Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed. by Steven S. Zumdahl, Donald J. DeCoste University of Illinois
Chapter 2 Measurements and Calculations
Measurement Quantitative observation Comparison based on an accepted scale e.g. Meter stick Has 2 parts number and unit Number tells comparison Unit tells scale
Scientific Notation Technique used to express very large or very small numbers Based on powers of 10 To compare numbers written in scientific notation First compare exponents of 10 Then compare numbers
Writing Numbers in Scientific Notation 1 Locate the decimal point 2 Move the decimal point to the right of the nonzero digit in the largest place The new number is now between 1 and 10 3 Multiply the new number by 10 n Where n is the number of places you moved the decimal point 4 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
Writing Numbers in Standard Form 1 Determine the sign of n of 10 n If n is + the decimal point will move to the right If n is the decimal point will move to the left 2 Determine the value of the exponent of 10 Tells the number of places to move the decimal point 3 Move the decimal point and rewrite the number
Related Units in the Metric System All units in the metric system are related to the fundamental unit by a power of 10 Power of 10 is indicated by a prefix Prefixes are always the same, regardless of the fundamental unit
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 (m 3 ) Commonly measure solid volume in cubic centimeters (cm 3 ) 1 ml = 1 cm 3
Mass Measure of the amount of matter present in an object SI unit = kilogram (kg) Commonly measure mass in grams (g) or milligrams (mg) 1 kg = 2.2046 pounds, 1 lb = 453.59 g
Uncertainty in Measured Numbers A measurement always has some amount of uncertainty Uncertainty comes from limitations of the techniques used for comparison To understand how reliable a measurement is, we need to understand the limitations of the measurement
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 Zeros Leading zeros never count as significant figures Captive zeros are always significant Trailing zeros are significant if the number has a decimal point Exact numbers have an 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 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 Don t forget to add place-holding zeros if necessary to keep value the same!!
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
Calculations with Significant Figures Calculators/computers do not know about significant figures!!! Exact numbers do not affect the number of significant figures in an answer Answers to calculations must be rounded to the proper number of significant figures Round at the end of a calculation
Multiplication/Division with Significant Figures Result has the same number of significant figures as the measurement with the smallest number of significant figures Count the number of significant figures in each measurement
Multiplication/Division with Significant Figures (cont.) Then round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures 4.5 cm x 0.200 cm = 0.90 cm 2 2 sig figs 3 sig figs 2 sig figs
Adding/Subtracting Numbers with Significant Figures Result is limited by the number with the smallest number of significant decimal places Find last significant figure in each measurement Find which one is left-most
Adding/Subtracting Numbers with Significant Figures (cont.) Then round answer to the same decimal place 450 ml + 27.5 ml = 480 ml precise to 10 s place precise to 0.1 s place precise to 10 s place
Problem Solving and Dimensional Analysis Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another Conversion factor = relationship between two units May be exact or measured Both parts of the conversion factor should have the same number of significant figures
Problem Solving and Dimensional Analysis (cont.) Conversion factors generated from equivalence statements e.g. 1 inch = 2.54 cm can give or 1in 2.54cm 2.54cm 1in
Problem Solving and Dimensional Analysis (cont.) Arrange conversion factors so starting unit cancels Arrange conversion factor so starting unit is on the bottom of the conversion factor May string conversion factors
Converting One Unit to Another Find the relationship(s) between starting and goal units. Write equivalence statement for each relationship. 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!
Temperature Scales
Density Density = property of matter representing the mass per unit volume Density = Mass Volume Volume of a solid can be determined by water displacement
Density (cont.)
Using Density in Calculations Density = Volume = Mass Volume Mass Density Mass = Density Volume