Measuring and Calculating in Chemistry

We use the Metric System for measurement in science Also called the SI system ( Systeme International d’Unites… from France) Everything is based on the power of 10 We use prefixes to determine the particular power of ten.

A physical quantity must include: Number + Unit + Unit

The Metric System from Industry Week, 1981 November 30

No Cursing! The following 4-Letter words are forbidden here: Inch Mile Foot Pint Yard Acre And we never swear the BIG F (use o C) Please keep it clean and Metric

SI System The International System of Units Derived Units Commonly Used in Chemistry Area and Volume: Derived Units Prefixes in the SI System Map of the world where red represents countries which do not use the metric system

SI System There are 7 base units in the SI system MeasurementBase unitAbbreviation Mass (m)Gramg Length (l)MeterM Time (t)Secondsec Temperature (T) Celsius oCoC Amt of substance Molesmol Electric CurrentAmpereA Luminous Intensity Candelacd VolumeLiterL

Converting within Metric System In order to convert from one unit to the other, you need to know the difference in magnitude between the two prefixes. Reference Table C

By using the info given on Table C, we can easily identify the difference in magnitude The exponents gives us the difference between each prefix Not listed on table C is the base unit, like grams for instance, which has no prefix. Base unit is always 10 0

General Rules… When moving up on table C, move decimal to the left. - As you move up you are going from small units to larger ones. For example if going from grams  kilograms, you will have less kilograms because they are so much larger. Therefore, we move the decimal to the left to get a smaller number. When moving down on table C, move decimal to the right. - As you move down, you are going from larger units to smaller ones. For example, going from grams  milligrams. You will have more milligrams than grams because milligrams are so much smaller. Therefore, we move the decimal to the right to get a larger number.

10 0 base unit g, L, mol Convert 25 grams to micrograms You are starting at grams and going to micrograms. Whenever you are traveling down the chart, you move decimal place to the right. To go from grams to micrograms is moving 6 down the chart. Therefore, the decimal point is going to move 6 places to the right. 25 grams  25,000,000 micrograms

10 0 base unit g, L, mol Convert 25 mg to kilograms If we are starting with milligrams and kilograms you know that you are traveling up on the chart. Whenever you are traveling up, you move the decimal point to the LEFT. In this case, you are moving up 6… So the decimal point is moved 6 places to the left. 25 mg  kg

10 0 base unit g, L, mol Convert 2.9x10 4 picograms to micrograms. 2.9x10 4  pg Traveling up on the chart, always moves the decimal point to the left. If you are starting at pg, and going to micrograms, that is moving 6 places up. Therefore, the decimal place moves 6 to the left pg  micrograms

Example… Convert 20.0 mm  m Answer: m

Example… How many km are there in 150m? Answer: km

Example… How many m are there in 20km? Answer: 20,000 m

Example… How many km are there in 100 cm? Answer: km

Mass vs. Weight Definition of Mass: - quantity of matter a substance possesses. Definition of Weight: - a force measuring the quantity of matter times the downward pull of gravity. Mass is always constant, weight can change from planet to planet. 1 kg (1000 g)

Volume Definition of Volume - amount of space an object takes up

Temperature Definition of Temperature - amount of average kinetic energy of particles in a sample - the higher the avg KE, the higher the temperature - 3 scales – only 2 used in science!

Temperature Scales Freezing Point of Water Boiling Point of water Main use and important info Scale Celsius0 o C100 o CSI unit, used globally, science Fahrenheit32 o F 212 o F USA only Kelvin273 K373 K Science

Celsius & Kelvin Temperature Scales Boiling point of water Freezing point of water Absolute zero Celsius 100 Celsius degrees 100 o C 0oC0oC -273 o C Kelvin 100 Kelvins 373 K 273 K 0 K

Temperature Scales Fahrenheit 212 o F 180 o F 32 o F Celcius 100 o C 0 o C Kelvin 373 K 100 K 273 K Boiling point of water Freezing point of water 1 kelvin degree = 1 degree Celcius Notice that 1 kelvin degree = 1 degree Celcius

Converting between temperatures Celsius  Kelvin (on ref tables!!!!!) K = o C + 273

Example…. Convert 37 o C  Kelvin K = o C = = 310 K

Example… Convert 298 K  Celsius C = K – 273 = 298 – 273 = 25 o C

Accuracy: how close you are to the standard or true value. If a rock is known to have a mass of 34.3 kg and you get 34.2 kg and 34.4 kg, you are accurate. This person is accurate because they were very close to their target, several times.

Precision: the reliability or reproducibility of measurements. In other words, how much several measurements agree. If the known mass of a rock is 34.3kg and you get 27.8kg, 27.9kg and 27.8kg, you are precise. This person is precise, because all of their darts landed very close to each other.

Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy (person)(instrument)

Error vs. Uncertainty Error refers to a disagreement between the measured value and the accepted valued. Uncertainty refers to the last digit of a measurement that is always estimated and reflects the precision of an instrument.

Uncertainty in Measurement When reading any measurement, the last digit is estimated and is therefore uncertain. Check for the smallest increment, and then estimate one place further.

