Unit 2 (Chapter 5) -Measurement and Problem Solving Slides adapted from Nivaldo Tro

What is a Measurement? quantitative observation comparison to an agreed upon standard every measurement has a number and a unit Tro’s Introductory Chemistry, Chapter 22

A Measurement… the unit tells you what standard you are comparing your object to the number tells you 1.what multiple of the standard the object measures 2.the uncertainty in the measurement Tro's Introductory Chemistry, Chapter 23

Scientists have measured the average global temperature rise over the past century to be 0.6°C °C tells you that the temperature is being compared to the Celsius temperature scale 0.6 tells you that 1.the average temperature rise is 0.6 times the standard unit 2.the uncertainty in the measurement is such that we know the measurement is between 0.5 and 0.7°C Tro's Introductory Chemistry, Chapter 24

Scientific Notation Scientific Notation A way of writing large and small numbers in….

Big and Small Numbers We commonly measure objects that are many times larger or smaller than our standard of comparison Writing large numbers of zeros is tricky and confusing ◦ not to mention the 8 digit limit of your calculator! Tro's Introductory Chemistry, Chapter 26 an atom’s average diameter is m the sun’s diameter is 1,392,000,000 m

Scientific Notation each decimal place in our number system represents a different power of 10 scientific notation writes the numbers so they are easily comparable by looking at the power of 10 Tro's Introductory Chemistry, Chapter 27 an atom’s average diameter is 3 x m the sun’s diameter is x 10 9 m

Exponents… when the exponent on 10 is positive, it means the number is that many powers of 10 larger ◦ sun’s diameter = x 10 9 m = 1,392,000,000 m when the exponent on 10 is negative, it means the number is that many powers of 10 smaller ◦ avg. atom’s diameter = 3 x m = m Tro's Introductory Chemistry, Chapter 28

Scientific Notation To Compare Numbers Written in Scientific Notation ◦ First Compare Exponents on 10 ◦ If Exponents Equal, Then Compare Decimal Numbers Tro's Introductory Chemistry, Chapter x10 -8 decimal partexponent part exponent 1.23 x 10 5 > 4.56 x x > 7.89 x x > 1.23 x 10 10

Writing Numbers in Scientific Notation Writing Numbers in Scientific Notation 1 Locate the Decimal Point 2 Move the decimal point to the right of the first non-zero digit from the left 3 Multiply the new number by 10 n ◦ where n is the number of places you moved the decimal point 4 if the number is  1, n is +; if the number is < 1, n is - Tro's Introductory Chemistry, Chapter 210

Writing a Number In Scientific Notation Locate the Decimal Point Move the decimal point to the right of the first non-zero digit from the left Multiply the new number by 10 n ◦ where n is the number of places you moved the decimal pt x if the number is  1, n is +; if the number is < 1, n is x 10 4 Tro's Introductory Chemistry, Chapter 211

Locate the Decimal Point Move the decimal point to the right of the first non-zero digit from the left Multiply the new number by 10 n ◦ where n is the number of places you moved the decimal pt x if the number is  1, n is +; if the number is < 1, n is x 10 0 Tro's Introductory Chemistry, Chapter 212

Locate the Decimal Point Move the decimal point to the right of the first non-zero digit from the left Multiply the new number by 10 n ◦ where n is the number of places you moved the decimal pt x if the number is  1, n is +; if the number is < 1, n is x Tro's Introductory Chemistry, Chapter 213

Writing a Number in Standard Form x since exponent is -6, make the number smaller by moving the decimal point to the left 6 places ◦ if you run out of digits, add zeros Tro's Introductory Chemistry, Chapter

Example The U.S. population in 2004 was estimated to be 293,168,000 people. Express this number in scientific notation. 293,168,000 people = x 10 8 people Tro's Introductory Chemistry, Chapter 215

Significant Figures Writing Numbers to Reflect Precision =ZuVPkBb-z2I

Exact Numbers vs. Measurements sometimes you can determine an exact value for a quality of an object ◦ often by counting  pennies in a pile ◦ sometimes by definition  1 ounce is exactly 1/16 th of 1 pound whenever you use an instrument to compare a quality of an object to a standard, there is uncertainty in the comparison Tro's Introductory Chemistry, Chapter 217

