 Quantity - number + unit UNITS MATTER!! Courtesy Christy Johannesson

 Quantitative- use numbers to describe  Qualitative- use description without numbers  4 feet  extra large  Hot  100ºF

 Quantitative  Quantitative - easy to check  Easy to agree upon, no personal bias  The measuring instrument limits how good the measurement is.

 Scientists use two word to describe how good the measurements are  Accuracy- how close the measurement is to the actual value  Precision- how well can the measurement be repeated

Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy (person)(instrument)

 Accuracy can be true of an individual measurement or the average of several  Precision requires several measurements before anything can be said about it  examples

Let’s use a golf anaolgy

Accurate? No Precise? Yes 10

Accurate?Yes Precise?Yes 12

Precise?No Accurate? Maybe? 13

Accurate?Yes Precise?We cant say! 18

 Accuracy  Accuracy - how close a measurement is to the accepted value  Precision  Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT Courtesy Christy Johannesson

 Converting into Scientific Notation: › Move decimal until there’s 1 digit to its left. Places moved = exponent. › Large # (>1)  positive exponent Small # (<1)  negative exponent › Only include sig figs. 65,000 kg  6.5 × 10 4 kg Courtesy Christy Johannesson

x In scientific notation, a number is separated into two parts. The first part is a number between 1 and 10. The second part is a power of ten.

Form:(# from 1 to 9.999) x 10 exponent 800= 8 x 10 x 10 = 8 x = x 10 x 10 x 10 = x = 1.4 / 10 / 10 / 10 = 1.4 x 10 -3

1. 2,400,000 g kg 3.7  km  10 4 mm Practice Problems 2.4  10 6 g 2.56  kg km 62,000 mm Courtesy Christy Johannesson

EXPEE

EE or EXP means “times 10 to the…” How to type out 6.02 x : 6EE y x x EE320y xy 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.

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

 Calculating with Scientific Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol = 6.7 × 10 2 g/mol Type on your calculator: Courtesy Christy Johannesson

How to enter this on a calculator: EE EXP = rounded to 6.7 x 10 2 ENTER Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52. Divide: (5.44 x 10 7 ) / (8.1 x 10 4 ) OR

 How do you make a measurement? › With most measuring devices, you should be able to estimate to one decimal place more than the smallest division on the device. The smallest division is a _____ of a centimeter, so you can guess to the _____________ (or ___ decimal places like 1.24). tenth hundredth 2

= 1.94 cm = 3.00 cm = 1.5 cm

123 1 = 2 = 3 =

 Indicate precision of a measurement.  Recording Sig. Figs. › Sig. figs. in a measurement include the known digits plus a final estimated digit 1.19 cm Courtesy Christy Johannesson Centimeters

 Significant Figures › All of the known digits plus the estimated digit are significant – they are not placeholders. › When we measured the volume of cylinder 1 on the last slide we got: 5.73 mL known estimated › This would mean 3 significant figures.

mL

 What is the smallest mark on a graduated cylinder that measures cm?  242 mL?  240 mL?  Here there’s a problem… does the zero count or not?

Significant Figure Rules 1. Every nonzero is significant g 4 sig figs 2. Zeros between nonzero digits are significant m4 sig figs 3. Zeros to left of nonzero are NOT significant g1 sig fig 4. Zeros to the right of a nonzero number if there is no decimal point are NOT significant 1200 g2 sig figs

 How many sig figs in the following measurements?  458 g  4085 g  4850 g  g  g  g

 Counting Sig Figs REVIEW › Count all numbers EXCEPT:  Leading zeros  Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

, Counting Sig. Figs. Examples , sig figs 3 sig figs 2 sig figs Courtesy Christy Johannesson

 g  4050 g  g  g  g  Next we learn the rules for calculations

 Look at the number behind the one you’re rounding.  If it is 0 to 4 don’t change it  If it is 5 to 9 make it one bigger  Round to four sig figs  to three sig figs  to two sig figs  to one sig fig

 Round the following to 3 significant figures › m › 527,254 g › mL › 959,600 m

 Write in Standard form  x x 10 3  Write in Scientific Notation  3) g4) m  Calculate~ Answers need to be in scientific notation!  5. (6.02 X ) X (9.54 x )  6. (5.23 X ) / (1.23 X )

 An answer can’t have more significance than the measurements upon which it is based.  YOUR ANSWER IS ONLY AS GOOD AS YOUR WORST MEASUREMENT!

