 4 page Class Notes was uploaded by Mikaela Notetaker on Thursday January 21, 2016. The Class Notes belongs to CHEM 110 at West Virginia University taught by Melissa G. Ely in Spring 2016. Since its upload, it has received 42 views. For similar materials see Introduction to Chemistry in Chemistry at West Virginia University.
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Date Created: 01/21/16
Numbers and Arithmetic Two types of numbers delt with in chemistry and other sciences. Ex. 69 students vs. 69 feet, the difference is that the students are an exact number and 69 feet is a measured number. Exact vs. Measure 1. Exact numbers a. Numbers that are exactly known b. Defined numbers within a given measurement system i. Ex. 12 inches = 1 foot, 60 minutes = 1 hour c. No error or uncertainty in value d. Numbers obtained by counting individual objects i. Ex. There are 95 chairs in the classroom, Sally has two dogs 2. Measured numbers a. Numbers that are measured b. A measured number is not exactly known due to the measuring process(a quantitative observation that is relative to a unit or a standard measuring device) c. Some error or uncertainty in the value d. Amount of error depends on the measuring device(increment and distance between markings) e. Numbers obtained by measuring an object with a measuring device i. Ex. 191 pound person weighed on a scale, 8.25 minute/mile as timed by a stop watch 3. Error in measured numbers a. Error is always +/- one in last digit unless told otherwise due to guesstimating during measuring process. i. Ex. Measurement of weight on a scale marked at every pound. Weight = 152.2 pounds, assume an error of +/- 1 in values of last digit. b. How does the increment and distance between markings have an effect on the error i. Ex. Measurement on the length of a pencil using two different rulers. Ruler one will have less tick marks than two but both will measure in centimeters. Ruler one goes 11, 12, 13. Ruler two 11.1, 11.2, 11.3, etc. Ruler two has better precision since it has more tick marks and could give us 12.95cm instead of 12.9cm. The amount of error in measured #’s depends on the measuring device and markings. Example measure the weight of a man on three different scales. Scale one has a tick mark for 190 and 200, Scale two 189, 190, and 191, scale three 190.4, 190.5, 190.6. Increment: 10 pound scale one, 1 pound scale two, .1 lb scale three Wt: 192 lb scale one, 190.2 lb scale two, 190.53 lb scale three Error: +/- 1 lb scale one, .1 lb scale two, .01 lb scale three Range: 191-193 lb scale one, 190.1 – 190.3 lb scale two, 190.52 – 190.54 lb scale three Scale three is the most precise since it gives the weight with the least amount of error. Note: as precision of scale increases amount of error decreases and # of digits used to represent the # increase the number of digits used to represent a measured number is called the significant figures the number of sig-figs tells about the amount of error in a measured number. Significant Figures – digits used to represent a number. Only the digit farthest to the right is uncertain because it is estimated, but it is still significant. Ex. 20.20 has four sig figs Note: the greater the number of sig figs, the more accurate the data and the less error the measured number has. Accurate- hitting what you are aiming for. Precision – reproducible, a cluster group. (does not have to be a bullseye like accuracy) Rules of Counting Sig Figs in Measured Numbers 1. Find the first non-zero digit. This first non-zero digit and everyone after it is a significant number. Ex: # # of Sig Figs 24.5 3 0.03 1 (The first sig fig is the first non-zero number which is three) 27 2 2. Measured Numbers ending in zero and with a value greater than one must be written in standard exponential form expressing the proper number of sig figs, otherwise the number is ambiguous in terms of significant numbers. Ex. 2400 is ambiguous since we don’t know the number of sig figs while 2400. Is four sig figs since it means we measured to 2400 (need a decimal for it to have sig figs otherwise it is ambiguous) # # sig fig 1200 ambiguous 3 1.2x10 2 1.20x10 3 3 Mathematical Manipulation of Measured Numbers Addition and subtraction of measured numbers. Rule: Number with the least number of decimal places limits the number of decimal places, so worry about the decimal places! 20.311 (3 decimal places) - 8.311 (3 decimal places) 12.000 (3 decimal places) (The zeroes are placed there as place holders since it must have three decimals) 0.089 (3 decimal places) - 0.01 (2 decimal places) 0.079 (Must have only two decimals since the smaller decimal is two) ⇩ 0.08 (The seven was rounded because of the nine. If the number next to the last number is five or higher round that last number) 1.59 (2 deci) +0.610 (3 deci) 0.980 (3 deci) ⇩ 0.98 (2 deci)
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