Presentation Ch. 2 CHM 160
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Chapter 2: Measurement, Problem Solving, and the Mole Concept 2.1: The Metric Mix-up: A $125 Million Unit Error 1998 – Mars Climate Orbiter • Onboard Computers programmed in metric • Ground engineers working in English units • Corrections to trajectory 4.45 times too small • Orbiter burned up in Mars’ atmosphere © 2015 Pearson Education, Inc. The Standard Units of Measurement • Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units ✓ Système International = International System © 2015 Pearson Education, Inc. Temperature • Measure of the average amount of kinetic energy caused by motion of the particles ✓ higher temperature = larger average kinetic energy • Heat flows from the matter that has ___________________ __________________________________________________ ✓ heat flows from hot object to cold ✓ heat is exchanged through molecular collisions between the two materials © 2015 Pearson Education, Inc. Temperature Scales • Fahrenheit scale, °F ✓ used in the U.S. • Celsius scale, °C ✓ used in all other countries • Kelvin scale, K ✓ absolute scale ➢no negative numbers ✓ _____________________ _______________________ _______________________ ✓ 0 K = absolute zero 4 © 2015 Pearson Education, Inc. Common Prefix Multipliers in the SI System © 2015 Pearson Education, Inc. Volume • Measure of the amount of space occupied • SI unit = cubic meter (m3) • Commonly measure solid volume in cubic centimeters (cm3) • Commonly measure liquid or gas volume in milliliters (mL) ✓1 L is slightly larger than 1 quart ✓1 L = 1 dm3 = 1000 mL = 103 mL ✓1 mL = 0.001 L = 10−3 L ✓ 1 mL = 1 cm3 © 2015 Pearson Education, Inc. Measurement and Significant Figures © 2015 Pearson Education, Inc. What Is a Measurement? • Quantitative observation • Comparison to an agreed • standard Every measurement has a number and a unit • The unit tells you what standard • you are comparing your object to The number tells you • what multiple of the standard the object measures • the uncertainty in the measurement © 2015 Pearson Education, Inc. Reliability of Measurements: Precision and Accuracy • Uncertainty comes from limitations of the instruments used for comparison, the experimental design, the experimenter, and nature’s random behavior • To understand how reliable a measurement is, we need to understand the limitations of the measurement • Accuracy _________________________________________________ _________________________________________________ _________________________________________________ • Precision is an indication of how close repeated measurements are to each other ✓ how reproducible a measurement is © 2015 Pearson Education, Inc. Precision and Accuracy • Measurements are said to be • precise if they are consistent with one another; • accurate only if they are close to the actual value. • Scientific measurements are reported so that _________ _______________________________________________ Consider the following reported value of 5.213: • The first three digits are certain; the last digit is estimated. Estimated value 5.213 Known with certainty © 2015 Pearson Education, Inc. © 2015 Pearson Education, Inc. Precision and Accuracy Example 2.1 Reporting the Correct Number of Digits. The graduated cylinder shown here has markings every 0.1 mL. Report the volume (which is read at the bottom of the meniscus) to the correct number of digits. © 2015 Pearson Education, Inc. Precision and Accuracy: An Illustration Problem Consider the results of three students who repeatedly weighed a lead block known to have a true mass of 10.00 g. © 2015 Pearson Education, Inc. Precision and Accuracy: An Illustration Problem Consider the results of three students who repeatedly weighed a lead block known to have a true mass of 10.00 g. From the above data, what can you conclude about each of the students’ recorded data? © 2015 Pearson Education, Inc. Precision and Accuracy: An Illustration Problem Lead block known to have a true mass of 10.00 g • Student A’s results are both _______________ (not close to the true value) and ____________________ (not consistent with one another). – Random error ___________________________________________________________ ___________________________________________________________ • Student B’s results are _____________ (close to one another in value) but _______________________. – Systematic error ___________________________________________________________ ___________________________________________________________ • Student C’s results display little systematic error or random error—they are both ___________________ and _________________. © 2015 Pearson Education, Inc. Significant Figures • Significant figures deal with writing numbers to reflect precision of their ___________________________. • The precision of a measurement depends on the instrument used to make the measurement. • The preservation of this precision during calculations can be accomplished by using significant figures. • The greater the number of significant figures, the greater the certainty of the measurement. © 2015 Pearson Education, Inc. Significant Figures • The non-place-holding digits in a reported measurement are called significant figures ✓ some zeros 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 © 2015 Pearson Education, Inc. 12.3 cm has 3 sig. figs. and its range is 12.2 to 12.4 cm 12.30 cm has 4 sig. figs. and its range is 12.29 to 12.31 cm Rules of Significant Figures 1. Nonzero digits are always significant. 96 61.4 2 significant digits 3 significant digits 2. Zeros that are “sandwiched” between nonzero digits are significant. 5.02 6004 3 significant digits 4 significant digits 3. Zeros used as placeholders are NOT significant. 7000 0.00783 1 significant digit 3 significant digits 4. One or more final zeros used after the decimal point are significant. 4.7200 0.250 © 2015 Pearson Education, Inc. 5 significant digits 3 significant digits Using Significant Figures in Mathematical Operations: Multiplication and Division: The answer has the same number of significant figures as the least precise factor in the calculations. 3.05 x 3 sig figs 1.3 = 2 sig figs 9.247 g (4 sig figs) 13.5 cm3 (3 sig figs) © 2015 Pearson Education, Inc. = 3.965 = answer in calc 4.0 correct ans w/ 2 sig figs .684962= (ans in calc) 0.685 g correct ans cm3 w/ 3 sig figs Review How many significant figures are in each of the following? 0.04450 m 5.0003 km 10 dm = 1 m 1.000 × 105 s 0.00002 mm 10,000 m © 2015 Pearson Education, Inc. Exact Numbers • Exact numbers have an unlimited number of significant figures. • Exact counting of discrete objects • Integral numbers that are part of an equation • Defined quantities • Some conversion factors are defined quantities, while others are not. © 2015 Pearson Education, Inc. Intensive and Extensive Properties • Extensive properties are properties whose value depends on amount of the substance ✓extensive properties cannot be used 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? • Intensive properties are properties whose value is independent of the amount of the substance ✓intensive properties are often used to identify the type of matter ➢samples with identical intensive properties are usually the same material © 2015 Pearson Education, Inc. Density Density = mass volume Density (d) = m V Density is a physical property: the ratio of mass to volume – is an intensive property • The physical properties of mass and volume that determine a substance’s density are EXTENSIVE. – Units of Density • Solids = g/cm3 Liquids = g/mL Gases = g/L ✓ 1 cm3 = 1 mL • Volume of a solid can be determined by water displacement • Density : solids > liquids >>> gases ✓ except ice is less dense than liquid water! © 2015 Pearson Education, Inc. Density • For equal volumes, denser object has larger mass • For equal masses, denser object has smaller volume • Heating an object generally causes it to expand, therefore the density changes with temperature © 2015 Pearson Education, Inc. Calculations and Solving Chemical Problems • Many problems in science involve using relationships to convert one unit of measurement to another – unit conversion problems. • Using units as a guide to solving problems is – dimensional analysis. • Units should always be included in calculations; they are multiplied, divided, and canceled like any other algebraic quantity. © 2015 Pearson Education, Inc. Dimensional Analysis • A unit equation is a statement of two equivalent quantities, such as 2.54 cm = 1 in. • A conversion factor is a unit equation written in fraction form with the units we are converting from on the bottom and the units we are converting to on the top. or • Conversion factors are relationships between two units ✓ may be exact or measured © 2015 Pearson Education, Inc. Problem Solving and Dimensional Analysis • Arrange conversion factors so the starting unit cancels ✓ arrange conversion factors so the starting unit is on the bottom of the first conversion factor • May string conversion factors ✓ so you do not need to know every relationship, as long as you can find something else the starting and desired units are related to © 2015 Pearson Education, Inc. Dimensional Analysis Units Raised to a Power: • When building conversion factors for units raised to a power, remember to raise both the number and the unit to the power. For example, to convert from square inches to square centimeters, we construct the conversion factor as follows: © 2015 Pearson Education, Inc. Problem Solving: Dimensional Analysis Example: The engineers involved in the Mars Climate Orbiter disaster entered the trajectory corrections in units of pound·second. Which conversion factor should they have multiplied their values by to conver them to the correcdt