 # Measurements and Calculations

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Measurements and Calculations
World of Chemistry

Numbers and measurements
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: meters For very large and small measurements, use scientific notation

In writing in scientific notation, you will
Make the number between 1 and 10 (move the decimal) 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 Example 93,000,000 miles = 9.3 x 106 miles metes = 6.2 x 10-6 meters

Put the following numbers into standard scientific notation:
238,000 = 1,500,000 = 24.7 = 0.135 = =

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 chemistry Quantity 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 Prefixes Prefix 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 mega – million times, k = thousand times, c – hundredth, m – thousandth, micro – millionth, nano – billionth size

Unit prefixes Prefixes can be used to replace powers of 10 in scientific notation Examples: 5000 m = 5 x 103 m = 5 km L = 3.15 x 10-3 L = 3.15mL s = 4.65 x 10-9 s = 4.65 ns 33000 m = 33 km L = 0.56υL (microliters)

Practice Problems Convert the following 382 g = _____kg
0.0056g = _____mg 490 mL = _____L 6,560,000 m = _____Mm (Megameters) 99 Mg = ____________g 8.8υg = ______g 1) ) ) ) ) 9,900,000 6)

Measurement Uncertainty
Measuring anything (especially mass, volume, length): certain and uncertain numbers meter stick

Uncertainty in measurements
4.75 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 In a measurement, specific numbers are considered significant figures What counts as sig fig? What does not count as sig fig? All regular integers (1457 = 4 sig figs) Leading zeros ( = 2 sig figs) Trapped zeros (12059 = 5 sig figs) Trailing zeros (only if there is a decimal involved) sig figs 78.0 = 3 sig figs 100 = 1 sig fig

Practice Problems Determine the number of sig figs: 0.000304g
1.270 x 102m. 125g 10 A L 6.5 x 103g 6.5mg 9.02 g 10.0 mL 21.40 s

Calculating using Sig Figs
1) Multiplication/Division: # of sig figs in answer is the same as the measurement with smallest # of sig figs Example: 4.56 x 1.4 = = 6.4 3 sig figs 2 sig figs Round off 2 sig figs

Calculating using Sig Figs
Example: ÷ 298 = = 4 sig figs 3 sig figs Round off 3 sig figs

Calculating using Sig Figs
Examples 5.4 / 3 = 2.5 x = (8.62 x 103) / (33) = (0.54 / 6.4) x =

Calculating using Sig Figs
2) Addition/subtraction: sig figs in answer determined by measurement with smallest number of decimal places Example: =  31.1 1 decimal place 1 decimal place

Calculating using Sig Figs
Example: – 0.1 =  0.6 1 decimal place 1 decimal place

Calculations Examples
Multiplication and division – count sig figs Addition and subtraction – count decimal places = 103.4 – = (1945)(17.1) = / 270 = (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 = 453g 1 in = 2.54cm 1 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

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 Density Example: Mass = 55.64 g Volume = 10.0 mL
Density = 55.64g = g/mL 10.0mL