Pre-AP Chemistry Measurements and Calculations

Nature of Measurement Measurement - quantitative observation consisting of 2 parts Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 x 10-34 Joule seconds

Why Is there Uncertainty? Measurements are performed by people with instruments No instrument can read to an infinite number of decimal places, & no person is perfect! A measurment is only as reliable as the equipment that is used and the person making the measurement!

Uncertainty in Measurement When making a measurement, the last digit MUST be estimated. This is to make the measurement as precise and accurate as possible. A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Reading Measurements

Reading Measurements

Reading Measurements

Reading Measurements

Reading Measurements

Reading Measurements

Sig Fig Practice #1 1.0070 m  5 sig figs 17.10 kg  4 sig figs How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76  13 (2 sig figs)

Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. 18.734  18.7 (3 sig figs) 11.934 + 6.8 Last place in least precise measurement

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL

The Fundamental SI Units (le Système International, SI)

SI Units

Derived SI Units we will use Volume = length x length x length SI unit = the Liter (L) Density = mass / volume SI unit = g / mL Molar Mass = mass / mol SI unit = g/mol Concentration = mol / volume SI unit = Molarity (M) = mol / L

SI Prefixes Common to Chemistry Unit Abbr. Kilo k Centi c Milli m Micro  Nano n

SI Unit Conversions How to convert between units NOT JUST MOVING DECIMALS! Must use a conversion factor for the prefix you are working with. Conversion Factors: 1 kilo________ = 1000 ________ 100 centi ________ = 1 ________ 1000 milli ________ = 1 ________ 1,000,000 micro ________ = 1 ________ 1,000,000,000 nano ________ = 1 ________ Kilo BASE UNIT Centi Milli Micro Nano Kilometer METER Centimeter Millimeter Micrometer Nanometer Largest Smallest

Using Conversion Factors Ex: 1000 mill ________ = 1 ________ Given 4.5 g, determine the # of mg. UNITS ARE IMPORTANT!!!! 4.5 g  ____ mg 1st Step- We will multiply and divide! 2nd- Units you know go on bottom, units you don’t go on top 3rd- Put the numbers in the equation that match the units from the conversion factor. 4th- Solve! g mg 4.5 g mg 1000 1 4500

Conversion Practice Convert: 220 m  km Convert : 22,000 us  s Conversion factor: 1 km = 1000m Convert : 22,000 us  s Conversion factor: 1,000,000 us = 1 s 1 1000 m km 220 m km .22 1 1,000,000 us s 22,000 us s .022

2 Step Conversions Convert: 8.4 mL  nL No conversion factor between mL & nL Do have conversion factors mL L & L  nL Conversion factor: 1 L = 1000 mL Conversion factor: 1,000,000,000 nL = 1 L 1 1000 mL L 8.4 mL L .0084 1,000,000,000 1 L nL .0084 L nL 8,400,000

Constructing Conversion Factors, i.e. Derived Units Any equality between numbers with different units is a conversion factor! EX: 1 week = 7 days, 1 day = 24 hrs, 1 hr = 60 min, 1 min = 70 heart beats. Derived Units combine different units together to measure 1 thing. EX Density = mass / volume. Volume = length x length x length

Constructing Conversion Factors, i.e. Derived Units 1 week = 7 days 1 day = 24 hrs 1 hr = 60 min 1 min = 70 heart beats Given the above info What is the derived units for: # of heart beats per minute? Hours per week? Calculate how many heartbeats would occur in 3.5 weeks.

Scientific Notation notes

Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602200000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg

Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 ???????????????????????????????????

Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n M is a number between 1 and 10 n is an integer

. 2 500 000 000 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

2.5 x 109 The exponent is the number of places we moved the decimal.

0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

5.79 x 10-5 The exponent is negative because the number we started with was less than 1.

Making Measurements- Error

Precision and Accuracy Accuracy: How close a measurement is to the ACCEPTED VALUE. Precision: How close measurements are to EACHOTHER. Neither accurate nor precise Precise but not accurate Precise AND accurate

Precision and Accuracy Is it better to be accurate or precise? WHY?

Percent Error Percent Error is a way of determining how “off” a measurement is from the accepted value. Accepted Value – Experimental Value Accepted Value X 100 % Error =

What is it, Why is it important? Density- What is it, Why is it important? Density is the amount of mass per unit volume an object contains. D = m/v This is a DERIVED UNIT Density is important because it is an INTENSIVE PROPERTY This means it doesn’t matter how much of a substance you have. Ex: 1 ounce of gold and 1 ton of gold have the exact same density!

Graphical Relationships Direct Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line

Graphical Relationships Inverse (or Indirect) Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

Review: M x 10n Scientific notation expresses a number in the form: n is an integer 1  M  10

IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 7 x 106

The same holds true for subtraction in scientific notation. 4 x 106 - 3 x 106 1 x 106

If the exponents are NOT the same, we must move a decimal to make them the same.

 Is this good scientific notation? Student A  Is this good scientific notation? 40.0 x 105 4.00 x 106 + 3.00 x 105 NO! 43.00 x 105 To avoid this problem, move the decimal on the smaller number! = 4.300 x 106

 Is this good scientific notation? 4.00 x 106 Student B + 3.00 x 105 .30 x 106 YES!  Is this good scientific notation? 4.30 x 106

A Problem for you… 2.37 x 10-6 + 3.48 x 10-4

Solution… 002.37 x 10-6 2.37 x 10-6 0.0237 x 10-4 + 3.48 x 10-4 3.5037 x 10-4

Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures. 3456 has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros - Leading zeros do not count as significant figures. 0.0486 has 3 sig figs.

Rules for Counting Significant Figures - Details Zeros - Captive zeros always count as significant figures. 16.07 has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 sig figs.

Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

Direct Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line

Inverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola