Chapter 1 Matter, Energy and Measurement. Scientific Method The Scientific Method is the systematic investigation of natural phenomena where: Observations

Chapter 1

Matter, Energy and Measurement

Scientific MethodThe Scientific Method is the systematic

investigation of natural phenomena where:

Observations are explained in terms of general scientific principles

Principles are formulated from hypotheses Hypotheses are tested by further experimentation Sufficient empirical support elevates hypothesis to

theory or natural law

In Science is there ALWAYS a “Right” answer?

• Most of the calculations you will encounter in this course (i.e., the homework problems no known answer- they propose a “best” explanation and exams) have “right” answers

• In “real life”, researchers investigate questions for which there is

Scientific Notation

• Scientific notation is a method of conveniently expressing extremely large or extremely small numbers. We will use scientific notation whenever dealing with large or small numbers.

• How to write numbers in scientific notation: Find the decimal point. Find the first non-zero digit (reading left to right). Move the decimal point to the right of the first non-zero

digit. Count the number of spaces moved. If the decimal point was moved to the left, the number of spaces moved is the positive exponent. If the decimal was moved right, it is the negative exponent.

Re-write the number with the decimal point in the new position. Drop all zeros to the left of the first non-zero digit. Drop all zeros to the right of the last non-zero digit only if the original number did not show the decimal.

Scientific Notation

• Distance to the moon = 380,000 km = 3.8 x 105 km

• Distance to the sun = 150,000,000 km = 1.5 x 108 km

• Diameter of a neuron = 0.00005 m = 5 x 10-5 m

• Diameter of plutonium atom = 0.0000000003 m =

3 x 10-10 m

• Number of water molecules in an drop = 1000000000000000000000 = 1 x 1021

Scientific Notation

• 180,000,000 g

• 0.00006 m

• 750,000 g

• 0.15 m

• 0.024 s

• 1,500 m3

Scientific Notation

Scientific Notation to Standard Numbers

• How to take numbers out of scientific notation: Write the number portion of the scientific notation

expression, including the decimal point. (Do not include “times ten to the power of…”)

If the exponent is positive, move the decimal point to the right and move the number of spaces indicated by the exponent. If the exponent is negative, move the decimal point to the left. You will need to add zeros as you are moving the decimal point.

• 3.6 x 10-5

• 8.75 x 104

• 3 x 10-2

• 2.12 x 105

Scientific Notation to Standard Numbers: Examples

• Write the following as standard numbers: 7.2 x 10-3 m 2.4 x 105 g 3.6 x 10-5 ml 8.75 x 104 m

Scientific Notation to Standard Numbers: Problems

• (7.2 x 103) x (8.2 x 102) = 5904000 = 5.904 x 106

• (4.5 x 10-4) x (3.2 x 10-2) = 0.0000144 = 1.44 x 10-5

• (1 x 104) x (1 x 104) = 100000000 = 1 x 108

• (5.2 x 10-4) x (6.8 x 10-2) = 0.0000354 = 3.54 x 10-5

Scientific Notation: Calculator Practice

Measured vs Exact Numbers• Measured numbers are those obtained from some

type of measuring device, like a thermometer (which measures temperature) or a scale (which measures mass) or a ruler (which measures length).

• Exact numbers are obtained from counting, like 12 eggs or 3 feet in a yard (conversions)

• The difference between a measured number and an exact number is the certainty or uncertainty of the number.

• Exact numbers are known with certainty. We are certain that there are exactly 12 eggs in a dozen. We do not wonder if there might really be 12.5 eggs, or 12.1 eggs.

• Measured numbers have a certain amount of uncertainty. When we take a measurement, we always are limited by the sensitivity of our measuring device. Typically, the last digit expressed in a measured number is approximated and therefore uncertain.

Measured vs Exact Numbers

• Identify the following numbers as measured or exact and give the number of sig figs in each measured number:

42.2 g 3 eggs 0.0005 cm450 000 km 3.500 x 105s


• Identify the numbers in each of the following statements as measured or exact: There are 31 students in the laboratory The oldest known flower lived 120 000 000 years ago The largest gem ever found has a mass of 104 kg A laboratory test shows a blood cholesterol level of 184

mg/dL


• In each of the sets of numbers, identify the exact number(s) if any: 5 pizzas and 50.0 g of cheese 6 nickels and 16 g of nickel 3 onions and 3 lb of potatoes 5 miles and 5 cars


Significant Figures• Significant figures (“Sig Figs”) are all the

certain digits in a measured number as well as the first uncertain digit. It is important for us to be able to recognize the significant figures of a number. When we multiply or divide numbers, there are rules that dictate how many digits in the answer are “Certain”

Significant Figures

• Significant figures: All non-zero digits are significant. All zeros in the middle of non-zero digits are significant. All zeros at the end of a number with a written decimal

point. All digits written in scientific notation

• Not significant figures: All zeros at the beginning of any number. All zeros at the end of a number written without a decimal

point. The zero is used as a placeholder

Significant Figures

• 20.60 g

• 1036.48 mL

• 4.00 mg

• 60,800,000 years

Significant Figures:Examples

• For each measurement, indicate if the zeros are significant: 20.05 g 5.00 m 0.000 02 L 120 000 years 8.05 x 102 g