Reporting Measurements measurements are written to indicate the uncertainty in the measurement the system of writing measurements we use is called significant figures when writing measurements, all the digits written are known with certainty except the last one, which is an estimate Tro's Introductory Chemistry, Chapter certain estimated

Estimating the Last Digit for instruments marked with a scale, you get the last digit by estimating between the marks ◦ if possible mentally divide the space into 10 equal spaces, then estimate how many spaces over the indicator is Tro's Introductory Chemistry, Chapter grams

Significant Figures the non-place-holding digits in a reported measurement are called significant figures ◦ some zero’s in a written number are only there to help you locate the decimal point significant figures tell us the range of values to expect for repeated measurements ◦ the more significant figures there are in a measurement, the smaller the range of values is Tro's Introductory Chemistry, Chapter cm has 3 sig. figs. and its range is 12.2 to 12.4 cm cm has 4 sig. figs. and its range is to cm

Counting Significant Figures All non-zero digits are significant ◦ 1.5 has 2 sig. figs. Interior zeros are significant ◦ 1.05 has 3 sig. figs. Trailing zeros after a decimal point are significant ◦ has 4 sig. figs. Tro's Introductory Chemistry, Chapter 221

Leading zeros are NOT significant has 4 sig. figs x Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation if 150 has 2 sig. figs. then 1.5 x 10 2 but if 150. has 3 sig. figs. then 1.50 x 10 2 Tro's Introductory Chemistry, Chapter 222

Significant Figures and Exact Numbers Exact Numbers have an unlimited number of significant figures A number whose value is known with complete certainty is exact ◦ from counting individual objects ◦ from definitions  1 cm is exactly equal to 0.01 m ◦ from integer values in equations  in the equation for the radius of a circle, the 2 is exact Tro's Introductory Chemistry, Chapter 223 radius of a circle = diameter of a circle 2

Example 2.4 – Determining the Number of Significant Figures in a Number How many significant figures are in each of the following numbers? × dozen = ,000 Tro's Introductory Chemistry, Chapter 224

Example 2.4 – Determining the Number of Significant Figures in a Number How many significant figures are in each of the following numbers? sig. figs. – leading zeros not sig sig. figs. – trailing & interior zeros sig sig. figs. – all digits sig × sig. figs. – only decimal parts count sig. 1 dozen = 12 unlimited sig. figs. – definition 100,000 ambiguous Tro's Introductory Chemistry, Chapter 225

Multiplication and Division with Significant Figures when multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures 5.02 × 89,665 × 0.10= = 45 3 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs ÷6.10= = sig. figs. 3 sig. figs. 3 sig. figs. Tro's Introductory Chemistry, Chapter 226

Rounding when rounding to the correct number of significant figures, if the number after the place of the last significant figure is 1. 0 to 4, round down ◦ drop all digits after the last sig. fig. and leave the last sig. fig. alone ◦ add insignificant zeros to keep the value if necessary 2. 5 to 9, round up ◦ drop all digits after the last sig. fig. and increase the last sig. fig. by one ◦ add insignificant zeros to keep the value if necessary Tro's Introductory Chemistry, Chapter 227

Rounding rounding to 2 significant figures 2.34 rounds to 2.3 ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less 2.37 rounds to 2.4 ◦ because the 3 is where the last sig. fig. will be and the number after it is 5 or greater rounds to 2.3 ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro's Introductory Chemistry, Chapter 228

Rounding rounding to 2 significant figures rounds to or 2.3 × ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less rounds to or 2.4 × ◦ because the 3 is where the last sig. fig. will be and the number after it is 5 or greater rounds to or 2.3 × ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro's Introductory Chemistry, Chapter 229

Rounding rounding to 2 significant figures 234 rounds to 230 or 2.3 × 10 2 ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less 237 rounds to 240 or 2.4 × 10 2 ◦ because the 3 is where the last sig. fig. will be and the number after it is 5 or greater rounds to 230 or 2.3 × 10 2 ◦ because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro's Introductory Chemistry, Chapter 230

Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result × 0.12 × ÷ 96 = × ÷ = Tro's Introductory Chemistry, Chapter 231

Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result × 0.12 × ÷ 96 = = × ÷ = = 1.52 Tro's Introductory Chemistry, Chapter sf2 sf4 sf2 sf result should have 2 sf 7 is in place of last sig. fig., number after is 5 or greater, so round up 4 sf 3 sf6 sf result should have 3 sf 1 is in place of last sig. fig., number after is 5 or greater, so round up

Addition and Subtraction with Significant Figures when adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places = = dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl = = dec. pl 3 dec. pl. 1 dec. pl. Tro's Introductory Chemistry, Chapter 233

Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result – 1.22 = – – 5.98 = Tro's Introductory Chemistry, Chapter 234

Determine the Correct Number of Significant Figures for each Calculation and Round and Report the Result – 1.22 = = – – 5.98 = = Tro's Introductory Chemistry, Chapter dp1 dp2 dp result should have 1 dp 8 is in place of last sig. fig., number after is 5 or greater, so round up 3 dp 2 dp result should have 2 dp 6 is in place of last sig. fig., number after is 4 or less, so round down

Both Multiplication/Division and Addition/Subtraction with Significant Figures when doing different kinds of operations with measurements with significant figures, do whatever is in parentheses first, find the number of significant figures in the intermediate answer, then do the remaining steps × (5.67 – 2.3) = 2 dp 1 dp × 3.37 = 12 4 sf 1 dp & 2 sf 2 sf Tro's Introductory Chemistry, Chapter 236

Basic Units of Measure

The Standard Units Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units ◦ Système International = International System Tro's Introductory Chemistry, Chapter 238 QuantityUnitSymbol lengthmeterm masskilogramkg timeseconds temperaturekelvinK

Some Standard Units in the Metric System Tro's Introductory Chemistry, Chapter 239 Quantity Measured Name of Unit Abbreviation Massgramg Lengthmeterm VolumeliterL Timesecondss TemperatureKelvinK

Length Measure of the two-dimensional distance an object covers SI unit = meter ◦ About 3½ inches longer than a yard  1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light Commonly use centimeters (cm) ◦ 1 m = 100 cm ◦ 1 cm = 0.01 m = 10 mm ◦ 1 inch = 2.54 cm (exactly) Tro's Introductory Chemistry, Chapter 240

Mass Measure of the amount of matter present in an object SI unit = kilogram (kg) ◦ about 2 lbs. 3 oz. Commonly measure mass in grams (g) or milligrams (mg) ◦ 1 kg = pounds, 1 lbs. = g ◦ 1 kg = 1000 g = 10 3 g, ◦ 1 g = 1000 mg = 10 3 mg ◦ 1 g = kg = kg, ◦ 1 mg = g = g Tro's Introductory Chemistry, Chapter 241

Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10 The power of 10 is indicated by a prefix The prefixes are always the same, regardless of the standard unit Tro's Introductory Chemistry, Chapter 242

Common Prefixes in the SI System PrefixSymbol Decimal Equivalent Power of 10 mega-M1,000,000Base x 10 6 kilo-k 1,000Base x 10 3 deci-d 0.1Base x centi-c 0.01Base x milli-m 0.001Base x micro-  or mc Base x nano-n Base x Tro's Introductory Chemistry, Chapter 243

Prefixes Used to Modify Standard Unit kilo = 1000 times base unit = 10 3 ◦ 1 kg = 1000 g = 10 3 g deci = 0.1 times the base unit = ◦ 1 dL = 0.1 L = L; 1 L = 10 dL centi = 0.01 times the base unit = ◦ 1 cm = 0.01 m = m; 1 m = 100 cm milli = times the base unit = ◦ 1 mg = g = g; 1 g = 1000 mg micro = times the base unit ◦ 1  m = m; 10 6  m = 1 m nano = times the base unit ◦ 1 nL = L; 10 9 nL = 1 L Tro's Introductory Chemistry, Chapter 244

Volume Measure of the amount of three-dimensional space occupied SI unit = cubic meter (m 3 ) ◦ a Derived Unit Commonly measure solid volume in cubic centimeters (cm 3 ) ◦ 1 m 3 = 10 6 cm 3 ◦ 1 cm 3 = m 3 = m 3 Commonly measure liquid or gas volume in milliliters (mL) ◦ 1 L is slightly larger than 1 quart ◦ 1 L = 1 dL 3 = 1000 mL = 10 3 mL ◦ 1 mL = L = L ◦ 1 mL = 1 cm 3 Tro's Introductory Chemistry, Chapter 245

