CHEM 2: An Introduction to Inorganic Chemistry

Transcription

1 Dimensional Analysis: Numbers and Units: The English System of units The Metric System of units (SI) Prefixes (kilo-, centi-, milli-, etc.) A systematic method for performing unit conversions Formulating different conversion factors Common errors & misconceptions Working with Compound Units Density: Intensive vs. Extensive Properties Calculations Next Week: Start lecture with Concept Check: A one question quiz through iclicker covering the today s material Be sure to bring iclicker remote In Lab: QUIZ 1 Consult CANVAS course website for topics & review materials Before coming to lecture: Read material for Lecture 3: Chapter 3: pp , CHEM 2: An Introduction to Inorganic Chemistry 1

2 Measurement in Chemistry Qualitative measurements Observations that describe a substance, mixture, reaction, or other process in WORDS. Quantitative measurements Observations that describe a property with NUMBERS and UNITS. In 1999, the Mars Climate Orbiter was lost in the Martian atmosphere because two separate engineering teams reported their calculations WITHOUT UNITS, & failed to communicate with the units to each other. The total cost of the mission was $327.6 MILLION! UNITS and Quantitative measurements Numbers often make no sense if we do not have some sort of reference or standard to compare them to. Nearly all numbers MUST be followed by a unit label. The unit indicates the standard against which the number is measured. 2

3 UNITS and Quantitative measurements The metric system is a system of measurement based on multiples of ten. In the metric system, a prefix may be added to the base unit to change the value of the unit by a factor of ten. The base unit is a reference to the standard. The English system of measurement is not based on powers of ten, and is therefore more difficult to use in calculations. Scientists almost exclusively work in the metric or SI system. Base units: The Système Internationale (SI) base units are defined from some physically observable and reproducible quantity. The base units are: Quantity Unit Symbol Length meter m Mass kilogram (gram) kg (g) Time second S Temperature kelvin K Amount of a substance mole mol Electric Current ampere A Luminous Intensity candela cd 3

4 Metric Prefixes: The prefixes below MODIFY any of the base or derived metric units into a power of 10. IN RED: prefixes common to chemistry. Prefix Symbol Multiple Multiple Tera- T ,000,000,000,000 Giga- G ,000,000,000 Mega- M ,000,000 kilo- k ,000 hecto- h deka- dk base unit deci- d centi- c milli- m micro nano- n pico- p Metric Prefixes: The prefixes below MODIFY any of the base or derived metric units into a power of 10. IN RED: prefixes common to chemistry. Prefix Symbol Multiple Multiple Mega- M ,000,000 kilo- k ,000 centi- c milli- m micro nano- n

5 Relationships of selected U.S. and Metric Units In the U.S., many of the everyday measurements we use are based on the older English system. We primarily use the metric system for measurements in labs in the U.S. However it is still often necessary to make some conversions to the metric system. These conversion factors will be given if necessary. Length Mass Volume 1 in = 2.54 cm 1 lb = kg 1 qt = L 1 yd = m 1 lb = 16 oz 4 qt = 1 gal 1 mi = km 1 oz = g 1 mi = 5280 ft Metric Conversions First think intuitively about the conversion: $1? cents Which unit is larger? Which unit is smaller? If converting a number from a larger unit to a smaller unit, the number should become bigger. Converting from a larger prefix to a smaller one: Move the decimal to the right: m mm Converting from a smaller prefix to a larger one: Move the decimal to the left: 750 ml cl 5

6 If converting a number from a larger unit to a smaller unit, the number should become bigger. Move the decimal to the left: COMMON MISTAKE 14.7 ml? L = = DIMENSIONAL ANALYSIS: A method of solving chemical problems in which the units are used to set up the solution to a problem. Dimensional analysis uses a series of ratios (conversion factors) to convert one unit into another unit. 24 inches How many feet? Starting Quantity ANSWER 24 inches 1 foot 12 inches = 2 feet Conversion Factor 6

7 Formulating & Making Sense of Conversion Factors Conversion factors are obtained from a statement of equivalence: CORRECT WRONG Steps in dimensional analysis Identify the conversion to be performed: GIVEN UNITS DESIRED UNITS Setup a Dimensional Analysis table. Insert conversion factors to ELIMINATE UNWANTED UNITS and introduce the desired units. Compute. Be careful to include parentheses where necessary. Note that a dimensional analysis table is identical to multiplying by fractions. 7

8 9/5/2013 Dimensional Analysis Examples ps = s 9.65 x 108 cg = kg iclicker Question: Converting between units of VOLUME How many cm3 are in 1.5 dm3? Given: 100 cm = 1 m & 10 dm = 1 m A cm3 B cm 3 C. 15 cm 3 D. 150 cm E cm3 8

9 Volume Conversion Factors Common Problem dm 3 cm 3 1 dm = 10 cm (1 dm) 3 = (10 cm) 3 1 dm 3 = 1000 cm 3 Compound Units Volume (space occupied by matter) can be considered a compound unit. The simplest formula for volume is for the volume of a box: Volume = (length) (width) (height) Consider a box with: length = 5.0 cm, width = 3.0 cm, height = 7.0 cm Volume = 5.0 cm x 3.0 cm x 7.0 cm = 105 cm 3 Just as the numbers are multiplied, so are the units. Velocity is another common compound unit. It combines distance and time. 9

10 9/5/2013 Compound Unit Conversion Convert: 1.5 in/yr? nm/s Density Density is a physical property of matter that describes the relationship between mass and volume of a substance. Density is an intensive property of matter - A substance will have a characteristic density that is independent of the amount of the substance present. In lay terms, we might say it describes how "heavy" a substance is (a misuse of the word). 10

11 Density from an Atomic Perspective Density from an Atomic Perspective 11

12 5-step Method for Problem-solving 1. Identify the UNKNOWN in the problem. 2. Identify the GIVEN quantities and useful information. 3. Choose the appropriate formulas & conversion factors. 4. Plan the solution. Identify how you will use formulas & conversion factors. Set up dimensional analysis tables. MAKE SURE UNITS ARE CONSISTENT. Isolate unknown variables in formulas. 5. Substitute the givens (in formulas) and SOLVE. (Plug & Chug!) Problem Solving Examples A neutron star has a density of about 100 million tons per teaspoon (ton/tsp). What volume of a neutron star (in cm 3 ) would have the same mass as a Boeing 747, which weighs 358,000 lbs.? Given: 1 ton = 2000 lbs. & 1 tsp 4.92 cm 3 12

13 Problem Solving Examples Pure ethanol has a density of g/cm 3. What is the volume of ethanol that must be measured (in fluid ounces) to equal 14 g? Given:: 1 fluid ounce 29.5 ml 13