uniots of newton.second? (1 pound·second = 4.45 newton·second) © 2015 Pearson Education, Inc. Problem-Solving Strategy • Identify the starting point (the given information). – Sort out information given in the problem. • Identify the endpoint (what we must find). – What is the problem asking you to solve for? What units does the answer need? • Devise a way to use the given information to get the answer. • Solve: – Most chemistry problems you will solve in this course are unit conversion problems. – Using units as a guide to solving problems (dimensional analysis) • Units should always be included in calculations; they are multiplied, divided, and canceled like any other algebraic quantity. • Check whether the numerical value and its units make sense. © 2015 Pearson Education, Inc. Example 2.3: Convert 1.76 yards to centimeters. Note: 1.094 yd = 1m and 1 cm = 10-2 m 1. Sort into a. Given b. Find 2. Strategize: Devise a conceptual plan from the given units, using the appropriate conversion factors and ending with the desired units. 3. Solve: Begin with the given quantity. Multiply by the appropriate conversion factors, canceling units to arrive at the find quantity. Round to correct number of significant figures. 4. Check: Correct units? Does the answer make sense? © 2015 Pearson Education, Inc. 1. Sort 2. Strategize 3. Solve 4. Check © 2015 Pearson Education, Inc. 1. Sort 2. Strategize 3. Solve 4. Check © 2015 Pearson Education, Inc. 1. Sort 2. Strategize 3. Solve 4. Check © 2015 Pearson Education, Inc. 1. Sort 2. Strategize 3. Solve 4. Check © 2015 Pearson Education, Inc. Moles © 2015 Pearson Education, Inc. Counting Atoms by Moles • If we can find the mass of a particular number of atoms, we can use this information to convert the mass of an element sample into the number of atoms in the sample • A mole (mol) of anything contains 6.02214 × 1023 of those things. – Examples: • 1 mol of marbles corresponds to 6.02214 × 1023 marbles. • 1 mol of sand grains corresponds to 6.02214 × 1023 sand grains. • This number is Avogadro’s number. © 2015 Pearson Education, Inc. Chemical Packages - The Mole • Mole = number of particles equal to the number of atoms in 12 g of C-12 ✓ 1 atom of C-12 weighs exactly 12 amu ✓ 1 mole of C-12 weighs exactly 12 g • The number of particles in 1 mole is called Avogadro’s Number = 6.0221421 x 1023 ✓ 1 mole of C atoms weighs 12.01 g and has 6.022 x 1023 atoms ➢ the average mass of a C atom is 12.01 amu © 2015 Pearson Education, Inc. Mole Conversions: Atoms to Moles or Moles to Atoms • Converting between number of moles and number of atoms is similar to converting between dozens of eggs and number of eggs. • For atoms, you use the conversion factor 1 mol atoms = 6.022 × 1023 atoms. • The conversion factors take the following forms: © 2015 Pearson Education, Inc. Practice — A silver ring contains 1.1 x 1022 silver atoms. How many moles of silver are in the ring? © 2015 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 40 Converting between Mass and Amount (Number of Moles) • To count atoms by weighing them, we need one other conversion factor—the mass of 1 mol of atoms. • The mass of 1 mol of atoms of an element is the molar mass. • An element’s molar mass in grams per mole is numerically equal to the element’s atomic mass in atomic mass units (amu). • The lighter the atom, the less a mole weighs • The lighter the atom, the more atoms there are in 1g © 2015 Pearson Education, Inc. Mole and Mass Relationships 1 mole sulfur 32.06 g © 2015 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 1 mole carbon 12.01 g 42 Converting between Mass and Moles • The molar mass of any element is the conversion factor between the mass (in grams) of that element and the amount (in moles) of that element. • Example: 12.01 g C atoms = 1 mol C atoms or 12.01 g C atoms/1 mol C atoms or 1 mol C atoms/12.01 g C atoms © 2015 Pearson Education, Inc. © 2015 Pearson Education, Inc. 44 Mass to Moles to Number of Particles: The Conceptual Plan For an element, Mass of element (grams) Moles of element Divide by atomic mass Number of atoms Multiply by Avogadro’s number For a molecule (compound), Moles of molecules Mass of molecule (grams) Divide by molar mass © 2015 Pearson Education, Inc. Number of molecules Multiply by Avogadro’s number Number of Particles to Moles to Mass: The Conceptual Plan For an element, Number of atoms Mass of element (grams) Moles of element Multiply by atomic mass Divide by Avogadro’s number For a molecule (compound), Moles of molecules Number of molecules Divide by Avogadro’s number © 2015 Pearson Education, Inc. Mass of molecule (grams) Multiply by molar mass Practice — Calculate the moles of sulfur in 57.8 g of sulfur © 2015 Pearson Education, Inc. 47 Practice — How many aluminum atoms are in a can weighing 16.2 g? © 2015 Pearson Education, Inc. 48
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