Chapter 1 (Part 2) Measurements in Chemistry 1.6 Physical Quantities

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1 Chapter 1 (Part 2) Measurements in Chemistry 1.6 Physical Quantities This is a property that can by physically measured. It consists of a number and a unit of measure. (e.g. ) Units Units are very important. Without them a number is meaningless. If I said I would pay you 125 to be my teaching assistant, is that good or bad? Scientific numbers are just as reliant on having proper units to have meaning. (Brian Regan UPS) English Units Those of us who were raised in the US are very accustomed to these. Elsewhere in the world, these are very confusing. Weight: ounce (oz) pound (lb) [16 ounces = 1 pound] ton [2000 pounds = 1 ton] Length: inch (in) foot (ft) [12 inches = 1 foot] yard (yd) [3 feet = 1 yard] mile (mi) [5280 feet = 1 mile] Volume: teaspoon (tsp) tablespoon (Tbsp) [3 tsp = 1 Tbsp] cup [16 Tbsp = 1 cup = 8 oz] pint (pt) [2 cups = 1 pint = 16 oz] quart (qt) [4cups = 2 pints = 1 quart = 32 oz] gallon (gal) [4 quarts = 1 gallon=64oz] SI Units The scientific community has chosen a modified version of the metric system as the standard for recording and reporting measurements. Designated as SI (Systeme International) or International System of Units. Developed by the French at time of French Revolution. Ch 1 (Part 2 - Measurement) Page15 Notice that the English system of units uses ounces to describe both weight and volume measurements, which adds to the confusion.

2 Some SI Base Units Measurement Name of Unit Abbr. Mass kilogram Length meter Time Temperature Amount of substance second Kelvin mole Derived Units Speed (distance) time Density ( mass ) volume Energy Joule J=kg x m 2 /sec 2 Know by heart Unit Prefixes Because the size of the observations that must be recorded in chemical observation, experimentation, and calculations vary from very, very small to very, very large, a series of prefixes has been developed. Prefix Abbr. Means Examples Selected Prefixes in the Metric System mega M Megawatt = 1,000,000 watts 1,000,000 watt = 1 Mwatt kilo- k kilogram = 1,000 grams 1000g = 1 kg deci- d dl = 0.1 liters 10 dl = 1 L centi- c cm = 0.01 meters 10 2 or 100 cm = 1 m milli- m mg = grams 10 3 or 1000 mg = 1 g micro- µ microliter = liters 10 6 µl = 1L nano- n nanometer = nm = 1 m meters pico- p picometer = meters pm= 1 m Ch 1 (Part 2 - Measurement) Page16

3 What is the symbol for microliter? a. ml b. µl c. ml d. ML Metric System This is a slight variation on the SI units of measure that is in common use in most countries other than the United States. Unit of mass is the rather than the kilogram (1kg =1000g). Unit of volume is the instead of the cubic meter (1 m 3 = 1000L). Unit of temperature is the rather than the Kelvin. Also known as the centigrade degree. 1.7 Measuring Mass, Length, & Volume Mass Measurements The terms mass and weight are often confused and interchanged. - A measure of the amount of matter in an object. (how much stuff is present) - A measure of the gravitational force that the earth or other large body exerts on an object. e.g. We weigh less on the moon than on earth, but we have the same mass. Most useful: 1 lb = 16 oz = 1 kg = Length, Area and Volume Measurements Length is a one-dimensional unit. (measure in only one direction) Area is a two-dimensional unit. Volume is a three-dimensional unit. Ch 1 (Part 2 - Measurement) Page17

4 For Length: Conversion factors for length: Most useful: 1 inch = For Areas, since the standard for length is the meter, that is easy to see: A square meter (m 2 ) is an area 1 meter on each side. For volumes this is also true, but the final unit is often given a new name. The SI unit for volume is the cubic meter. This is very large and not very useful for chemistry. The metric unit of a Liter is much more useful. We will also frequently use the unit of Ch 1 (Part 2 - Measurement) Page18

5 Conversion factors for volume Most useful: 1.8 Measurement and Significant Figures Numbers vs Data Significant Figures In math class, numbers are theoretical, exact species. In science, most numbers are associated with measurements. Uncertainty of Data All measurements contain some We make errors Tools have limits We need to be able to show what degree of confidence we have in a piece of data. The value recorded should use all the digits known with certainty, plus estimated digit. Ch 1 (Part 2 - Measurement) Page19

6 Significant figures (sig figs) The number of digits used to express a value. The number of sig figs that may be used for a measurement often depends on the equipment used for making the measurement. Determining Significant Digits in Numbers Last digit is uncertain Non-zero digits are significant. (If written!) Example: has sf Zeros depend on whether they are leading, captive, or trailing LEADING zeroes are significant Example: has sf IMBEDDED zeros are significant Example: has sf TRAILING zeroes Example: has sf after a decimal point significant at the end of a # with no decimal point Example: has or or sf We will see there is a way to remove the ambiguity using scientific notation! Ch 1 (Part 2 - Measurement) Page20

