Chapter 2 Measurements and Calculations

Scientific Notation Technique used to express very large or very small numbers: for example, 2,009,345,234 or 0.00000045723 Expressed as a product of a number between 1 and 10 and a power of 10 3

Writing Numbers in Scientific Notation Locate the decimal point. Count the number of places the decimal point must be moved to obtain a number between 1 and 10. Multiply the new number by 10n where n is the number of places you moved the decimal point. Determine the sign on the exponent n. If the decimal point was moved left, n is + If the decimal point was moved right, n is – If the decimal point was not moved, n is 0 4

Write the following numbers in scientific notation: 2,009,345,234 B. 0.00000045723

Converting from Scientific Notation to Standard Form Determine the sign of n in 10n If n is + the decimal point will move to the right. If n is – the decimal point will move to the left. Determine the value of the exponent of 10. Tells the number of places to move the decimal point Move the decimal point and rewrite the number. 5

Convert from Scientific Notation to Standard Form: 2.0684 x 105 3.28409 x 10-4

Related Units in the Metric System All units in the metric system are related to the fundamental unit by a power of 10. A power of 10 is indicated by a prefix. Prefixes are always the same, regardless of the fundamental unit. Examples: kilogram = 1000 grams kilometer = 1000 meters 6

Some Fundamental SI Units

Prefixes All units in the metric system utilize the same prefixes

Length 7

Volume Measure of the amount of 3-D space occupied by a substance SI unit = cubic meter (m3) Commonly measure solid volume in cubic centimeters (cm3) 1 mL = 1 cm3 8

Mass Measure of the amount of matter present in an object SI unit = kilogram (kg) 1 kg = 2.205 pounds, 1 lb = 453.59 g 68 kg = 150 lbs Commonly measure mass in grams (g) or milligrams (mg) 9

Uncertainty in Measured Numbers A measurement always has some amount of uncertainty. To understand how reliable a measurement is, we must understand the limitations of the measurement. Example: 10

Reporting Measurements Significant figures: system used by scientists to indicate the uncertainty of a single measurement Last digit written in a measurement is the number that is considered uncertain Unless stated otherwise, uncertainty in the last digit is ±1. 11

Rules for Counting Significant Figures Nonzero integers are always significant. example: 4.675 = 4 sig figs Zeros Leading zeros never count as significant figures. example: 0.000748 = 3 sig figs Captive zeros are always significant. example: 2.0087 = 5 sig figs Trailing zeros are significant if the number has a decimal point. example: 6.980 = 4 sig figs 12

Exact Numbers Exact numbers: numbers known with certainty Counting numbers number of sides on a square Defined numbers 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm 1 minute = 60 seconds Have unlimited number of significant figures 14

Rules for Rounding Off If the digit to be removed: is less than 5, the preceding digit stays the same. example: is equal to or greater than 5, the preceding digit is increased by 1. In a series of calculations, carry the extra digits to the final result, then round off. When rounding off use only the first number to the right of the last significant figure. 13

Round these numbers to four significant figures: 157.387 443,678 80, 332 7.8097

Multiplication/Division with Significant Figures Result must have the same number of significant figures as the measurement with the smallest number of significant figures: example: 3.5 x 3.5609 = example: 4.98/11.76 = 16

Adding/Subtracting Numbers with Significant Figures Result is limited by the number with the smallest number of significant decimal places example: 17

Problem Solving and Dimensional Analysis Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another. Conversion factors are generated from equivalence statements. e.g. 1 mi = 5,280. ft can give: 1 mi/5280. ft or 5280. ft/1 mi 18

Converting One Unit to Another Find the relationship(s) between starting and goal units. Write equivalence statement for each relationship. Given quantity x unit factor = desired quantity Write a conversion factor for each equivalence statement. Arrange the conversion factor(s) to cancel with starting unit and result in goal unit. 20

Converting One Unit to Another (cont.) Check that units cancel properly. Multiply and divide the numbers to give the answer with the proper unit. Check significant figures. Check that your answer makes sense! 21

Convert the following: (Use Table 2.7) 180 lbs to kg 12.3 mi to in.

Temperature Scales 22

Some facts concerning the temperature scales: The size of each degree is the same for the Celsius and Kelvin scales. The Fahrenheit degree is smaller than the Celsius and Kelvin unit. F – 180 degrees between freezing and boiling point of water C – 100 degrees between freezing and boiling point of water All three scales have different zero points.

Converting between Kelvin and Celsius Scales ToC + 273 = K Celsius to Kelvin: add 273 to C temperature example: Convert 46o C to K Kelvin to Celsius: subtract 273 from K temperature example: Convert 4 K to C

Converting from Celsius to Fahrenheit Requires two adjustments: 1. Different size units; 180 F degrees = 100 C degrees 2. Different zero points ToF = 1.80(ToC) + 32 Convert 30oC to oF

Converting from Fahrenheit to Celsius ToC = (ToF – 32)/1.80 Convert 102oF to oC

Density Volume of a solid can be determined by water displacement. 23

Using Density in Calculations 24

Using Density in Calculations Calculate the density of an object which weighs 35.7 g and occupies a volume of 21.5 mL. Calculate the mass of a piece of copper which occupies 2.86 cm3. (density = 8.96 g/cm3) Calculate the volume of an object with a density of 4.78 g/mL and mass of 20.6 grams.