Measurements and Calculations

World of Chemistry

• Quantitative observations like measurements must have units

• Measurements can be very small or very large• Example: – Distance from Earth to Sun = 93,000,000 miles– Average size of eukaryotic cell: 0.0000062 meters

• For very large and small measurements, use scientific notation

Numbers and measurements

• In writing in scientific notation, you will1) Make the number between 1 and 10 (move the

decimal)2) Determine the power of 10 - if the regular number is >1, move decimal to the right, positive exponent- if the regular number is <1, move decimal to left, negative exponent

• Example1) 93,000,000 miles = 9.3 x 106 miles2) 0.0000062 metes = 6.2 x 10-6 meters

Put the following numbers into standard scientific notation:

1) 238,000 =2) 1,500,000 = 3) 24.7 =4) 0.135 = 5) 0.0024 =

Units

• All measurements must have units• USA – English system, most international

countries – metric system• Science community – International System (SI) • when it comes to scale, use prefixes

SI Units for chemistryQuantity Unit Abbreviation Symbol

Mass Kilogram kg m

Time Second s t

Temperature Kelvin K T

Amount of substance

Mole mol n

Although not included, volume is measured in liters (L) and represented by V.

Unit PrefixesPrefix Symbol Power of 10

Mega M 106

kilo k 103

centi c 10-2

milli m 10-3

micro υ 10-6

nano n 10-9

Unit prefixes

Prefixes can be used to replace powers of 10 in scientific notationExamples:– 5000 m = 5 x 103 m = 5 km– 0.00315 L = 3.15 x 10-3 L = 3.15mL– 0.00000000465 s = 4.65 x 10-9 s = 4.65 ns – 33000 m = 33 km– 0.00000056 L = 0.56υL (microliters)

Practice Problems

Convert the following1) 382 g = _____kg2) 0.0056g = _____mg3) 490 mL = _____L4) 6,560,000 m = _____Mm (Megameters)5) 99 Mg = ____________g6) 8.8υg = ______g

Measurement Uncertainty

• Measuring anything (especially mass, volume, length):

certain and uncertain numbers

meter stick

Uncertainty in measurements4.75 cm

Measurement Uncertainty

• Determine the “certain” numbers of the measurement• Meter stick broken down into centimeters and millimeters

4.7 cm• Determine “uncertain” numbers (estimate)– value between millimeters– 4.75 cm

• Every measuring device (ruler, graduated cylinder, balance) has some degree of uncertainty…except for digital measuring devices

Significant Figures

What counts as sig fig?1) All regular integers (1457 = 4

sig figs)2) Trapped zeros (12059 = 5 sig

figs)3) Trailing zeros (only if there is a

decimal involved)

100. 3 sig figs

78.0 = 3 sig figs

100 = 1 sig figWhat does not count as sig fig?Leading zeros (0.00025 = 2 sig figs)

In a measurement, specific numbers are considered significant figures

Practice ProblemsDetermine the number of sig figs:

1) 0.000304g2) 1.270 x 102m.3) 125g 4) 10 A5) 0.09020L6) 6.5 x 103g7) 6.5mg8) 9.02 g9) 10.0 mL10) 21.40 s

Calculating using Sig Figs1) Multiplication/Division: # of sig figs in answer is the same as the measurement with smallest # of sig figs

Example: 4.56 x 1.4 = 6.384 = 6.4

3 sig figs

2 sig figs

Round off 2 sig figs

Calculating using Sig FigsExample: 8.315 ÷ 298 = 0.0279027 =

0.0279

4 sig figs

3 sig figs

Round off

3 sig figs

Calculating using Sig FigsExamples5.4 / 3 =2.5 x 5.230 =(8.62 x 103) / (33) =(0.54 / 6.4) x 100.00 =

Calculating using Sig Figs2) Addition/subtraction: sig figs in answer determined by measurement with smallest number of decimal places

Example: 12.11 + 18.0 + 1.013 = 31.123 31.1

1 decimal place

1 decimal place

Calculating using Sig Figs

Example: 0.6875 – 0.1 = 0.5875 0.6

1 decimal place

1 decimal place

Calculations Examples• Multiplication and division – count sig figs• Addition and subtraction – count decimal places1) 8.90 + 63.45 =

2) 103.4 – 34.94 =

3) (1945)(17.1) =

4) 32.789 / 270 =

5) (13.3 x 105)(45.45) =

Dimensional Analysis• Dimensional analysis is used to convert units

Ex: g mol g L • Use conversion factors as bridges• Examples of conversion factors include..

1 lb = 453g1 in = 2.54cm1 mol carbon = 12.01g

• Use railroad method to cancel out units

Dimensional Analysis

Convert the following

12 ft into cm

3.2 L into ounces

32.0 ft in km

5.7 Temperature• Temperature is the measure of heat • Three scales:– Celsius (°C)– Fahrenheit (°F)– Kelvin (K)

Celsius• Anders Celsius• Original 1742 “Centigrade” scale– 100°C water boils– 0°C water freezes

• 100 degree scale

Fahrenheit• Daniel Gabriel Fahrenheit• Scale based on three fixed points:– “Brine” mixture: water, ice, ammonium chloride =

0°F– Water and ice mixture = 32°F– Human body = 96°F

• 180 degree scale– 32°F water freezes– 212°F water boils

Kelvin• William Thomson (Lord Kelvin)• SI unit• 273 K water freezes• 373 K water boils• 100 degree scale• Absolute zero = 0 K– all molecular motion ceases– has never been reached

Temperature Conversion Equations°C to °F T°F = (1.8)T°C + 32

°F to °C T°C = (T°F - 32) x (0.56)

K to °C TK =T°C + 273

5.8 Density• Physical property, specific for a pure substance• Ratio of mass and volume• Density = mass

volume • Volume units– solids cm3

– liquid mL– gas L

World of Chemistry, pg. 143

Determining DensityExample:Mass = 55.64 gVolume = 10.0 mL

Density = 55.64g = 5.56 g/mL 10.0mL