Common Units and Their Equivalents Tro's Introductory Chemistry, Chapter 246 Length 1 kilometer (km)= mile (mi) 1 meter (m)=39.37 inches (in.) 1 meter (m)=1.094 yards (yd) 1 foot (ft)=30.48 centimeters (cm) 1 inch (in.)=2.54 centimeters (cm) exactly

Common Units and Their Equivalents Tro's Introductory Chemistry, Chapter 247 Volume 1 liter (L)=1000 milliliters (mL) 1 liter (L)=1000 cubic centimeters (cm 3 ) 1 liter (L)=1.057 quarts (qt) 1 U.S. gallon (gal)=3.785 liters (L) Mass 1 kilogram (km)=2.205 pounds (lb) 1 pound (lb)= grams (g) 1 ounce (oz)=28.35 (g)

Which is Larger? 1 yard or 1 meter? 1 mile or 1 km? 1 cm or 1 inch? 1 kg or 1 lb? 1 mg or 1  g? 1 qt or 1 L? 1 L or 1 gal? 1 gal or 1000 cm 3 ? Tro's Introductory Chemistry, Chapter 248

Which is Larger? 1 yard or 1 meter? 1 mile of 1 km? 1 cm or 1 inch? 1 kg or 1 lb? 1 mg or 1  g? 1 qt or 1 L? 1 L or 1 gal? 1 gal or 1000 cm 3 ? Tro's Introductory Chemistry, Chapter 249

Units Always write every number with its associated unit Always include units in your calculations ◦ you can do the same kind of operations on units as you can with numbers  cm × cm = cm 2  cm + cm = cm  cm ÷ cm = 1 ◦ using units as a guide to problem solving is called dimensional analysis Tro's Introductory Chemistry, Chapter 250

Problem Solving and Dimensional Analysis Many problems in Chemistry involve using relationships to convert one unit of measurement to another Conversion Factors are relationships between two units ◦ May be exact or measured ◦ Both parts of the conversion factor have the same number of significant figures Conversion factors generated from equivalence statements ◦ e.g. 1 inch = 2.54 cm can giveor Tro's Introductory Chemistry, Chapter 251

Problem Solving and Dimensional Analysis Arrange conversion factors so starting unit cancels ◦ Arrange conversion factor so starting unit is on the bottom of the conversion factor May string conversion factors ◦ So we do not need to know every relationship, as long as we can find something else the beginning and ending units are related to Tro's Introductory Chemistry, Chapter 252 unit 1 unit 2 unit 1 unit 2x=

Solution Maps a solution map is a visual outline that shows the strategic route required to solve a problem for unit conversion, the solution map focuses on units and how to convert one to another for problems that require equations, the solution map focuses on solving the equation to find an unknown value Tro's Introductory Chemistry, Chapter 253

Systematic Approach 1) Write down Given Amount and Unit 2) Write down what you want to Find and Unit 3) Write down needed Conversion Factors or Equations a)Write down equivalence statements for each relationship b)Change equivalence statements to Conversion Factors with starting unit on the bottom Tro's Introductory Chemistry, Chapter 254

Systematic Approach 4) Design a Solution Map for the Problem ◦ order conversions to cancel previous units or ◦ arrange Equation so Find amount is isolated 5) Apply the Steps in the Solution Map ◦ check that units cancel properly ◦ multiply terms across the top and divide by each bottom term 6) Check the Answer to see if its Reasonable ◦ correct size and unit Tro's Introductory Chemistry, Chapter 255

Solution Maps and Conversion Factors Convert Inches into Centimeters 1)Find Relationship Equivalence: 1 in = 2.54 cm 2)Write Solution Map Tro's Introductory Chemistry, Chapter 256 in cm 3)Change Equivalence into Conversion Factors with Starting Units on the Bottom