7 Note: Numbers that are definitions (e.g. 1 gallon = 4 quarts) have an infinite number of significant figures. (They are integers.) Anything that gets counted in integer values is treated as exact. ( sig figs) example: All digits in numbers with decimal points will be considered to be significant. metric to metric conversions are exact. Example: 1000 ml = 1 L English to English conversions are exact. Example: 4 cups = 1 qt English to metric conversion is exact. 1 in = 2.54 cm Problem: How many significant figures are in the following measurements? a) 4009 b) c) d) e) f) g) 4200 Ch 1 (Part 2 - Measurement) Page21

8 Scientific Notation Scientific notation is typically used to express very large or very small numbers or to clarify the number of significant digits present Scientific notation A number expressed as the product of a number between and, times 10 raised to a power. The exponent on the 10 tells how many the decimal point was moved to position it just after the first non-zero digit. In scientific notation, all digits are significant. When converting a number to scientific notation: For every place you move the decimal to the left, add a power of 10. Example: 1 2 3, 0 0 0, = 1.23 x 10 8 For every place you move the decimal to the Right, subtract a power of 10. Example: = 1.23 x 10-7 Problem: Write the following in scientific notation: a) 2734 b) c) to 2 sf d) to 3 sf We also need to be able to convert values that are shown in scientific notation back to standard notation. Ch 1 (Part 2 - Measurement) Page22

9 Problem: Write the following in standard notation: a) 2.85 x 10-4 b) x 10 3 c) x 10 2 d) x 10 3 Every digit written down in scientific notation was significant so we must not lose any!!!!!! 1.9 Rounding Off Numbers Calculators often display more digits than are significant. The last digit to be retained is increased by one if the following digit is 5 or greater. (i.e., 5,6,7,8, or 9) Example: rounded to 2 sf = The last digit to be retained is left unchanged if the following digit is 4 or less. (i.e., 0,1,2,3, or 4) Example: rounded to 3 sf = Round off the following numbers to the correct number of sig figs: Raw # Sig Figs Rounded In sci. not In the second half of the above example, we cannot tell once the number is rounded, how many significant figures the number represents. Ch 1 (Part 2 - Measurement) Page23

10 Scientific Notation (and Sig Figs) on Calculators When calculators display numbers in scientific notation, the display may show an E followed by a number 10 x simply a number set off to the right side. To change a value to scientific notation: Using your calculator, convert the following to scientific notation: a) b) c) 1300 to 2 sf d) 1300 to 3 sf To change a value to standard notation: For example: 4.07x10-4 would initially be entered as: 4.07 EE +/- 4 Then 2 nd 4 The display will give you Ch 1 (Part 2 - Measurement) Page24

11 Using your calculator, convert the following to standard notation: a) 4.85 x 10-3 b) x 10 3 c) x 10 2 d) x 10-6 e) x 10 3 Calculators do not give us significant figures. We must figure that part out for ourselves! Express the following in scientific notation. a) b) c) to 4sf d) to 7 sf e) to 4 sf f) to 2 sf Significant Digits in Calculations The answer to a problem cannot have more significance (accuracy) than the quantities used to produce it. Rule 1: Multiplying or Dividing The answer should have the same number of significant figures as the quantity with the fewest significant figures. Problem: Calculate (3.23 x )/(250. x 15) to the correct # of s.f. Ch 1 (Part 2 - Measurement) Page25

12 Problem: Calculate 1.68 x 10-1 / x 10 2 to the correct # of sig figs. Rule 2: Adding or Subtracting The number of decimal places the answer should equal to the number of decimal places in the number with the fewest decimal places. Problem: Add to the correct # of sig figs. Problem:Subtract 4.2 from to the correct # of sig figs. Mixed Operations When you have mixed multiplication and division, determine the # of sig figs in each intermediate result as you go along. round any answers until the very end. Problem: Calculate ( )/( ) to the correct # of sig figs. Ch 1 (Part 2 - Measurement) Page26

13 1.10 Problem Solving: Unit Conversion Information is often not given in the units we need or that we can relate to. The simplest way to carry out calculations involving different units is to use the (aka dimensional analysis or unit cancellation). Units are treated like numbers and can thus be multiplied and divided. Anything divided by itself = Anything multiplied by 1 = (but maybe in new units) Set up an equation so that all unwanted units. Problem : How many hours are in exactly 23 weeks? SOLUTION STEP 1: Put given information at left. STEP 2: Put answer units at right. STEP 3: Identify conversion factor(s). and the unit that should be on top vs bottom STEP 4: Write calculational setup, check that units cancel and Solve: Ch 1 (Part 2 - Measurement) Page27

14 Example Problem: if a horse stands 16 hands tall, the average person would want to know the height in feet or meters to better comprehend the information. To solve the problem above we would need to know that 1 hand = For above problem: SOLUTION STEP 1: Put given information at left. STEP 2: Put answer units at right. STEP 3: Identify conversion factor(s). and the unit that should be on top vs bottom STEP 4: Write calculational setup, check that units cancel and solve: To get the height in ft: To get the height in m: When converting from one prefix to another, go back to the base unit as a middle step. Problem: How many centimeters are in a kilometer? Ch 1 (Part 2 - Measurement) Page28