CHAPTER 2 Metric System. THE METRIC SYSTEM Measuring The numbers are only half of a measurement. It...

CHAPTER 2Metric System

THE METRIC SYSTEM

Measuring• The numbers are only half of a measurement.• It is 10 long.• 10 what?• Numbers without units are meaningless.• How many feet in a yard?• A mile?• A rod?

The Metric System

• Easier to use because it is a decimal system.• Every conversion is by some power of 10.• A metric unit has two parts.• A prefix and a base unit.• prefix tells you how many times to divide or multiply by 10.

Length meter m

Mass gram g

Time Second s

Temperature Kelvin K

Amount of a substance

Mole Mol

Volume Liter L

Length - straight distance between two points-Meters (m) Mass - how much matter in an object-grams (g) Volume - amount of space taken up by an objectCubic meters (m3) or -Liters (L)

Base Units

• Length - meter - more than a yard - m• Mass - grams - about a raisin - g• Time - second - s• Temperature - Kelvin or ºCelsius K or ºC• Energy - Joules- J• Volume - Liter - half of a two liter bottle- L• Amount of substance - mole - mol

Metric System

Prefixes convert the base units into units that are appropriate for the item being measured.

© 2009, Prentice-Hall, Inc.

Kilo- Hecta- Deka- UNITS Deci- Centi- Mili-

k h da d c m

Prefix

Prefixes• giga- G 1,000,000,000 109

• mega - M 1,000,000 106

• kilo - k 1,000 103

• deci- d 0.1 10-1

• centi- c 0.01 10-2

• milli- m 0.001 10-3

• micro- 0.000001 10-6

• nano- n 0.000000001 10-9

Prefixes

• kilo k 1000 times• deci d 1/10• centi c 1/100• milli m 1/1000• kilometer - about 0.6 miles• centimeter - less than half an inch• millimeter - the width of a paper clip wire

DIMENSIONAL ANALYSISUsing the units to solve problems

Chapter 1: Chemistry: Matter and Measurement 13

A Problem-Solving Method

Chemistry problems usually require calculations, and yield quantitative (numerical) answers

For example,1 inch = 2.54 cm

EOS

The unit-conversion method is useful for solving most chemistry problems – the focus here is on “unit equivalents”

4m = ________ cm 5km = ____________m 40mm = __________m 67m = __________ hm 135cm = _____________km 0.1km = _________dm 2km = ________________mm

.34km = ________ cm 5km = ____________m 19cm = __________mm 98m = __________km 135m = _____________km 33 km = _________dm 87m = ________________mm

Converting

• how far you have to move on this chart, tells you how far, and which direction to move the decimal place.

• The box is the base unit, meters, Liters, grams, etc.

k h D d c m

Conversions

• convert 25 mg to grams• convert 0.45 km to mm• convert 35 mL to liters• It works because the math works, we are dividing or

multiplying by 10 the correct number of times.

k h D d c m


Other Equivalents and Conversion Factors

A conversion factor is the fractional expression of the equivalents

EOS

1 2.54

2.54 1

inch cmor

cm inch

Dimensional Analysis

• We use dimensional analysis to convert one quantity to another.

• Most commonly dimensional analysis utilizes conversion factors (e.g., 1 in. = 2.54 cm)


1 in.

2.54 cm

2.54 cm

1 in.or


Use the form of the conversion factor that puts the sought-for unit in the numerator.


Given unit desired unitdesired unit

given unit

Conversion factor


• For example, to convert 8.00 m to inches,• convert m to cm• convert cm to in.


8.00 m100 cm

1 m

1 in.

2.54 cm 315 in.

Dimensional Analysis• Use conversion factors to change the units• Conversion factors = 1• 1 foot = 12 inches (equivalence statement)

• 12 in = 1 = 1 ft.

1 ft. 12 in• 2 conversion factors• multiply by the one that will give you the correct units in your

answer.


Two Examples

EOS

How many cm are in 26 inches?

26 in × cmin

2.541

= 66 cm

Examples• 11 yards = 2 rod• 40 rods = 1 furlong• 8 furlongs = 1 mile• The Kentucky Derby race is 1.25 miles. How long is

the race in rods, furlongs, meters, and kilometers?• A marathon race is 26 miles, 385 yards. What is this

distance in rods and kilometers?

Units to a Power

• How many m3 is 1500 cm3?

1500 cm33 1 m100 cm

1 m100 cm

1 m100 cm

1500 cm33 1 m

100 cm

33

Units to a Power• How many cm2 is 15 m2?• 36 cm3 is how many mm3?

Multiple units• The speed limit is 65 mi/hr. What is this in m/s?

• 1 mile = 1760 yds• 1 meter = 1.094 yds

65 mihr

1760 yd1 mi 1.094 yd

1 m 1 hr60 min

1 min60 s

Multiple units• Lead has a density of 11.4 g/cm3. What is this in pounds

per quart?• 454 g = 1 lb• 1 L = 1.094 qt

UNCERTAINY IN MEASUREMENT


Significant Figures• The term significant figures refers to digits that were

measured.• When rounding calculated numbers, we pay attention to

significant figures so we do not overstate the accuracy of our answers.



Significant Figures

EOS

• All digits in a number that are known with certainty plus the first uncertain digit

• The more significant digits obtained, the better the precision of a measurement

• The concept of significant figures applies only to measurements

• Exact values have an unlimited number of significant figures

Significant Figures1. All nonzero digits are significant.

