Ch. 2: Measurement, Problem Solving, and the Mole Concept

Dr. Namphol Sinkaset

Chem 200: General Chemistry I

I. Chapter Outline

I. Introduction

II. Measurements and Certainty

III. Significant Figures

IV. Accuracy vs. Precision

V. Energy and Its Units

VI. Unit Conversions and Density

VII. The Mole

I. $125 Million Calculation Error

II. Reporting Measurements

• Scientists report measurements with certainty reflected in the number of digits. e.g. Age of the universe: 13.7 billion years

vs. 14 billion years Uncertainty is understood to be ±1 in the

last digit. Thus, the last digit is always an estimate.

II. Getting the Estimate

• We obtain the last estimated digit by reading between the graduations on an instrument.

• Often, glassware will indicate which decimal place should be estimated.

II. Sample Problem

• What is the temperature reading on the thermometer below?

III. Uncertainty in Measurement

• If we always estimate between lines, then quantities cannot be measured exactly.

• Thus, every measurement carries uncertainty in the last digit.

III. Significant Figures

• The number of certain and uncertain figures in a measurement is the number of significant figures (sig figs) in that measurement.

III. Determining Sig Figs

1. All nonzero numbers are significant: 27622. Zeros in between nonzero numbers are

significant: 1001 or 20.00043. Leading zeros are not significant: 0.000464. Trailing zeros…

a) Are significant after a decimal point: 45.0 or 3.560b) Are significant before a decimal point: 10. or 140.00c) Are significant if indicated with a bar: 6200d) Are ambiguous* before implied decimal point: 1200

III. Exact Numbers

• Exact numbers have no ambiguity (because they are not measured) and therefore, have an “infinite” number of sig figs.

• These include counts, defined quantities, and integers in an equation.

• e.g. 5 pencils, 1000 m in 1 km, C = 2πr.

III. Sample Problem• Indicate the number of sig figs in the

following measurements.

a) 2.036 cmb) 20 mLc) 6.720 x 103 kmd) 7920 gallonse) 135,001,000 cif) 0.0000260 Lg) 820. Wh) 1.000 x 1021 J

III. Calculations w/ Sig Figs

• When doing calculations with measurements, it’s important that we don’t have an answer w/ more certainty (sig figs) than what we started with.

• Sig figs are handled based on what math operation is being performed.

III. Rounding Rules1. Round up if preceding digit is > 5.2. Don’t round up if preceding digit is < 5.3. If preceding digit is 5, round up only if it will

make the number even. If there are more digits after the 5, follow this rule only if all of the extra digits after the 5 are zeros.

• e.g. For 3 sig figs, 17.75 17.8, but 17.65 17.6

• e.g. For 3 sig figs, 17.65000000 17.6, but 17.65000001 17.7

4. For multi-step calcs, avoid rounding at intermediate steps or be sure to carry extra digits and round at the end.

III. Multiplication/Division

• The answer is limited by the number with the least sig figs.

• e.g. 1.0235 x 7.123 x 3 = ?

III. Addition/Subtraction

• The answer is limited by the number with the fewest places. *Note that the number of sig figs could increase or decrease.

• e.g. Add 83.5 and 23.28.

• e.g. Subtract 65.2 from 72.31.

III. Addition/Subtraction

• Addition and subtraction operations could involve numbers without decimal places.

• The general rule is: “The number of significant figures in the result of an addition/subtraction operation is limited by the least precise number.”

III. Multi-Step Calculations

• Keep track of the number of sig figs using dropped digit, underline, or bar method.

6.2

6.2

44.0903.501.54562.5903.5

339186

62

III. Sample Problem

• Perform the following calculations to the correct number of sig figs.1. (85.3 – 21.489) ÷ 0.0059

2. (12.01 × 0.3) + 4.811

IV. The “Right” Answer

• The correctness of a measurement can be determined IF the actual value is known.

• In this case, we can speak of the accuracy of a measurement.

• Accuracy refers to how close a measured value is to the actual value.

IV. Multiple Trials

• What if the measurement has never been done in human history?

• We repeat the measurement to see if we keep getting the same value.

• Precision refers to how close measurements are to one another or how reproducible they are.

• High experimental precision indicates the measurement may be correct.

IV. Possible Outcomes

• All measurements are subject to random error (equal chance of being high or low).

• Poor technique or miscalibrated equipment leads to systematic error (values consistently too high or too low).

