11/11/ The numerical side of chemistry Chapter 2

11/11/20152 Outline Precision and Accuracy Uncertainty and Significant figures Zeros and Significant figures Scientific notation Units of measure Conversion factors and Algebraic manipulations

11/11/20153 Accuracy and Precision

11/11/20154 Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

11/11/20155 Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low.Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration. This can result in measurements that are precise, but not accurate.

11/11/20156 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.  Measurements are performed with instruments  No instrument can read to an infinite number of decimal places

11/11/20157 Nature of Measurement Part 1 - number Part 2 - scale (unit) Examples: 20 grams 34.5 mL 45.0 m Measurement - quantitative observation consisting of 2 parts consisting of 2 parts

11/11/20158 Significant figures or significant digits Digits that are not beyond accuracy of measuring device The certain digits and the estimated digit of a measurement

11/11/20159 Rules significant digits 1 significant digit 2 significant digits 1 significant digit 4 significant digit 3 significant digit

11/11/ Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.Nonzero integers always count as significant figures has 4 sig figs.

11/11/ Rules for Counting Significant Figures - Details ZerosZeros - Leading zeros do not count as significant figures. – has 3 sig figs.

11/11/ Rules for Counting Significant Figures - Details ZerosZeros - Captive zeros always count as significant figures. –16.07 has 4 sig figs.

11/11/ Rules for Counting Significant Figures - Details ZerosZeros Trailing zeros are significant only if the number contains a decimal point has 4 sig figs.

11/11/ Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

11/11/ Sig Fig Practice #1 How many significant figures in each of the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

11/11/ 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.Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement =  18.7 (3 sig figs)

11/11/ Sig Fig Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L lb lb lb lb mL mL 0.16 mL mL

11/11/ 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 x 2.0 =  13 (2 sig figs)

11/11/ Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s lb x 3.23 ft lb·ft 5870 lb·ft g ÷ 2.87 mL g/mL2.96 g/mL

11/11/ Why do we use scientific notation? To express very small and very large numbers To indicate the precision of the number Use it to avoid with sig digs

11/11/ In science, we deal with some very LARGE numbers: 1 mole = In science, we deal with some very SMALL numbers: Mass of an electron = kg Scientific Notation

11/11/ Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n

11/11/ x 10 9 The exponent is the number of places we moved the decimal.

11/11/ Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n 12345

11/11/ x The exponent is negative because the number we started with was less than 1.

11/11/ Review: Scientific notation expresses a number in the form: M x 10 n 1  M  10 n is an integer

SI measurement Le Système international d'unitésLe Système international d'unités The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularlyThe only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly Metrication is a process that does not happen all at once, but is rather a process that happens over time.Metrication is a process that does not happen all at once, but is rather a process that happens over time. Among countries with non- metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1866.Among countries with non- metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in Information from U.S. Metric Association

11/11/ The Fundamental SI Units (le Système International, SI)

Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

11/11/ Derived SI units Physical quantity NameAbbreviation Volume cubic meterm 3 Pressure pascalPa Energy jouleJ

11/11/ Metric System System used in science Decimal system Measurements are related by factors of 10 Has one standard unit for each type of measurement Prefixes are attached in front of standard unit

Metric Prefixes Kilo- means 1000 of that unitKilo- means 1000 of that unit –1 kilometer (km) = 1000 meters (m) Centi- means 1/100 of that unitCenti- means 1/100 of that unit –1 meter (m) = 100 centimeters (cm) –1 dollar = 100 cents Milli- means 1/1000 of that unitMilli- means 1/1000 of that unit –1 Liter (L) = 1000 milliliters (mL)

11/11/ SI Prefixes Common to Chemistry PrefixUnit Abbr.Exponent MegaM10 6 Kilok10 3 Decid10 -1 Centic10 -2 Millim10 -3 Micro  Nanon10 -9 Picop10 -12

Metric Prefixes

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

How many minutes are in 2.5 hours ? Conversion factor 2.5 hr x 60 min = 150 min 1 hr 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

Steps to Problem Solving 1.Write down the given amount. Don’t forget the units! 2.Multiply by a fraction. 3.Use the fraction as a conversion factor. Determine if the top or the bottom should be the same unit as the given so that it will cancel. 4.Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end. 5.Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units. 6.Multiply and divide the units (Cancel). 7.If the units are not the ones you want for your answer, make more conversions until you reach that point. 8.Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)

Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b)244 cm c)24.4 cm

Solution A rattlesnake is 2.44 m long. How long is the snake in cm? b)244 cm 2.44 m x 100 cm = 244 cm 1 m

Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day

Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min 24 hr 1 hr 1 min

Dealing with Two Units If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

What about Square and Cubic units? Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Best way: Square or cube the ENTIRE conversion factorBest way: Square or cube the ENTIRE conversion factor Example: Convert 4.3 cm 3 to mm 3Example: Convert 4.3 cm 3 to mm cm 3 10 mm 3 1 cm 1 cm ( ) = 4.3 cm mm cm cm 3 = 4300 mm 3

Learning Check A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

Solution 1000 cm 3 1 dm 3 10 cm 10 cm ( ) = 1 dm 3 So, a dm 3 is the same as a Liter ! A cm 3 is the same as a milliliter.

