2 - 1 Measurement The Metric System and SI Units Converting Units Uncertainty in Measurement Significant Figures Measuring Volume and Mass Extensive and Intensive Properties Density Measuring Temperature and Time The Mole and Atomic and Formula Masses

2 - 2 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.

2 - 3 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

2 - 4 Units are important has little meaning, just a number $45,000 has some meaning - money $45,000/yr more meaning - person’s salary

2 - 5 Measurements in chemistry English units. - Still commonly used in the United States. Weightounce, pound, ton Lengthinch, foot, yard, mile Volumecup, pint, quart, gallon Not often used in scientific work - Very confusing and difficult to keep track of the conversions needed.

2 - 6 Measurement in chemistry English units. 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

2 - 7 Example How many teaspoons in a barrel of oil? 1 barrel of oil= 42 gallons 1 gallon= 4quarts 1 quart= 4cups 1 cup= 16tablespoons 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 = tsp

2 - 8 Metric Units Metric Units One base unit for each type of measurement. Use a prefix to change the size of unit. Some common base units. TypeNameSymbol Massgram g Lengthmeter m Volumeliter L Timesecond s Energyjoule J Measurement in chemistry

2 - 9 Metric prefixes Changing the prefix alters the size of a unit. Prefix Symbol Factor megaM kilok hectoh dekada base decid centic millim

SI units System International SI - System International Systematic subset of the metric system. Only uses certain metric units. Mass kilograms Lengthmeters Timeseconds Temperaturekelvin Amountmole 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 = mg kg g mg g

Converting units Factor label method Regardless of conversion, keeping track of units makes thing 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 Factor EnglishFactor 1 gallon= 4 quarts 4 qt/gal 1 mile= 5280 feet5280 ft/mile 1 ton= 2000 pounds2000 lb/ton Common English to Metric conversions Factor 1 liter= quarts1.057 qt/L 1 kilogram= 2.2 pounds2.2 lb/kg 1 meter= yards1.094 yd/m 1 inch= 2.54 cm2.54 cm/inch

Example Creatinine is a substance found in blood. If an analysis of blood serum sample detected 0.58 mg of creatinine, how many micrograms were present?  = = micro mg = 580  g g 1 mg ( ) 1  g g ( )

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

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

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

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

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

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

Types of errors Instrument not ‘zeroed’ properly Reagents made at wrong concentration Temperature in room varies ‘wildly’ Person running test is not properly trained Random Systematic

Errors Systematic Errors in a single direction (high or low). Can be corrected by proper calibration or running controls and blanks.Random Errors in any direction. Can’t be corrected. Can only be accounted for by using statistics.

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

Significant figures The number of significant digits is independent of the decimal point These numbers All have three significant figures!

Significant figures: Rules for zeros are not Leading zeros are not significant three significant figures Leading zero are Captive zeros are significant four significant figures are Trailing zeros are significant five significant figures Captive zero 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 or $3,000,000,000,000.00

Significant figures In science, all of our numbers are either measured or exact. Exact Exact - Infinite number of significant figures. Measured 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 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 = 3.21 x Three Significant Figures Three Significant Figures

Scientific notation Method to express really big or small numbers. Format isMantissa x Base Power Decimal part of original number Decimals you moved We just move the decimal point around.

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 10 X. The exponent is the number of places you moved the decimal point = 1.23 x 10 8

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 = 1.23 x 10 -7

Most calculators use scientific notation when the numbers get very large or small. How scientific notation is displayed can vary. It may use x10 n or may be displayed using an E. They usually have an Exp or EE This is to enter in the exponent. Scientific notation E-2

Examples x x x x

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? 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 g g g g 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 kg / [ (18.5 m) ( m) (2.1m) ] = 2.8 kg / m 3 (2.1 m - only has two significant figures)

Example 257 mg \__ 3 significant figures 120 miles \__ 3 significant figures kg \__ 3 significant figures 23, $/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.

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

Measuring volume Volume Volume - the amount of space that an object occupies. liter (L)The base metric unit is the liter (L). milliliter (mL)The common unit used in the lab is the milliliter (mL). cm 3One milliliter is exactly equal to one cm 3. SIm 3The derived SI unit for volume is the m 3 which is too large for convenient use.

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

Extensive and intensive properties Extensive properties Depend on the quantity of sample measured. Example Example - mass and volume of a sample. Intensive properties Independent of the sample size. Properties that are often characteristic of the substance being measured. Examples Examples - density, melting and boiling points.

Density Density is an intensive property of a substance based on two extensive properties. Common units are g / cm 3 or g / mL. g / cm 3 Air Bone Water 1.0Urine Gold19.3Gasoline Density = Mass Volume cm 3 = mL

Example. Density calculation 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 somass = volume x density mass = 1.00 L x 1000 x 1.05 = 1.05 x 10 3 g ml L g mL

Specific gravity The density of a substance compared to a reference substance. Specific Gravity = Specific Gravity is unitless. Reference is commonly water at 4 o C. At 4 o C, density = specific gravity. Commonly used to test urine. density of substance density of reference

Specific gravity measurement Hydrometer Float height will be based on Specific Gravity.

