Ch. 2: Measurement and Ch. 2: Measurement and Problem SolvingProblem Solving

Dr. Namphol Sinkaset

Chem 152: Introduction to General Chemistry

I. Chapter OutlineI. Chapter Outline

I. Introduction

II. Scientific Notation

III. Significant Figures

IV. Units of Measurement

V. Unit Conversions

VI. Density as a Conversion Factor

I. IntroductionI. Introduction

• Global warming measurement.

• Value?

• Method?

• Uncertainty?

II. Scientific NotationII. Scientific Notation

• Science deals with the very large and the very small.

• Writing large/small numbers becomes very tedious, e.g. 125,200,000,000.

• Scientific notation is a shorthand method of writing numbers.

II. Scientific NotationII. Scientific Notation

• Scientific notation consists of three different parts.

II. Converting to Scientific II. Converting to Scientific NotationNotation

II. Steps for Writing Scientific II. Steps for Writing Scientific NotationNotation

1. Move decimal point to obtain a number between 1 and 10.

2. Write the result of Step 1 multiplied by 10 raised to the number of places you moved the decimal point.a) If decimal point moved left, use positive

exponent.

b) If decimal point moved right, use negative exponent.

II. Practice with Scientific II. Practice with Scientific NotationNotation

• Express the following in proper scientific notation.a) 3,677,000,000

b) 0.00024709

c) 93

d) 0.004

e) 0.0040

III. Measurement in ScienceIII. Measurement in Science

• Measurements are written to reflect the uncertainty in the measurement.

• A “scientific” measurement is reported such that every digit is certain except the last, which is an estimate.

III. Reading a ThermometerIII. Reading a Thermometer

• e.g. What are the temperature readings below?

III. Uncertainty in III. Uncertainty in MeasurementMeasurement

• Quantities cannot be measured exactly, so every measurement carries some amount of uncertainty.

• When reading a measurement, we always estimate between lines – this is where the uncertainty comes in.

III. Significant FiguresIII. Significant Figures

• The non-place-holding digits in a measurement are significant figures (sig figs).

• The sig figs represent the precision of a measured quantity.

• The greater the number of sig figs, the better the instrument used in the measurement.

III. Determining Sig FigsIII. Determining Sig Figs1. All nonzero numbers are significant.2. Zeros in between nonzero numbers are

significant.3. Trailing zeros (zeros to the right of a

nonzero number) that fall AFTER a decimal point are significant.

4. Trailing zeros BEFORE a decimal point are not significant unless indicated w/ a bar over them or an explicit decimal point.

5. Leading zeros (zeros to the left of the first nonzero number) are not significant.

III. Exact NumbersIII. Exact Numbers

• Exact numbers have no ambiguity 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. Determining Sig FigsIII. Determining Sig Figs• e.g. Indicate the number of sig figs in

the following.

a) 2.036b) 20c) 6.720 x 103

d) 7920e) 135,001,000f) 0.0000260g) 820.h) 1.000 x 1021

III. Calculations w/ Sig FigsIII. 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. MultiplicationIII. Multiplication

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

III. DivisionIII. Division

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

III. AdditionIII. Addition• The answer has the same number of

PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

III. SubtractionIII. Subtraction• The answer has the same number of

PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

III. Addition/SubtractionIII. 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. RoundingIII. Rounding

• When rounding, consider only the last digit being dropped; ignore all following digits.

• Round down if last digit is 4 or less.• Round up if last digit is 5 or more.• e.g. Rounding 2.349 to the tenths place

results in 2.3!

III. Sample ProblemsIII. Sample Problems

• Evaluate the following to the correct number of sig figs.a) 1.10 0.0025 31.09 3.0540 = ?

b) 89.456 0.000005 = ?

c) 94.25 + 20.4 = ?

d) 20 + 273.15 = ?

e) 25.432567 – 73.259 = ?

f) 1252 – 360 = ?

III. Mixed OperationsIII. Mixed Operations

• In calculations involving both addition/subtraction and multiplication/division, we evaluate in the proper order, keeping track of sig figs.

• DO NOT ROUND IN THE MIDDLE OF A CALCULATION!!

• Carry extra digits and round at the end.• e.g. 3.897 (782.3 – 451.88) = ?

III. Sample ProblemsIII. Sample Problems

• Evaluate the following to the correct number of sig figs.a) (568.99 – 232.1) 5.3 = ?

b) (9443 + 45 – 9.9) 8.1 106 = ?

c) (455 407859) + 1.00098 = ?

d) (908.4 – 3.4) 3.52 104 = ?

IV. UnitsIV. Units

• All measured quantities have a number and a unit!!!!

• Without a unit, a number has no meaning in science.

• e.g. The string was 8.2 long.• ANY ANSWER GIVEN W/OUT A UNIT

WILL BE GRADED HARSHLY.

IV. International System of IV. International System of UnitsUnits

• More commonly known as SI units.

• Based on the metric system which uses a set of prefixes to indicate size.

• There are a set of standard SI units for fundamental quantities.

IV. Prefix MultipliersIV. Prefix Multipliers

IV. Derived UnitsIV. Derived Units

• Combinations of fundamental units lead to derived units.

• e.g. volume, which is a measure of space, needs three dimensions of length, or m3.

• e.g. speed, distance covered over time, m/s.

V. Unit ConversionsV. Unit Conversions

• Problem solving is a big part of chemistry.

• Converting between different units is the first type of problem we will cover.

• Problems in chemistry generally fall into two categories: unit conversions or equation-based.

V. Units in CalculationsV. Units in Calculations

• Always carry units through your calculations; don’t drop them and then add them back in at the end.

• Units are just like numbers; they can be multiplied, divided, and canceled.

• Unit conversions involve what are known as conversion factors.

V. General ConversionsV. General Conversions

• Typically, we are given a quantity in some unit, and we must convert to another unit.

unit desiredunitgiven

unit desiredunit given

soughtn informatio factor(s) conversiongiven n informatio

V. Conversion FactorsV. Conversion Factors

• conversion factor: ratio 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

V. Conversion ExampleV. Conversion Example

• If 1 in equals 2.54 cm, convert 24.8 inches to centimeters.

cm 9.62in 1

cm 2.54in 24.8

unit desiredunitgiven

unit desiredunit given

992

V. Conversion FactorsV. Conversion Factors

V. Sample ProblemsV. Sample Problems

• Perform the following multistep unit conversions.a) Convert 2400 cm to feet.

b) Convert 10 km to inches.

c) How many cubic inches are there in 3.25 yd3?

VI. DensityVI. 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 ProblemVI. Density Problem

• Density differs between substances, so it can be used for identification.

• If a ring has a mass of 9.67 g and displaces 0.452 mL of water, what is it made of?

VI. Density as a Conversion VI. Density as a Conversion FactorFactor

• 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 ProblemVI. Sample Problem

• If the density of ethanol is 0.789 g/mL, how many liters are needed in order to have 1200 g of ethanol?