Chapter-2: Analyzing Data (measurements) Dr. Chirie Sumanasekera CHEMISTRY Lecture_3 Dr. Chirie Sumanasekera 8/28/2018 TOPICS covered today: Metric (SI) BASE units and symbols Important Metric Definitions Why use Metric (SI)? TABLE of Metric Prefixes Metric Conversions Math review: Exponents

Metric (SI) System common BASE units and symbols The English System (Imperial System) of measurements is not very standardized and is complicated to use. The Metric (SI) Units System is simple and systematic, with a single Base Unit for each physical quantity: Physical quantity Metric Base Unit (Symbol) Volume: liter (L) Mass: gram (g) Amount of Substance: mole (mol) Concentration molar (M) Length: meter (m) Time: second (s) Temperature: Kelvin (K)

Important Metric Definitions: 1 meter = 1/10,000,000 of the distance from the north pole to the equator 1 kilogram = mass of a cube of pure water measuring 10 cm on each side = 0.1 m x 0.1m x 0.1 m = 0.1 m3 pure water 1 liter = volume of 1 kg of pure water at 4◦C = 0.1 m3 pure water

Why use Metric (SI)? The Metric system is based on a decimal system - easy to use Can make a vast range of precise measurements It uses prefixes to reduce or enlarge the Base Unit (except for Temperature) Prefixes are added before the base unit to indicate the increase or decrease of the Base unit value: Prefix: Meaning: Kilo = increases the Base Unit by a factor of 1000 deci = increases the Base Unit by a factor of 10 centi = decreases the Base Unit by a factor of 100 milli = decreases the Base Unit by a factor of 1000 micro = decreases the Base Unit by a factor of 1000,000 Note: Temperature scales do NOT use prefixes! ex: No such thing as mK (millikelvin) or KK (kilo Kelvin). Kelvin is Kelvin!

TABLE of Metric Prefixes: µ TABLE of Metric Prefixes: , mole Or here’s another ways to look at the same table without the exponents

TABLE of Metric Prefixes: d c m µ n p = Increase by 1012 = Increase by 109 = Increase by 106 = Increase by 103 = 1 = Decrease by 101 = Decrease by 102 = Decrease by 103 = Decrease by 106 = Decrease by 109 = Decrease by 1012 T G M K PREFIX SYMBOL MULTIPLE tera - giga - mega - kilo - deci - centi - milli - micro - nano - pico - Base Unit: gram, liter, meter, mole, molar Smaller Larger Find change in magnitude Size between prefixes: 1023 deci meters to km = 2.3 milligrams and gigagrams = 50 picomoles and micromoles = Small to large Large to small Small to Large

PREFIX SYMBOL MULTIPLE Metric Conversions d c m µ n p = Increase by 1012 = Increase by 109 = Increase by 106 = Increase by 103 = 1 = Decrease by 101 = Decrease by 102 = Decrease by 103 = Decrease by 106 = Decrease by 109 = Decrease by 1012 T G M K PREFIX SYMBOL MULTIPLE tera - giga - mega - kilo - deci - centi - milli - micro - nano - pico - Base Unit: gram, liter, meter, mole, molar 1012 104 106 Find change in magnitude Size between prefixes: add the exponents: 1023 deci meters to km = 2.3 milligrams and gigagrams = 50 picomoles and micromoles = 106 1012 104

Large Small X Find change in magnitude Size between prefixes: Divide Large Small X Multiply Find change in magnitude Size between prefixes: add the exponents: 1023 deci meters to km = 2.3 milligrams and gigagrams = 50 picomoles and micromoles = 106 1012 104 Small to large Large to small Small to Large

Math Review: 1. EXPONENTS Exponent: a number written as a superscript that indicates a power Exponent Base Power Meaning Actual value 103 10 3 10 x 10 x 10 1000 102 2 10 x 10 100 101 1 10-1 -1 1/10 0.1 10-2 -2 1/10x10 0.01 10-3 -3 1/10 x 10 x 10 0.001 1. Dividing exponents: when the base is the same we subtract : Ex-1: 103 = 103 – (101) = 10 (3-1) = 102 101 Ex-2: 103 = 103 –(10-4) = 10 (3+ 4) = 107 10-4

Math Review: 1. EXPONENTS continued 3. Multiplying exponents: when the base is the same we add the powers : Ex-1: 103 x 101 = 10 (3+1) = 104 Ex-2: 103 x 10-4 = 10 [3+(-4)] = 10 [3-4] = 10 -1 4. Adding exponents: when the base is the same we subtract : Ex-1: 103 + 101 = 1000 +10 = 1010 Ex-2: 103 + 10-4 = 1000 + 1/10000 = 1000 + 0.0001 = 1000.00001 5. subtracting exponents: when the base is the same we subtract : Ex-1: 103 - 101 = 1000 -10 = 990 Ex-2: 103 - 10-4 = 1000 + 1/10000 = 1000 - 0.0001 = 999.9999

Scientific Notation Scientists have to often work with extremely large or extremely small numbers EX: Astrophysicists calculating the distance from earth to the sun in meters =14,960,000,000,0000 m Or the height in km of a person who is 5 feet 9 inches tall = In cm = 175.3 cm In m = In km = 1.753 m 0.001753 km Can we write the person’s height in km and the distance from the earth to the Sun in meters in a easier way? Yes We CAN, using Scientific Notation!

1.851 x 10-8 m Exponent Coefficient Scientific Notation Scientific notation = all numbers are expressed as a coefficient between 1 and 10 multiplied by 10 raised to a power Coefficient Exponent 1.851 x 10-8 m Ex: Write the following in scientific notation: 14,960,000,000,0000 m = 175.3 cm = 1.753 m = 0.001753km = 1.496 x 1014 m 1.753 x 102 cm 1.753 x 101 m 1.753 x 10-3 m

Math Review: 1. Equation Dynamics Consider the density equation: D= density m = mass v = volume v = m D m = D x v D = m v How can you predict what happens to one value in an equation when another is changed? This analyzing the dynamics of values in any given equation.

Math Review: 1. Equation Dynamics D = m v If M= 4 g and V=2 ml, Find Density: D = 4 g = 2 g/ml 2 ml EX-1: If the mass increases to 8 g and volume remains constant, D will increase because the numerator is larger than before: D = 8 g = 4 g/ml (this number is twice as large as 2g/ml) 2 ml EX-2: If the mass remains constant but V increases to 3ml then the density will decrease because the denominator is larger than before: D = 2 g = 0.6666 g/ml (this number is much smaller than 2g/ml) 3 ml

Math Review: Manipulation equations D = m v Original : If M= 4 g and V=2 ml, Find Density: D = 4 g = 2 g/ml 2 ml EX-3: If the density remains unchanged, but the mass increased to 8g, what is the volume? You can guess that since the mass doubled, the volume doubled as well. (this is the question I asked you in the Measurements lab-2) 2 g/ml = 8 g V 2 g/ml x V = 8 g x V V 2 g x V = 8 g ml 2 x V = 8 ml Multiply both sides of the equation by ml: ml x 2 x V = 8 ml ml 2V = 8 ml v = 8ml = 4ml 2 So the volume also increased by 2-fold!

Math Review: Dimensional analysis Solve these: Number of seconds are in 2.0 years 2. Convert 4.5 mg/ml into Kg/L

Dimensional Analysis Dimensional Analysis (Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one 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.

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.) (5) What is the density of mercury (13.6 g/cm3) in units of kg/m3

(6) How many atoms of hydrogen can be found in 45 g of ammonia, NH3 (6) 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.