Chapter 2 Measurements and Calculations

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

Writing Numbersin 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

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.

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

Some Fundamental SI Units

Prefixes • All units in the metric system utilize the same prefixes

Length

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

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)

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:

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.

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

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

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. example: In a series of calculations, carry the extra digits to the final result, then round off. example: • When rounding off use only the first number to the right of the last significant figure. example:

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

Multiplication/Division withSignificant 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 =

Adding/SubtractingNumbers with Significant Figures • Result is limited by the number with the smallest number of significant decimal places example:

Problem Solvingand 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

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.

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!

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

Temperature Scales

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 ScalesToC + 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.

Using Density in Calculations

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.

Chapter 2 Measurements and Calculations