Convert 7.8 km to miles 1.Write down the Given quantity and its unit Given:7.8 km 2.Write down the quantity you want to Find and unit Find:? miles 3.Write down the appropriate Conversion Factors Conversion Factors: 1 km = mi 4.Write a Solution MapSolution Map: 5.Follow the Solution Map to Solve the problem Solution: 6.Sig. Figs. and RoundRound: mi = 4.8 mi 7.CheckCheck:Units & Magnitude are correct kmmi

Example 2.8: Unit Conversion

Example: Convert 7.8 km to miles Tro's Introductory Chemistry, Chapter 259

Example: Convert 7.8 km to miles Write down the given quantity and its units. Given:7.8 km Tro's Introductory Chemistry, Chapter 260

Example: Convert 7.8 km to miles Write down the quantity to find and/or its units. Find: ? miles Information Given:7.8 km Tro's Introductory Chemistry, Chapter 261

Example: Convert 7.8 km to miles Collect Needed Conversion Factors: 1 mi = km Information Given:7.8 km Find:? mi Tro's Introductory Chemistry, Chapter 262

Example: Convert 7.8 km to miles Write a Solution Map for converting the units : Information Given:7.8 km Find:? mi Conv. Fact.1 mi = km Tro's Introductory Chemistry, Chapter 263 kmmi

Example: Convert 7.8 km to miles Apply the Solution Map: Information Given:7.8 km Find:? mi Conv. Fact.1 mi = km Soln. Map:km  mi Tro's Introductory Chemistry, Chapter 264 = mi = 4.8 mi Sig. Figs. & Round:

Example: Convert 7.8 km to miles Check the Solution: Information Given:7.8 km Find:? mi Conv. Fact.1 mi = km Soln. Map:km  mi Tro's Introductory Chemistry, Chapter km = 4.8 mi The units of the answer, mi, are correct. The magnitude of the answer makes sense since kilometers are shorter than miles.

Solution Maps and Conversion Factors Convert Cups into Liters 1)Find Relationship Equivalence: 1 L = qt, 1 qt = 4 c 2)Write Solution Map Tro's Introductory Chemistry, Chapter 266 L L qt 3)Change Equivalence into Conversion Factors with Starting Units on the Bottom c c

How many cups of cream is 0.75 L? 1.Write down the Given quantity and its unit Given:0.75 L 2.Write down the quantity you want to Find and unit Find:? cu 3.Write down the appropriate Conversion Factors Conversion Factors: 1 L = qt 1 qt = 4 cu 4.Write a Solution MapSolution Map: 5.Follow the Solution Map to Solve the problem Solution: 6.Sig. Figs. and RoundRound:3.171 cu = 3.2 cu 7.CheckCheck:Units & Magnitude are correct Lqtcu

Example 2.10: Solving Multistep Unit Conversion Problems

Example: An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Tro's Introductory Chemistry, Chapter 269

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Write down the given quantity and its units. Given:0.75 L Tro's Introductory Chemistry, Chapter 270

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Write down the quantity to find and/or its units. Find: ? cups Information Given:0.75 L Tro's Introductory Chemistry, Chapter 271

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Collect Needed Conversion Factors: 4 cu = 1 qt qt = 1 L Information Given:0.75 L Find:? cu Tro's Introductory Chemistry, Chapter 272

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Write a Solution Map for converting the units : Information Given:0.75 L Find:? cu Conv. Fact.4 cu = 1 qt; qt = 1 L Tro's Introductory Chemistry, Chapter 273 Lqtcu

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Apply the Solution Map: Information Given:0.75 L Find:? cu Conv. Fact.4 cu = 1 qt; qt = 1 L Sol’n Map:L  qt  cu Tro's Introductory Chemistry, Chapter 274 = cu = 3.2 cu Sig. Figs. & Round:

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Check the Solution: Information Given:0.75 L Find:? cu Conv. Fact.4 cu = 1 qt; qt = 1 L Sol’n Map:L  qt  cu Tro's Introductory Chemistry, Chapter L = 3.2 cu The units of the answer, cu, are correct. The magnitude of the answer makes sense since cups are smaller than liters.