Temperature Scales FahrenheitFahrenheit CelsiusCelsius KelvinKelvin Anders Celsius Lord Kelvin (William Thomson)

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Temperature Scales 1 Kelvin = 1 degree Celsius Notice that 1 Kelvin = 1 degree Celsius Boiling point of water Freezing point of water Celsius 100 ˚C 0 ˚C 100˚C Kelvin 373 K 273 K 100 K Fahrenheit 32 ˚F 212 ˚F 180˚F

Calculations Using Temperature Generally require temp’s in kelvinsGenerally require temp’s in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 KBody temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 KLiquid nitrogen = -196 ˚C = 77 K Generally require temp’s in kelvinsGenerally require temp’s in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 KBody temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 KLiquid nitrogen = -196 ˚C = 77 K

Fahrenheit Formula – 180°F = 9°F =1.8°F 100°C 5°C 1°C Zero point: 0°C = 32°F °F = 9/5 °C + 32 °F = 9/5 °C + 32

Celsius Formula – Rearrange to find T°C °F = 9/5 °C + 32 °F - 32 = 9/5 °C ( ) °F - 32 = 9/5 °C 9/5 9/5 9/5 9/5 (°F - 32) * 5/9 = °C (°F - 32) * 5/9 = °C

Temperature Conversions – A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? °F = 9/5 (29.1°C) + 32 = = = 84.4°F

11/11/ Temperature measurements Kelvin temperature scale is also called absolute temperature scale There is not negative Kelvin temperature K= 0 C F = /5 0 C 0 C = 5/9 ( 0 F –32)

11/11/ What is temperature? Measure of how hot or cold an object is Determines the direction of heat transfer Heat moves from object with higher temperature to object with lower temperature

Learning Check – Pizza is baked at 455°F. What is that in °C? 1) 437 °C 2) 235°C 3) 221°C

11/11/ Density: m/v Density tells you how much matter there is in a given volume. Usually expressed in g/ml or g/cm 3

11/11/ Densities of some common materials MaterialDensity g/cm 3 MaterialDensity g/L Gold19.3Chlorine2.95 Mercury13.6CO Lead11.4Ar1.66 aluminum2.70Oxygen1.33 Sugar1.59Air1.20 Water1.000Nitrogen1.17 Gasoline Helium0.166 Ethanol0.789Hydrogen.0084

11/11/ Intensive properties do not depend on amount of matter (density, boiling point, melting point) Extensive properties do depend on amount of matter(mass, volume, energy content). Intensive and Extensive properties

11/11/ Energy Capacity to do work Work causes an object to move (F x d) Potential Energy: Energy due to position Kinetic Energy: Energy due to the motion of the object

11/11/ The Joule The unit of heat used in modern thermochemistry is the Joule Non SI unit calorie 1Cal=1000cal 4.184J =1cal or 4.184kJ=Cal

11/11/ Law of conservation of energy Energy is neither created nor destroyed; it only changes form

11/11/ Calorimetry The amount of heat absorbed or released during a physical or chemical change can be measured… …usually by the change in temperature of a known quantity of water 1 calorie is the heat required to raise the temperature of 1 gram of water by 1  C 1 BTU is the heat required to raise the temperature of 1 pound of water by 1  F

11/11/ Calorimeter

11/11/ A Cheaper Calorimeter

11/11/ Specific heat Amount of heat energy needed to warm 1 g of that substance by 1 o C Units are J/g o C or cal/g o C

11/11/ Specific Heat Notes Specific heat – how well a substance resist changing its temperature when it absorbs or releases heat Water has high s – results in coastal areas having milder climate than inland areas (coastal water temp. is quite stable which is favorable for marine life).

11/11/ More Specific Heat Organisms are primarily water – thus are able to resist more changes in their own temperature than if they were made of a liquid with a lower s

11/11/ Specific heats of some common substances Substance Water Iron Aluminum Ethanol (cal/g° C) (J/g ° C)

11/11/ Calculations Involving Specific Heat s = Specific Heat Capacity q = Heat lost or gained  T = Temperature change OR

11/11/ Principle of Heat Exchange The amount of heat lost by a substance is equal to the amount of heat gained by the substance to which it is transferred. m x ∆ t x s = m x ∆ t x s heat lost heat gained

11/11/ How to calculate amount of heat ? H= specific heat x mass x change in T Example Calculate the energy required to raise the temperature of a 387.0g bar of iron metal from 25 o C to 40 o C. The specific heat of iron is J/g o C