2. Zeroes between two significant figures are themselves significant.

3. Zeroes at the beginning of a number are never significant.

4. Zeroes at the end of a number are significant if a decimal point is written in the number.



Rules for Zeros inSignificant Figures

Zeros between two other significant digits ARE significant

e.g., 10023

A zero preceding a decimal point is not significant e.g., 0.10023

EOS

Zeros between the decimal point and the first nonzero digit are not significant

e.g., 0.0010023


Rules for Zeros inSignificant Figures

Zeros at the end of a number are significant if they are to the right of the decimal point

e.g., 0.1002300 1023.00

EOS

Zeros at the end of a number may or may not be significant if the number is written without a decimal point

e.g., 1000. compared to 1000


Rules for Significant Figuresin Calculations

KEY POINT: A calculated quantity can be no more precise than the least precise data used in the calculation

EOS

Analogy: a chain is only as strong as its weakest link

… and the reported result should reflect this fact

Significant Figures• When addition or subtraction is performed, answers

are rounded to the least significant decimal place.• When multiplication or division is performed, answers

are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.



Significant Figuresin Calculations

Multiplication and Division: the reported results should have no more significant figures than the factor with the fewest significant figures

1.827 m × 0.762 m = ?

EOS

0.762 has 3 sigfigs so the reported answer is 1.39 m2


Significant Figuresin Calculations

Addition and Subtraction: the reported results should have the same number of decimal places as the number with the fewest decimal places

EOS

NOTE - Be cautious of round-off errors in multi-step problems. Wait until calculating the final answer before rounding.

Conservation of Mass• Law of Conservation of Mass- in a physical or chemical

reaction, mass is neither created nor destroyed; it is conserved.

• All mass can be accounted for.• Mass of the Reactants = Mass of Products

Weight vs. Mass

Weight Mass

• Measures the force of gravity on an object

• Weight can change if the force of gravity acting on the object changes

• How much matter is in an object

• Remains constant (the same) no matter where it is

Mass and Weight• Mass is measure of resistance to change in motion • Weight is force of gravity.• Sometimes used interchangeably• Mass can’t change, weight can

Mass

• Weight is a force. Mass is the amount of matter.

• 1 gram is defined as the mass of 1 cm3 of water at 4 ºC.

• 1000 g = 1000 cm3 of water• 1 kg = 1 L of water

Mass

• 1 kg = 2.5 lbs• 1 g = 1 paper clip• 1 mg = 10 grains of salt

Volume

• calculated by multiplying L x W x H • Liter the volume of a cube 1 dm (10 cm) on a side• 1L = 1 dm3

• so 1 L = 10 cm x 10 cm x 10 cm

• 1 L = 1000 cm3

• 1/1000 L = 1 cm3

• 1 mL = 1 cm3

Volume

• 1 L about 1/4 of a gallon - a quart• 1 mL is about 20 drops of water or 1 sugar cube

Uncertainty• Basis for significant figures • All measurements are uncertain to some degree• Precision- how repeatable • Accuracy- how correct - closeness to true value.• Random error - equal chance of being high or low-

addressed by averaging measurements - expected

Accuracy versus Precision

• Accuracy refers to the proximity of a measurement to the true value of a quantity.

• Precision refers to the proximity of several measurements to each other.


Uncertainty• Systematic error- same direction each time• Want to avoid this• Bad equipment or bad technique.• Better precision implies better accuracy• You can have precision without accuracy• You can’t have accuracy without precision (unless

you’re really lucky).

Measuring Temperature

• Celsius scale.• water freezes at 0ºC• water boils at 100ºC• body temperature 37ºC• room temperature 20 - 25ºC

0ºC

Measuring Temperature

• Kelvin starts at absolute zero (-273 º C)• degrees are the same size• C = K -273• K = C + 273• Kelvin is always bigger.• Kelvin can never be negative.

273 K

Temperature is different

• from heat.• Temperature is which way heat will flow. (from hot to cold)• Heat is energy, ability to do work.• A drop of boiling water hurts,• kilogram of boiling water kills.

Units of heat are

• calories or Joules• 1 calorie is the amount of heat needed to raise the

temperature of 1 gram of water by 1ºC.• A food Calorie is really a kilocalorie.• How much energy is absorbed to heat 15 grams of water

by 25ºC.• 1 calorie = 4.18 J

Conservation of Mass• Law of Conservation of Mass- in a physical or chemical

reaction, mass is neither created nor destroyed; it is conserved.

• All mass can be accounted for.• Mass of the Reactants = Mass of Products

Energy

• The ability to do work.• Work - cause a change or move an object.• Many types- all can be changed into the other.

Types of energy

• Potential- stored energy• Kinetic Energy- energy something has because its moving• Heat- the energy that moves because of a temperature

difference.• Chemical energy- energy released or absorbed in a

chemical change.• Electrical energy - energy of moving charges

Types of Energy

• Radiant Energy- energy that can travel through empty space (light, UV, infrared, radio)

• All types of energy can be converted into others.• If you trace the source far enough back, you will end up at

nuclear energy.

Conservation of Energy

• Energy can be neither created or destroyed in ordinary changes (not nuclear), it can only change form.

• Its not just a good idea, its the law.

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