Measurement The Metric System and SI Units Converting Units Uncertainty in Measurement Significant Figures Measuring Volume and Mass Density Measuring Temperature and Time

SI Units Many different systems for measuring the world around us have developed over the years. People in the U.S. rely on the English System. Scientists make use of SI units so that we all are speaking the same measurement language.

Data, results and units Data Measurements and observations. Results Data obtained from an experiment. May be converted using known equations. Units Defines the quantities being measured. All measurements must have units. To communicate our results, we must use standard units

Units are important 45 000 has little meaning, just a number $45,000 has some meaning - money $45,000/yr more meaning - person’s salary

Measurements in chemistry English units. - Still commonly used in the United States. Weight ounce, pound, ton Length inch, foot, yard, mile Volume cup, pint, quart, gallon Not often used in scientific work - Very confusing and difficult to keep track of the conversions needed.

Measurement in chemistry English units. Vary in size so you must memorize many conversion factors. Common English measures of volume 1 tablespoon = 3 teaspoons 1 cup = 16 tablespoons 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts 1 peck = 2 gallons 1 bushel = 4 pecks

Example How many teaspoons in a barrel of oil? 1 barrel of oil = 42 gallons 1 gallon = 4 quarts 1 quart = 4 cups 1 cup = 16 tablespoons 1 tablespoon = 3 teaspoons 1 bbl x 42 x 4 x 4 x 16 x 3 gal bbl qt gal cup qt tbl cup tsp tbl = 32 256 tsp

Measurement in chemistry Metric Units One base unit for each type of measurement. Use a prefix to change the size of unit. Some common base units. Type Name Symbol Mass gram g Length meter m Volume liter L Time second s Energy joule J

Metric prefixes Changing the prefix alters the size of a unit. Prefix Symbol Factor mega M 106 1 000 000 kilo k 103 1 000 hecto h 102 100 deka da 101 10 base - 100 1 deci d 10-1 0.1 centi c 10-2 0.01 milli m 10-3 0.001

SI units SI - System International Systematic subset of the metric system. Only uses certain metric units. Mass kilograms Length meters Time seconds Temperature kelvin Amount mole Other SI units are derived from SI base units.

Example. Metric conversion How many milligrams are in a kilogram? 1 kg = 1000 g 1 g = 1000 mg 1 kg x 1000 x 1000 = 1 000 000 mg kg g mg g

Converting units Factor label method Regardless of conversion, keeping track of units makes things come out right Must use conversion factors - The relationship between two units Canceling out units is a way of checking that your calculation is set up right!

Common conversion factors English Factor 1 gallon = 4 quarts 4 qt/gal 1 mile = 5280 feet 5280 ft/mile 1 ton = 2000 pounds 2000 lb/ton Common English to Metric conversions Factor 1 liter = 1.057 quarts 1.057 qt/L 1 kilogram = 2.2 pounds 2.2 lb/kg 1 meter = 1.094 yards 1.094 yd/m 1 inch = 2.54 cm 2.54 cm/inch

Example A nerve impulse in the body can travel as fast as 400 feet/second. What is its speed in meters/min ? Conversions Needed 1 meter = 3.3 feet 1 minute = 60 seconds

....Fast Example m 400 ft 1 m 60 sec min 1 sec 3.3 ft 1 min ? = x x 7273

Uncertainty in Measurement All measurements contain some uncertainty. We make errors Tools have limits Uncertainty is measured with Accuracy How close to the true value Precision How close to each other

Accuracy How close our values agree with the true value. Here the average value would give a good number but the numbers don’t agree. Large random error

Precision How well our values agree with each other. Here the numbers are close together so we have good precision. Poor accuracy. Large systematic error.

Accuracy and precision Our goal! Good precision and accuracy. These are values we can trust.

Accuracy and precision Predict the effect on accuracy and precision. Instrument not ‘zeroed’ properly Reagents made at wrong concentration Temperature in room varies ‘wildly’ Person running test is not properly trained

Significant figures Method used to express accuracy and precision. You can’t report numbers better than the method used to measure them. 67.2 units = three significant figures Certain Digits Uncertain Digit

Significant figures The number of significant digits is independent of the decimal point. 255 25.5 2.55 0.255 0.0255 These numbers All have three significant figures!