V. Energy• Physical and chemical changes are

accompanied by energy changes• energy: the capacity to do work• work: force acting through a distance• At its core, energy involves moving something.

V. Two Types of Energy

• potential energy (PE): energy due to the position or composition of an object

• kinetic energy (KE): energy due to motion of an object

• An object’s total energy is the sum of its PE and KE

V. Energy Conversions

• The Law of Conservation of Energy states that energy is neither created nor destroyed.

• Explain how energy is conserved in the diagram.

V. Chemical PE

• chemical potential energy: the PE of a substance that results from the relative positions and attractions and repulsions among all its particles

• Naturally, some substances have more chemical PE than others

• e.g. gasoline/food have more than their waste products

V. Relationship Between PE and KE

V. Relationship between PE and KE

• e.g. Draw a potential energy diagram involving two positively-charged spheres.

V. Energy Units

• The units of energy can be determined by looking at the equation for KE.

V. The Joule and the Calorie

• These combination of fundamental SI units is the derived SI unit known as the joule (J). 1 kg·m2/s2 = 1 J.

• Sometimes, energy is given in calories (cal), initially defined as heat needed to raise temp. of 1 g of water by 1 °C.

• Note that calorie ≠ Calorie!• Also, 1 cal = 4.184 J.

V. Typical Energy Values

V. System and Surroundings

• Since energy is conserved, it is only transferred between two objects/places.

• We need to define points of view to observe where energy goes.

• system: part of universe we are observing

• surroundings: anything with which system can interact

V. Energy Exchanges

• If a system loses energy, then the surroundings must gain that energy.

V. Exothermic/Endothermic

• When a system loses energy, the process is exothermic, and the energy change is negative.

• When a system gains energy, the process is endothermic, and the energy change is positive.

VI. Dimensional Analysis• Often, conversion factors are needed to

solve a problem.• conversion factor: fraction used to

express a measured quantity in different units

• For the equivalency statement “5280 feet are in 1 mile,” two conversion factors are possible.

1 mi

5280 ft5280 ft

1 miOR

VI. Conversion Factors

• e.g. Convert 120 miles to cm. Note that 1 in = 2.54 cm exactly.

• TO ENSURE MAXIMUM PARTIAL CREDIT YOU SHOULD SHOW THIS TECHNIQUE!!

VI. Density

• The density of a substance is ratio of its mass to its volume.

• Density is a characteristic physical property of a substance.

• Density is an intensive property (as opposed to an extensive property).

VI. Density

• Density is a ratio of a substances mass to its volume (units of g/mL or g/cm3 are most common).

• To calculate density, you just need an object’s mass and its volume.

VI. Density as a Conversion Factor

• Since density is a ratio between mass and volume, it can be used to convert between these two units.

• If the density of water is 1.0 g/mL, the complete conversion factor is:

watermL 1.0

waterg 1.0

VI. Sample Problem

• If the density of mercury is 13.55 g/mL, how many liters are needed in order to have 1200 g of mercury?

VII. How Much vs. How Many

• Countable vs. not countable• In the lab, we say, “How much water do

we need?”• However, matter is particulate, so it is

countable.• When matter interacts, it does so on a

particle by particle basis.

VII. Using Mass to “Count”

• We can relate counts to mass. e.g. 21-30 shrimp vs. 8-10 shrimp

• In chemistry, we use the mole. A mole is the amount of material that

contains 6.02214 × 1023 particles. Defined by the # of atoms in exactly 12 g of

pure carbon-12. This number is Avogadro’s number.

VII. Avogadro’s Number

• We can use Avogadro’s number as a conversion factor to calculate # of atoms.

6.022 x 1023 atoms

1 mole atoms 6.022 x 1023 atoms

1 mole atomsOR

VII. Grams and Moles• The mass of 1 mole of atoms of an

element is its molar mass. The value of an element’s molar mass in g/mole is numerically equal to the element’s atomic mass in amu (from periodic table).

• In general, one mole scales up to a “touchable” amount of an element or molecule.

VII. Mole of Atoms & Compounds

• 1 Fe atom weighs 55.85 amu, so 1 mole of Fe atoms weighs 55.85 g.

• 1 O atom weighs 16.00 amu, so 1 mole of O atoms weighs 16.00 g.

• Same applies for compounds. 1 molecule H2O weighs 18.02 amu, so 1

mole H2O weighs 18.02 g.

VII. Sample Problems

• If a silicon chip has a mass of 5.89 mg, how many Si atoms are in the chip?