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Chapter 2: Measurements in Chemistry •Chemistry is an observation science •Observations frequently require taking measurements •Measurements have some degree of uncertainty •All measured numbers have 2 parts: Scientists use the Metric System: Units of Measurement Measurement Length Volume Mass Temperature Time Metric Base Unit Metric Prefixes: Prefix Symbol Numerical Value Sci Notation Equality Prefixes that Increase the Size of the Unit: Giga G 1,000,000,000 1 x 109 mega M 1,000,000 1 x 106 1 Mg = 106 g or 1 g = 10-6 Mg kilo 1,000 1 x 103 1 km = 1000 m or 1 m = 10-3 km 1 dL = 0.1 L or 1 L = 10 dL k Prefixes that Decrease the Size of the Unit: deci d 0.1 1 x 10-1 centi c 0.01 1 x 10-2 1 cm = 0.01 m or 1 m = 100 cm milli m 0.001 1 x 10-3 1 ms = 10-3 s or 1 s = 1000 ms micro m 0.000001 1 x 10-6 1 mg = 10-6 g or 1 g = 106 mg nano n 0.000000001 1 x 10-9 What is the relationship between volume and length? 1 Liter = the space occupied by a 10 cm cube Exact and Inexact Numbers? Exact number = number whose value has no uncertainty • defined numbers • counted numbers Inexact number = a number with a degree of uncertainty • measured numbers Uncertainty in Measurement Significant figures = all digits that are known with certainty + 1 estimated digit Precision = the degree to which a measurement is reproducible The precision of a measurement is determined by the instrument used: • Digital equipment – record all digits • Analog equipment – incremental (closest) marks Guidelines for Determining Significant Figures in Measured Numbers Significant Figures Digits known with certainty + one estimated digit Nonzero Digits 1, 2, 3 … 9 are always significant Leading Zeros Zeros at the beginning of a number are never significant Zero May or may not be significant Confined Zeros Zeros between non-zero digits are always significant Trailing Zeros Are significant only if the decimal point is shown How many Significant Figures? 562.00 0.033 45,100 348 Calculations & Significant Figures: The answer to a calculation involving measured numbers cannot have greater significance than any of the measurements! Addition and Subtraction: The answer has the same precision as the least precise measurement. Example: A graduted cylinder contained 25.5 ml of water. A glass marble was added to the cylinder and the volume reading increased to 33.2 ml. What was the volume of the marble? Multiplication and Division: The answer has the same number of significant figures as the measurement with the fewest significant figures. Example: The marble (from the previous example) has a mass of 22.0186 grams. What is it’s density? Rules for rounding: •If the digit to be dropped is less than 5, simply drop it •If the digit to be dropped is 5 or greater, round up Round to 2 significant figures: 258.59 0.06617 182,540 Perform the following calculations involving measured numbers, express your answer to the proper number of significant figures: a) 6.731 x 0.0021 = b) 8.4 1.8 + 5.2 c) 120 0.0045 = (write the answer in scientific notation) Scientific Notation: a convenient way of expressing large or small numbers 1.23 x 10-34 A number in Scientific Notation has 2 parts: coefficient - a number between 1 and 10 it includes only significant figures exponential term – a number expressed as x 10n n = an integer (positive or negative) Convert to scientific notation: 47,000 0.00211 Convert to standard notation: 5.442 x 103 8.25 x 10-5 Scientific Notation & Calculators: -enter the coefficient as you would for a regular number -press EXP or EE -enter the exponent Examples: a. (9.41 x 1012) x (2.7722 x 10-5) = b. (2.5 x 104) (6.8 x 106) = Conversion Factors—Metric System: What does it mean? 1 cm = 0.01 meter or 100 cm = 1 meter Write the equality as a ratio: A ratio can be used as a conversion factor. Consider a meterstick: 1 meter = 100 cm How many cm are equal to 2.5 meters? 1 meter = 1000 mm How many meters are equal to 650 mm? Unit Conversion within the Metric System: •Start with the given measured number •What units are to be changed? •Find the relationship between units (equality) •Write as a ratio with the “old” unit in the denominator & the “new” unit in the numerator •Cancel the units •Multiply/divide the numbers •Record your answer to the proper number of sig. figs. a. Convert 1.5x105 milliseconds (ms) to seconds b. Convert 35 microliters (mL) to Liters c. Convert 2130 decigrams (dg) to kilograms (kg) Unit Conversion within the English System: a. Convert 349 inches to feet English-to-Metric & Metric-to-English Conversions: Example: Convert 128 lb to kiligrams Example: Convert 36.5 inches to cm Multistep conversions: •Start with the given measured number •What units are to be changed? (make a unit map) •Find the relationship between units for each step •Write each as a ratio with the “old” unit in the denominator & the “new” unit in the numerator •Write the conversion as a series of multiplication steps. •Cancel the units • Multiply/divide the numbers •Record your answer to the proper number of sig. figs. Example: convert 9.85 Liters to gallons (given that 1 Liter = 1.057 qt; 1 gallon = 4 qt.) Example: Convert 35 mi/hr to m/min (given that 1 mile = 1609 meters) Example: A 150 lb. man requires a drug dosage of 2.5 mg/kg. How many milligrams of the drug should he take? (1 kg = 2.205 lb.) Converting squared or cubed units: 1. Convert 0.25 m2 to cm2. 2. One side of a sheet of paper has an area of 93.5 in2. Convert this to square cm? Density = mass volume Density = mass volume Density Animation http://www.wiredchemist.com/anim-density Example: A piece of metal has a mass of 78.12 g and a volume of 9.5 cm3. What is it’s density? What metal is it? Metal Density (g/cm3) Mg 1.7 Al 2.7 Zn 7.1 Sn 7.3 Fe 7.9 Brass 8.4 Cu 8.9 Pb 11.4 Au 19.3 Pt 21.1 Example: A shiny gold-colored nugget has a mass of 26.5 grams and a volume of 3.4 cm3. Is it gold? Example: Carbon dioxide has a density of 0.001963 g/ml. What is the mass of a 5.0Liter sample of CO2? Example: An empty graduated cylinder has a mass of 215 grams. After filling it with liquid (946 ml) it is weighed again; the mass of the cylinder + liquid is 1854 grams. What is the density of the liquid? 215 grams 1854 grams Temperature - a measure of the intensity of heat Temperature Scales: • Celcius (C) • Fahrenheit (F) • Kelvin (K) Conversions between temperature scales: Converting from Celcius to Fahrenheit: A mixture of salt and water has a temperature of -5.0C. What is the temp on the Fahrenheit scale? Converting from Fahrenheit to Celcius: A child has a temperature of 103.1F. What is the temp on the Celcius scale? Converting from Celcius to Kelvin: On the planet Mercury, the average daytime temperature is 683 K. What is the temp on the Celcius scale?