Significant figures: Rules for zeros Leading zeros are not significant. 0.421 - three significant figures Leading zero Captive zeros are significant. 4012 - four significant figures Captive zero Trailing zeros are significant. 114.20 - five significant figures Trailing zero

Significant figures Zeros are what will give you a headache! They are used/misused all of the time. Example The press might report that the federal deficit is three trillion dollars. What did they mean? $3 x 1012 or $3,000,000,000,000.00

Significant figures In science, all of our numbers are either measured or exact. Exact - Infinite number of significant figures. Measured - the tool used will tell you the level of significance. Varies based on the tool. Example Ruler with lines at 1/16” intervals. A balance might be able to measure to the nearest 0.1 grams.

Significant figures: Rules for zeros Scientific notation - can be used to clearly express significant figures. A properly written number in scientific notation always has the the proper number of significant figures. 0.00321 = 3.21 x 10-3 Three Significant Figures

Scientific notation If a number is larger than 1 The original decimal point is moved X places to the left. The resulting number is multiplied by 10X. The exponent is the number of places you moved the decimal point. 1 2 3 0 0 0 0 0 0. = 1.23 x 108

Scientific notation If a number is smaller than 1 The original decimal point is moved X places to the right. The resulting number is multiplied by 10-X. The exponent is the number of places you moved the decimal point. 0. 0 0 0 0 0 0 1 2 3 = 1.23 x 10-7

Scientific notation Most calculators use scientific notation when the numbers get very large or small. How scientific notation is displayed can vary. It may use x10n or may be displayed using an E. They usually have an Exp or EE This is to enter in the exponent. 1.44939 E-2

Examples 378 000 3.78 x 10 5 8931.5 8.9315 x 10 3 0.000 593 5.93 x 10 - 4 0.000 000 4 4 x 10 - 7

Significant figures and calculations An answer can’t have more significant figures than the quantities used to produce it. Example How fast did you run if you went 1.0 km in 3.0 minutes? 0.333333333 speed = 1.0 km / 3.0 min = 0.33 km / min

Significant figures and calculations Addition and subtraction Report your answer with the same number of digits to the right of the decimal point as the number having the fewest to start with. 123.45987 g + 234.11 g 357.57 g 805.4 g - 721.67912 g 83.7 g

Significant figures and calculations Multiplication and division. Report your answer with the same number of digits as the quantity have the smallest number of significant figures. Example. Density of a rectangular solid. 25.12 kg / [ (18.5 m) ( 0.2351 m) (2.1m) ] = 2.8 kg / m3 (2.1 m - only has two significant figures)

Example 257 mg \__ 3 significant figures 120 miles 0.002 30 kg 23,600.01 $/yr \__ 7 significant figures

Rounding off numbers After calculations, you may need to round off. If the first insignificant digit is 5 or more, - you round up If the first insignificant digit is 4 or less, - you round down.

1st insignificant digit Rounding off If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then - 2.5795035 becomes 2.580 34.204221 becomes 34.20 1st insignificant digit

Measuring volume Volume - the amount of space that an object occupies. The base metric unit is the liter (L). The common unit used in the lab is the milliliter (mL). One milliliter is exactly equal to one cm3. The derived SI unit for volume is the m3 which is too large for convenient use.

Measuring mass Mass - the quantity of matter in an object. Weight - the effect of gravity on an object. Since the Earth’s gravity is relatively constant, we can interconvert between weight and mass. The SI unit of mass is the kilogram (kg). However, in the lab, the gram (g) is more commonly used.

Density What is the density of 5.00 mL of a fluid if it has a mass of 5.23 grams? d = mass / volume d = 5.23 g / 5.00 mL d = 1.05 g / mL What would be the mass of 1.00 liters of this sample?

Example. Density calculation What would be the mass of 1.00 liters of the fluid sample? The density was 1.05 g/mL. density = mass / volume so mass = volume x density mass = 1.00 L x 1000 x 1.05 = 1.05 x 103 g ml L g mL

Temperature conversion Temperature - measure of heat energy. Three common scales used Fahrenheit, Celsius and Kelvin. 9oF 5oC oF = 32oF + (oC) X oC = (oF - 32oF) K = (oC + 273) X 5oC 9oF SI unit 1 K 1oC

Measuring time The SI unit is the second (s). For longer time periods, we can use SI prefixes or units such as minutes (min), hours (h), days (day) and years. Months are never used - they vary in size.