When measuring the line above… 1st determine what the SMALLEST LINE is counting by… in this case they are counting by the tenths place. This means you have to estimate to the hundredths place The line above measures: 1.08cm

How to Read a Thermometer (Celcius) o C o C o C o C

Reading a Meniscus line of sight too high reading too low reading too high line of sight too low proper line of sight reading correct graduated cylinder 10 mL

20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL

Percent Error Calculations % Error = Measured Value – Accepted Value Accepted Value x 100 %

Example.. % Error = Measured Value – Accepted Value Accepted Value x 100 % In a lab experiment, you find the melting point of Cesium to 30.1oC. The accepted value is 28.4oC. What is your percent error? % Error = 30.1 o C – 28.4 o C 28.4 o C X 100% % Error = 5.99% (3 sig figs)

Significant Figures… -Sig Figs are used to indicate the exactness or precision of a measurement The more increments on a device, the more precise it is, which means you will have more significant figures.

Sig Figs Sig Figs in a measurement include all those digits known with certainty and the uncertain or estimated digit. You must have units! Sig Figs only apply to things we can measure.

Sig Fig Rules To determine how many sig figs a measurement contains, follow the rules: Count all numbers except… Leading zeroes m Trailing zeroes without a decimal point m 2 sig figs

, Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs Courtesy Christy Johannesson

Calculating with Sig Figs Addition and Subtraction… The number that has the lowest decimal value determines the place of the last sig fig in the answer.

Significant Figures Adding/ Subtracting Examples…. 224 g g 354 g  350 g 224 g g 354 g Courtesy Christy Johannesson mL mL 7.85 mL 7.9mL

Significant Figures Multiplication and Division - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF Courtesy Christy Johannesson

Significant Figures 1. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g g g 4 SF2 SF  2.4 g/mL 2 SF Courtesy Christy Johannesson

Ex Because we are adding, we look at the number with the least amount of decimal places to tell us where to round to… CALCULATOR SHOWS: ROUNDED ANSWER: 268.1

Ex: – CALCULATOR SHOWS: ROUNDED ANSWER: decimal places 3 decimal places

Ex. 45 x 3.00 CALCULATOR SHOWS: 135 ROUNDED ANSWER sig figs 3 sig figs

Ex / Calculator shows: Rounded Answer: sig figs5 sig figs

Scientific Notation… Scientific notation is useful in handling very small or very large numbers. Expressing a number as a multiple of a power of 10.

Scientific Notation… When a number is expressed in scientific notation it has three parts First Sig Fig Decimal Point Rest of Sig Figs X 10 (# of places back to the ones place) For large numbers: exponent is greater than 1 For small numbers: exponent is less than 1 (negative)

A fossil is 4,600,000,000 years old… How can we express this in scientific notation? First sig fig is 4, followed by decimal point and then the other sig fig, 6. After the four, there are 9 places back to the ones place… that means the exponent is 9. Final Answer: 4.6x10 9

Change to scientific notation. 12,340 = = = 1,000,000,000 = x x 10 –1 8 x 10 –3 1 x 10 9

Expanding numbers To convert from scientific notation back to standard form… Write all the sig figs, then exponent will tell you how many places to move the decimal point. When exponent is positive: move RIGHT When exponent is negative: move LEFT

Scientific Notation 2,400,000  g kg 7  km 6.2  10 4 mm Practice Problems 2.4  10 6  g 2.56  kg km 62,000 mm Courtesy Christy Johannesson

Using the Exponent Key on a Calculator EXPEE

EE or EXP means “times 10 to the…” How to type out 6.02 x : 6EE y x x EE320y x 32 x Don’t do it like this… …or like this… …or like this: How to type out 6.02 x : 6EE WRONG! TOO MUCH WORK.

Also, know when to hit your (–) sign… …before the number, …after the number, …or either one.

Example: 1.2 x x But instead is written… = 1. 2EE Type this calculation in like this: This is NOT written…4.3 – –09 Calculator gives… E–09 or… 4.3 x 10 –9 4.3 E –9or

= x = x 10 3 or = x report -6.5 x (2 sig. figs.) report 5.35 x 10 3 (3 sig. figs.) report 5.84 x (3 sig. figs.) = x report 2.9 x (2 sig. figs.) = x report -3.1 x (2 sig. figs.)

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot = 12 inches

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1

Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1 12 inches 1 foot = 1

Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors”

Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors” 3 feet 3 feet 12 inches 12 inches 1 foot 1 foot = 36 inches ( ( ) ) ( ( ) )

How many cm are in 1.32 meters? applicable conversion factors: equality: or X cm = 1.32 m= 1 m = 100 cm ______1 m 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 m 100 cm () ______ 1 m 100 cm 132 cm (or 0.01 m = 1 cm)

How many meters is 8.72 cm? applicable conversion factors: equality: or X m = 8.72 cm= 1 m = 100 cm ______1 m 100 cm Again, the units must cancel. ______ 1 m 100 cm () ______ m 1 m 100 cm

How many feet is inches? applicable conversion factors: equality: or X ft = in= 1 ft = 12 in ______1 ft 12 in Again, the units must cancel. () ____ 3.28 ft 1 ft 12 in ______ 1 ft 12 in

How many kilometers is 15,000 decimeters? X km = 15,000 dm= 1.5 km () ____ 1,000 m 1 km 10 dm 1 m () ______

How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ X s = 4.38 d 378,432 s3.78 x 10 5 s If we are accounting for significant figures, we would change this to…