Temperature conversion Temperature - measure of heat energy. Three common scales used Fahrenheit, Celsius and Kelvin. o F= 32 o F + ( o C) X o C = ( o F - 32 o F) K = ( o C + 273) X SI unit 5oC9oF5oC9oF 9oF5oC9oF5oC 1 K 1 o C

Example. o F to o C If it is 20 o F outside, what is it in o C ? o C = ( o F - 32 o F) 5oC5oC 9oF9oF o C = (20 o F - 32 o F) 5oC5oC 9oF9oF o C = -6.7 (two significant figures in 20 o F)

Example. o F to K If the temperature is 75.0 o F, what is it in K? First convert to o C Then convert to K o C = (75.0 o F - 32) 5 9 = 23.9 K= 23.9 o C = 297

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.

Atomic masses Atoms are composed of protons, neutrons and electrons. Almost all of the mass of an atom comes from the protons and neutrons. All atoms of the same element will have the same number of protons. The number of neutrons may vary - isotopes. Most elements exist as a mixture of isotopes.

Isotopes Isotopes Isotopes Atoms of the same element but having different masses. Each isotope has a different number of neutrons. Isotopes of hydrogenHHH Isotopes of carbon CCC

Isotopes Most elements occur in nature as a mixture of isotopes. ElementNumber of stable isotopes H 2 C 2 O 3 Fe 4 Sn 10 This is one reason why atomic masses are not whole numbers. They are based on averages.

The atomic symbol & isotopes Determine the number of protons, neutrons and electrons in each of the following. P3115Ba U

Atomic masses As a reference point, we use the atomic mass unit (u) - 1/12 th of a 12 C atom. Using this relative system, the mass of all other atoms can be assigned. Examples 7 Li = u 14 N = u 29 Si = u

Average atomic masses Most elements exits as a mixture of isotopes. Each isotope may be present in different amounts. The masses listed in the periodic table reflect the world-wide average for each isotope. One can calculate the average atomic weight of an element if the abundance of each isotope for that element is known.

Average atomic masses Example. Silicon exists as a mixture of three isotopes. Determine it’s average atomic mass based on the following data. Isotope Mass (u) Abundance 28 Si % 29 Si % 30 Si %

Average atomic masses ( u) = u ( u) = 1.35 u ( u) = u 28 Si 29 Si 30 Si Average atomic mass for silicon = u

The mole Number of atoms in grams of 12 C 1 mol = x atoms mol = grams / formula weight u Atoms, ions and molecules are too small to directly measure - measured in u. Using moles gives us a practical unit. thegram We can then relate atoms, ions and molecules, using an easy to measure unit - the gram.

The mole If we had one mole of water and one mole of hydrogen, we would have the name number of molecules of each. 1 mol H 2 O = x molecules 1 mol H 2 = x molecules We can’t weigh out moles -- we use grams. We would need to weigh out a different number of grams to have the same number of molecules

Moles and masses Atoms come in different sizes and masses. A mole of atoms of one type would have a different mass than a mole of atoms of another type. H u or grams/mol O u or grams/mol Mo u or grams/mol Pb u or grams/mol We rely on a straight forward system to relate mass and moles.

Masses of atoms and molecules Atomic mass The average, relative mass of an atom in an element. Atomic mass unit (u) Arbitrary mass unit used for atoms. Relative to one type of carbon. Molecular or formula mass The total mass for all atoms in a compound.

Molar masses Once you know the mass of an atom, ion, or molecule, just remember: Mass of one unit - use u Mass of one mole of units - use grams/mole DON’T The numbers DON’T change -- just the units.

Masses of atoms and molecules H 2 O H 2 O - water 2 hydrogen 2 x1.008 u 1 oxygen1 x u mass of molecule u g/mol Rounded off based on significant figures Rounded off based on significant figures

Another example CH 3 CH 2 OH CH 3 CH 2 OH - ethyl alcohol 2 carbon2 x12.01 u 6 hydrogen6 x1.008 u 1 oxygen1 x16.00 u mass of molecule46.07 u g/mol

Molecular mass vs. formula mass Formula mass Add the masses of all the atoms in formula - for molecular and ionic compounds. Molecular mass Calculated the same as formula mass - only valid for molecules. Both have units of either u or grams/mole.

Formula mass, FM The sum of the atomic masses of all elements in a compound based on the chemical formula. You must use the atomic masses of the elements listed in the periodic table. CO 2 1 atom of C and 2 atoms of O 1 atom C x u = u 2 atoms O x u = u Formula mass = u Formula mass = u or g/mol or g/mol

Example - (NH 4 ) 2 SO 4 OK, this example is a little more complicated. The formula is in a format to show you how the various atoms are hooked up. ( N H 4 ) 2 S O 4 ( N H 4 ) 2 S O 4 We have two (NH 4 + ) units and one SO 4 2- unit. Now we can determine the number of atoms.

Example - (NH 4 ) 2 SO 4 Ammonium sulfate contains 2 nitrogen, 8 hydrogen, 1 sulfur & 4 oxygen. 2 Nx14.01 = Hx1.008 = Sx32.06 = Ox16.00=64.00 Formula mass= The units are either u or grams / mol.

Example - (NH 4 ) 2 SO 4 How many atoms are in 20.0 grams of ammonium sulfate? Formula weight = grams/mol Atoms in formula= 15 atoms / unit moles = 20.0 g x = mol 1 mol g atoms = mol x 15 x 6.02 x10 23 atoms unit units mol atoms = 1.36 x10 24