Numbers in Chemistry Measurement (Ch 3)

Scientific Measurement a quantity that has both a number and a unit. Accuracy: The closeness of a measurement to its accepted value. Precision: A measure of how close a series of measurements is to one another.

Percent Error Experimental Value: Accepted Value: % Error = experimental value – accepted value x 100% accepted value Used to determine accuracy and precision. Experimental Value: value measured in lab Accepted Value: correct value based on reliable references

The Number Comfort Zone We are used to Small Numbers Lunch for $2.25 or $5.50 Tickets for $25, $50, or $125 Car for $2,500, or $23,000 But $9,000,000,000,000 deficit is too big to get our mind around. (Nine Trillion Dollars) Science uses very large or very small numbers

Two ways Scientists get numbers into the comfort zone Use units to express amount Kilobuck $ 1000 Milligram 60 milligram Tylenol tablet has 0.060 grams ingredient. Use Scientific Notation 6.023 x 1023 atoms per mole

Scientific Notation Scientific Notation was developed in order to easily represent numbers that are either very large or very small. Scientific Notation is based on powers of the base number 10. Examples: The number 200,000,000,000 grams in scientific notation is written as 2 x 1011 grams The number 0. 000,006,645 kilometers in scientific notation is written as 6.645 x 10-6 kilometers

Writing Scientific Notation 6.645 x 10-6 Liters   Coefficient Must be greater or equal to 1 and less than 10 Base Must ALWAYS be 10 Exponent (Power of 10) Shows the number of places the decimal needs to be moved to change the number to standard notation A negative exponent means the standard notation is less than one

Changing from Standard Form to Scientific Notation 1. Place decimal point such that there is one non-zero digit to the left of the decimal point. For example: 42864900000 = 42864900000. Move the decimal: 4.2864900000

Changing from Standard Form to Scientific Notation 2. Count number of decimal places the decimal has "moved" from the original number.  This will be the exponent of the 10. 4.2864900000. Originally the decimal was at the end. The decimal moved 10 places to the LEFT.

Changing from Standard Form to Scientific Notation 3. Determine if the exponent is negative or positive. If the original number was less than 1, the exponent is negative. i.e. 0.00001114 = negative exponent If the original number was greater than 1, the exponent is positive. i.e. 111,400,000 = positive exponent

Practice Write the following numbers in Scientific Notation: 96,400 0.361 0.0057300 6,587,234,000 8.00 = 9.64 x 104 = 3.61 x 10-1 = 5.7300 x 10-3 = 6.587234 x 109 = 8.00 x 100

Changing from Scientific Notation to Standard Form 1. Determine the number of places the decimal must be moved from the exponent. 2. Decide if the standard form will be a number greater than one or less than one. 3. Move the decimal in the coefficient adding place holders if necessary.

Practice Write the following numbers in Standard Notation: 3.97 x 103 8.862 x 10-1 6.251 x 109 5.12 x 10-8 3.159 x 102 = 3,970 = 0.8862 = 6,251,000,000 = 0.0000000512 = 315.9

Factor-Label Method What does “Factor-Label” mean? Most important mathematical process in Chemistry! What does “Factor-Label” mean? Factors are the numbers Labels are the units i.e. 84.465 milliliter All measurements must have a number and a unit!

Factor-Label Method 1. a known beginning – GIVEN When using the factor-label method, problems consist of three parts: 1. a known beginning – GIVEN 2. a desired end – WANTED 3. a connecting path – CONVERSION FACTORS

Conversion Factors What are conversion factors? EQUALITIES For example: 12 in = 1 ft 1 mi = 5280 ft Conversion factors will be written as “tops & bottoms” For example: 12 in 1 ft 1 mi 5280 ft Conversion factors can be “flipped” depending on which unit needs to be canceled.

Commonly Used Metric Prefixes Meaning Factor Mega (M) 1 million times larger than the unit it precedes 106 kilo (k) 1000 times larger than the unit it precedes 103 1 (base unit) 10 0 deci (d) 10 times smaller than the unit it precedes 10-1 centi (c) 100 times smaller than the unit it precedes 10-2 milli (m) 1000 times smaller than the unit it precedes 10-3 micro (m) 1 million times smaller than the unit it precedes 10-6 nano (n) 1000 million times smaller than the unit it precedes 10-9 pico (p) 1 trillion times smaller than the unit it precedes 10-12

Practice Answer: 68 elephant legs 4 legs x Elephants tend to travel in herds, which consist of 10-20 elephants. If a herd of elephants contain 17 elephants, how many elephant legs are there? (HINT: 1 elephant=4 legs) <-usually 4 legs 1 elephant 17 elephants x Answer: 68 elephant legs

Examples 1 day x 24 hr 1 day x 60 min 1 hr x 60 sec 1 min Calculate the number of seconds in one day. Conversion Factors needed: 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds The conversion factors are written as: WANTED GIVEN 1 day x 24 hr 1 day x 60 min 1 hr x 60 sec 1 min

SI Unit Prefixes SI = Standard International Metric System (based on power of 10) Mega- (M) = 1,000,000 (1 x 106) Kilo- (k) = 1,000 (1 x 103) Hecto- (h) = 100 (1 x 102) Deca- (dc) = 10 (1 x 101) BASE = 1 (1 x 100) Deci- (d) = .1 (1 x 10-1) Centi- (c) = .01 (1 x 10-2) Milli- (m) = .001 (1 x 10-3) Micro- (μ) = .000001 (1 x 10-6) Nano- (n) = .000000001 (1 x 10-9) Pico- (p) = .000000000001 (1 x 10-12)

Converting Between Units How many grams are in 3.4 kg? 1 kg = 1x103 g Therefore: 3.4 kg x 1x103 g 1 kg = 3400 g

Practice 250 cm = ________ m 1.46 L = ________ mL 4.6 x 10-4 dg = _______ g 87.9 μm = ________ pm 6.2 x 106 Mg = ________ ng 2.50 1460 4.6 x 10-5 87900000 6.2 x 1021

SI Base Units Base Quantity Base Unit Symbol Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of Substance Mole mol Pressure Atmosphere atm Electric Current Ampere A Volume Liter L Energy Joule J

Temperature Conversions Two temperature systems used: oC (Celcius scale) K (Kelvin scale) Reference Tables: K = oC + 273 The Kelvin Scale can NEVER go below zero. Absolute zero (0 Kelvin) is when all particles stop moving.

Examples -273 0 K = _______ oC 1538 oC = _______ K 0 - 273 = -273 -273 1538 + 273 = 1811 1811 5778 - 273 = 5505 5505