Solution Maps and Conversion Factors Convert Cubic Inches into Cubic Centimeters 1)Find Relationship Equivalence: 1 in = 2.54 cm 2)Write Solution Map Tro's Introductory Chemistry, Chapter 276 in 3 cm 3 3)Change Equivalence into Conversion Factors with Starting Units on the Bottom

Convert 2,659 cm2 into square meters Convert 2,659 cm 2 into square meters 1.Write down the Given quantity and its unit Given:2,659 cm 2 2.Write down the quantity you want to Find and unit Find:? m 2 3.Write down the appropriate Conversion Factors Conversion Factors: 1 cm = 0.01 m 4.Write a Solution MapSolution Map: 5.Follow the Solution Map to Solve the problem Solution: 6.Sig. Figs. and RoundRound: m 2 7.CheckCheck:Units & Magnitude are correct cm 2 m2m2

Example 2.12: Converting Quantities Involving Units Raised to a Power

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Tro's Introductory Chemistry, Chapter 279

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Write down the given quantity and its units. Given:2,659 cm 2 Tro's Introductory Chemistry, Chapter 280

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Write down the quantity to find and/or its units. Find: ? m 2 Information Given:2,659 cm 2 Tro's Introductory Chemistry, Chapter 281

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Collect Needed Conversion Factors: 1 cm = 0.01m Information Given:2,659 cm 2 Find:? m 2 Tro's Introductory Chemistry, Chapter 282

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Write a Solution Map for converting the units : Information Given:2,659 cm 2 Find:? m 2 Conv. Fact.:1 cm = 0.01 m Tro's Introductory Chemistry, Chapter 283 cm 2 m2m2

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Apply the Solution Map: Information Given:2,659 cm 2 Find:? m 2 Conv. Fact.1 cm = 0.01 m Sol’n Map:cm 2  m 2 Tro's Introductory Chemistry, Chapter 284 = m 2 = m 2 Sig. Figs. & Round:

Example: A circle has an area of 2,659 cm 2. What is the area in square meters? Check the Solution: Information Given:2,659 cm 2 Find:? m 2 Conv. Fact.1 cm = 0.01 m Sol’n Map:cm 2  m 2 Tro's Introductory Chemistry, Chapter 285 2,659 cm 2 = m 2 The units of the answer, m 2, are correct. The magnitude of the answer makes sense since square centimeters are smaller than square meters.

Density ?v=5QWXLZ91DUM&feature =related

Mass & Volume two main characteristics of matter cannot be used by themselves to identify what type of matter something is ◦ if you are given a large glass containing 100 g of a clear, colorless liquid and a small glass containing 25 g of a clear, colorless liquid - are both liquids the same stuff? even though mass and volume are individual properties - for a given type of matter they are related to each other! Tro's Introductory Chemistry, Chapter 287

Mass vs Volume of Brass Brass Tro's Introductory Chemistry, Chapter 288

Tro's Introductory Chemistry, Chapter 289 Volume vs Mass of Brass y = 8.38x Volume, cm3 Mass, g

Density Ratio of mass:volume Solids = g/cm 3 ◦ 1 cm 3 = 1 mL Liquids = g/mL Gases = g/L Volume of a solid can be determined by water displacement – Archimedes Principle Density : solids > liquids >>> gases ◦ except ice is less dense than liquid water! Tro's Introductory Chemistry, Chapter 290

Density For equal volumes, denser object has larger mass For equal masses, denser object has smaller volume Heating objects causes objects to expand ◦ does not effect their mass!! ◦ How would heating an object effect its density? In a heterogeneous mixture, the denser object sinks ◦ Why do hot air balloons rise? Tro's Introductory Chemistry, Chapter 291

Using Density in Calculations Tro's Introductory Chemistry, Chapter 292 Solution Maps: m, VD m, DV V, Dm

Platinum has become a popular metal for fine jewelry. A man gives a woman an engagement ring and tells her that it is made of platinum. Noting that the ring felt a little light, the woman decides to perform a test to determine the ring’s density before giving him an answer about marriage. She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces cm 3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm 3 ) Tro's Introductory Chemistry, Chapter 293

She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces cm 3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm 3 ) Tro's Introductory Chemistry, Chapter 294 Given: Mass = 5.84 grams Volume = cm 3 Find: Density in grams/cm 3 Equation: Solution Map: m and V  d