 Calculating with Sig Figs › Multiply/Divide - 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

 Same rules for division Practice  4.5 /  4.5 x  x.043  / 1983  / 714

 Calculating with Sig Figs (con’t) › Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer mL mL 7.85 mL 224 g g 354 g  7.9 mL  350 g 3.75 mL mL 7.85 mL 224 g g 354 g Courtesy Christy Johannesson

For example First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place

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

 500 is only 1 significant figure  If it really has two, how can I write it?  A zero at the end only counts after the decimal place  Scientific notation  5.0 x 10 2  Now the zero counts.

x x x x 10 -3

 Calculating with Sig Figs (con’t) › Exact Numbers do not limit the # of sig figs in the answer.  Counting numbers: 12 students  Exact conversions: 1 m = 100 cm  “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson

 Addition Subtraction › Round your answer to the same number of decimal places as your least significant number. › Think of it as the leftmost uncertainty m +.12 m 420 m m540 m

 Multiplication and Division › Round answer to the same number of significant digits as the measurement with the least number of significant digits m × 12.0 m m m 2

2. Metric – Developed in France in Simple base units Interchangeable prefixes Decimal (base 10) system

PrefixSymbolMeaning kilo-k hecto-h deca-da deci-d centi-c milli-m 1 km = 1000 m 1 hm = 100 m 1 dam = 10 m 10 dm = 1 m 100 cm = 1 m 1000 mm = 1 m

QuantityUnitSymbol Lengthmeterm Masskilogramkg Timeseconds TemperaturekelvinK Amount of Substance molemol Electrical currentampereA Luminous intensitycandelacd

No Cussing! 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

kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) To convert from 1 prefix to another, just move the decimal to the left or right that many places! /10 1/100 1/1000 Metric Conversions

kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many centigrams (cg) are in 5dag? Just move the decimal ___ places to the ________! right cg

kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many kilometers (km) are in 12 meters m? Just move the decimal ___ places to the ________! left km

 calculated by multiplying L x W x H  Liter the volume of a cube 1 dm (10 cm) on a side  so 1 L = 10 cm x 10 cm x 10 cm  1 L = 1000 cm 3  1/1000 L = 1 cm 3  1 mL = 1 cm 3

Zumdahl, Zumdahl, DeCoste, World of Chemistry  2002, page 143

 1 kg = 2.5 lbs  1 g = 1 paper clip  1 mg = 10 grains of salt or 2 drops of water.

D M V ensity ass olume D = MVMV M = D x V V = MDMD

*at 0 o C and 1 atm pressure Substance Density (g / cm3) Air * Lithium 0.53 Ice Water 1.00 Aluminum 2.70 Iron 7.86 Lead 11.4 Gold 19.3

The more massive object (the gold cube) has the _________ density. Equal volumes… …but unequal masses aluminum gold GREATER Density = Mass Volume Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 71

Consider Equal Masses Equal masses… …but unequal volumes. The object with the larger volume (aluminum cube) has the smaller density. aluminum gold Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 71

Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK: M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,200 g Courtesy Christy Johannesson

 A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK: V = M D V = 25 g 0.87 g/mL V = 29 mL Courtesy Christy Johannesson

 Heat – type of energy transferred because of a difference in temperature. › Can’t be measured directly  Temperature – measure of the average kinetic energy of the particles in a sample of matter. › Determines the direction of heat transfer

2.12 Temperature What contains more heat? a glass of boiling water or an iceberg What does your body sense? temperature or heat

 Fahrenheit (  F) – zero based on equal mix of snow and ammonium chloride. 32  F = freezing point of water 212  F = boiling point of water Celsius (  C) – based on water 0  C = freezing point of water 100  C = boiling point of water

 Kelvin (K) - only temperature scales that is proportional to the speed of the particles. 0 K = all particle motion stops 273 K = freezing point of water 373 K = boiling point of water

 T(K) = t(  C) t(  C) = T(K) – 273 What is 25  C (room temp.) in kelvin? T(K) = 25  C = 298 K

 Accuracy is very important when making measurements in the lab.  In order to evaluate the accuracy of a measurement, you must be able to compare the experimental value to the accepted value.  Accepted value = the true or correct value based on reliable references  Experimental value = the measured value determined in the experiment in the lab.

 Indicates accuracy of a measurement expressed as a percentage Courtesy Christy Johannesson

 A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 % Courtesy Christy Johannesson