She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces cm 3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm 3 ) Tro's Introductory Chemistry, Chapter 295 Apply the Solution Map: Since 10.5 g/cm 3  21.4 g/cm 3 the ring cannot be platinum

Density as a Conversion Factor can use density as a conversion factor between mass and volume!! ◦ density of H 2 O = 1 g/mL  1 g H 2 O = 1 mL H 2 O ◦ density of Pb = 11.3 g/cm 3  11.3 g Pb = 1 cm 3 Pb How much does 4.0 cm 3 of Lead weigh? Tro's Introductory Chemistry, Chapter 296 = 4.0 cm 3 Pb 11.3 g Pb 1 cm 3 Pb 45 g Pb x

Measurement and Problem Solving Density as a Conversion Factor The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of g/cm 3. What is the volume? Given: 60.0 kg Find: Volume in L Conversion Factors: ◦ grams/cm 3 ◦ 1000 grams = 1 kg Tro's Introductory Chemistry, Chapter 297

Measurement and Problem Solving Density as a Conversion Factor Solution Map: kg  g  cm 3 Tro's Introductory Chemistry, Chapter 298

Example 2.16:Density as a Conversion Factor

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Tro's Introductory Chemistry, Chapter 2100

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Write down the given quantity and its units. Given:m = 55.9 kg V = 57.2 L Tro's Introductory Chemistry, Chapter 2101

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Write down the quantity to find and/or its units. Find: density, g/cm 3 Information Given:m = 55.9 kg V = 57.2 L Tro's Introductory Chemistry, Chapter 2102

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Design a Solution Map: Information: Given:m = 55.9 kg V = 57.2 L Find: density, g/cm 3 Tro's Introductory Chemistry, Chapter 2103 m, V D

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Collect Needed Conversion Factors:  Mass:1 kg = 1000 g  Volume:1 mL = L; 1 mL = 1 cm 3 Information: Given:m = 55.9 kg V = 57.2 L Find: density, g/cm 3 Equation: Tro's Introductory Chemistry, Chapter 2104

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Write a Solution Map for converting the Mass units Write a Solution Map for converting the Volume units Information: Given:m = 55.9 kg V = 57.2 L Find: density, g/cm 3 Solution Map:m,V  D Equation: Conversion Factors: 1 kg = 1000 g 1 mL = L 1 mL = 1 cm kgg LmLcm 3

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Apply the Solution Maps Information: Given:m = 55.9 kg V = 57.2 L Find: density, g/cm 3 Solution Map:m,V  D Equation: Tro's Introductory Chemistry, Chapter 2106 = 5.59 x 10 4 g

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Apply the Solution Maps Information: Given:m = 5.59 x 10 4 g V = 57.2 L Find: density, g/cm 3 Solution Map:m,V  D Equation: Tro's Introductory Chemistry, Chapter 2107 = 5.72 x 10 4 cm 3

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Apply the Solution Maps - Equation Information: Given:m = 5.59 x 10 4 g V = 5.72 x 10 4 cm 3 Find: density, g/cm 3 Solution Map:m,V  D Equation: 108 = g/cm 3 = g/cm 3

Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm 3 ? Check the Solution Information: Given:m = 5.59 x 10 4 g V = 5.72 x 10 4 cm 3 Find: density, g/cm 3 Solution Map:m,V  D Equation: 109 The units of the answer, g/cm 3, are correct. The magnitude of the answer makes sense. Since the mass in kg and volume in L are very close in magnitude, the answer’s magnitude should be close to 1. D = g/cm 3

110 Energy there are things that do not have mass and volume these things fall into a category we call Energy Energy is anything that has the capacity to do work even though Chemistry is the study of matter, matter is effected by energy ◦ it can cause physical and/or chemical changes in matter

111 Law of Conservation of Energy “Energy can neither be created nor destroyed” the total amount of energy in the universe is constant – there is no process that can increase or decrease that amount however we can transfer energy from one place in the universe to another, and we can change its form

112 Kinds of Energy Kinetic and Potential Kinetic Energy is energy of motion, or energy that is being transferred from one object to another Potential Energy is energy that is stored

113 Some Forms of Energy Electrical ◦ kinetic energy associated with the flow of electrical charge Heat or Thermal Energy ◦ kinetic energy associated with molecular motion Light or Radiant Energy ◦ kinetic energy associated with energy transitions in an atom Nuclear ◦ potential energy in the nucleus of atoms Chemical ◦ potential energy in the attachment of atoms or because of their position

114 Units of Energy calorie (cal) is the amount of energy needed to raise one gram of water by 1°C ◦ kcal = energy needed to raise 1000 g of water 1°C ◦ food Calories = kcals Energy Conversion Factors 1 calorie (cal)=4.184 joules (J) 1 Calorie (Cal)=1000 calories (cal) 1 kilowatt-hour (kWh)=3.60 x 10 6 joules (J)

115 The Meaning of Heat Heat is the exchange of thermal energy between samples of matter heat flows from the matter that has high thermal energy to matter that has low thermal energy ◦ until … heat is exchanged through molecular collisions between two samples

116 The Meaning of Temperature Temperature is a measure of the average kinetic energy of the molecules in a sample Not all molecules in a sample have the same amount of kinetic energy higher temperature means a larger average kinetic energy

117 Temperature Scales CelsiusKelvinFahrenheit -273°C -269°C -183°C -38.9°C 0°C 100°C 0 K 4 K 90 K K 273 K 373 K -459 °F -452°F -297°F -38°F 32°F 212°F Absolute Zero BP Helium BP Oxygen BP Mercury MP Ice BP Water Room Temp 25°C 298 K75°F

118 Fahrenheit vs. Celsius a Celsius degree is 1.8 times larger than a Fahrenheit degree the standard used for 0° on the Fahrenheit scale is a lower temperature than the standard used for 0° on the Celsius scale

119 The Kelvin Temperature Scale both the Celsius and Fahrenheit scales have negative numbers ◦ but real physical things are always positive amounts! the Kelvin scale is an absolute scale, meaning it measures the actual temperature of an object 0 K is called Absolute Zero. It is too cold for matter to exist at because all molecular motion would stop ◦ 0 K = -273°C = -459°F ◦ Absolute Zero is a theoretical value obtained by following patterns mathematically

120 Kelvin vs. Celsius the size of a “degree” on the Kelvin scale is the same as on the Celsius scale ◦ we don’t call the divisions on the Kelvin scale degrees; we called them kelvins! ◦ But the Kelvin scale starts at a much lower temperature – absolute zero

121 Energy and the Temperature of Matter Increase in temperature of an object depends on the amount of heat added (q). ◦ If you double the added heat energy the temperature will increase twice as much. Increase in temperature of an object ALSO depends on its mass (m) ◦ If you double the mass it will take twice as much heat energy to raise the temperature the same amount.

122 Heat Capacity heat capacity is the amount of heat a substance must absorb to raise its temperature 1°C ◦ cal/°C or J/°C ◦ metals have low heat capacities, insulators high specific heat = heat capacity of 1 gram of the substance ◦ cal/g°C or J/g°C ◦ waters specific heat = J/g°C for liquid  or cal/g°C  less for ice and steam

123 Specific Heat Capacity Specific Heat is the amount of energy required to raise the temperature of one gram of a substance by one Celsius degree the larger a material’s specific heat is, the more energy it takes to raise its temperature a given amount like density, specific heat is a property of the type of matter ◦ it doesn’t matter how much material you have ◦ it can be used to identify the type of matter water’s high specific heat is the reason it is such a good cooling agent ◦ it absorbs a lot of heat for a relatively small mass

124 Specific Heat Capacities

125 Heat Gain or Loss by an Object the amount of heat energy gained or lost by an object depends on 3 factors – how much material there is, what the material is, and how much the temperature changed Amount of Heat = Mass x Heat Capacity x Temperature Change q = m x C x  T

126 Example: How much heat must 2.5 g of gallium absorb from your hand to raise its temperature from 25.0°C to 29.9°C? The heat capacity of gallium is J/g°C

127 Example: If the temperature of 28 g of ethanol increases from 15°C to 65.5°C, how much heat was absorbed by the ethanol? (Specific heat ethanol = 2.44 J/g°C)

128 Bomb Calorimeter

129 Video Specific Heat Specific Heat Video