Significant Figures:Problems

• How many sig figs are in each of the following measured quantities:– 20.60 L– 1036.48 g– 4.00 m– 60 8000 000 g– 20.8 °C– 5.0 x 10-3 L


• Write each of the following in scientific notation with 2 sig figs– 5 100 000 g– 26 000 s– 40 000 m– 0.000 820 kg– 0.000 004 5 m


Rounding Numbers

• When rounding a number, look to the digit immediately to the right of the last significant digit. If that number (the number to the right) is 0, 1, 2,

3, or 4, simply drop all insignificant digits. If that number (the number to the right) is 5, 6, 7,

8, or 9, round the last significant figure up and drop all significant digits.

Significant Zeros

• When a number needs to be expressed to more significant figures, add “significant zeros” to the right of the number. If the number is a decimal, simply add more zeros to the

right of the number. If the number does not have a decimal, it is easiest to write

the number in scientific notation (which requires you to write a decimal point) and then add zeros to the right of the number.

Rounding-Examples

• Re-write the following numbers to three significant digits. 1.854 184.2038 0.004738265 8800

Sig Figs in Calculations

• Rule for multiplying and dividing: Express the final answer to the lowest number of

significant figures.

• Rule for adding and subtracting: Express the final answer to the lowest number of decimal

places

• Perform the following calculations and express the answer to the proper number of sig figs: 45.7 x 0.034 0.00278 x 5 34.56 x 1.25 (0.2465 x 25) x 1.78

Sig Figs in Calculations:Examples

• Perform the following calculations and express the answer to the proper number of sig figs: 45.48 + 8.057 23.45 + 104.1 + 0.025 145.675 – 24.2 1.08 – 0.585

Sig Figs in Calculations:Examples

• Round off each of the following numbers to three sig figs: 35.7823 m 0.002627 L 3826.8 g 1.2836 kg

Sig Figs in Calculations:Problems

• Perform the following calculations of measured numbers. Give the answers with the correct number of sig figs: 56.8 x 0.37 71.4/11 (2.075 x 0.585)/(8.42 x 0.00450) 25.0/5.00


• Perform the following calculations and give the answers with the correct number of decimal places: 27.8 cm + 0.235 cm 104.45 mL + 46 mL + 0.838 mL 153.247 g - 14.82 g


• Round off each of the following numbers to three sig figs: 1.854 184.2038 0.004738265 8807 1.832149

• Round the numbers above to 2 sig figs:


• For the following calculations, give answers with the correct number of significant figures: 400 x 185 2.40/(4 x 125) 0.825 x 3.6 x 5.1 (3.5 x 0.261)/(8.24 x 20.0)


• For the following calculations, give answers with the correct decimal places: 5.08 cm + 25.1 cm 85.66 cm + 104.10 cm + 0.025 cm 24.568 mL - 14.25 mL 0.2654 L - 0.2585 L


Practice Problems

• Problem 1.1 page 9

The Metric System of Measurement

DIMENSION COMMON UNIT SYMBOLMass gram gLength meter mTime second sTemperature kelvin K

deg Celsius ºCVolume liter L

The Metric System

• Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Burma, Liberia and the United States

http://upload.wikimedia.org/wikipedia/commons/e/ec/Non-Metric_User.svg

Length

• Distance from one point to another– US Customary Units: Inch, foot, yard, mile

– Metric Units: Meter, centimeter, millimeter, kilometer, etc.

– SI Unit: Meter

Volume

Amount of space an object occupies US Customary Units: Pint, quart, gallon, etc. Metric Units: Liter, milliliter, cubic centimeter,

etc. SI Unit: Cubic meter

Mass

• Quantity of an object (note that mass and weight are not the same!)– US Customary Units: Pound, ounce, ton, etc.

– Metric Units: Gram, kilogram, etc.

– SI (International System of Units) Unit: Kilogram

Time

• US Customary Unit: Second, minute, hour, day, etc.

• Metric Unit: Second, millisecond, etc.

• SI Unit: Second

Temperature

• Measurement of the heat of an object– US Customary Unit: Degrees Fahrenheit

– Metric Unit: Degrees Celsius

– SI Unit: Kelvin

Three Temperature Scales

The Metric System:Metric prefixes

Prefix Symbol Multiple Examplenano n 10-9 nm (molecule

size)micro 10-6 m (cell size)milli m 10-3 mL (flu shot)centi c 10-2 cm (ski length)kilo k 103 kg (weights)mega M 106 MW (power)giga G 109 GB (memory)

Prefixes

• Prefixes are added to metric base units to increase or decrease the metric unit by some factor of ten.

• Liter is the base unit of volume. • Gram is the base unit of mass. • Meter is the base unit of length.• Table 1.2 Page 9: All prefixes must be

memorized, including the symbol and numerical value.

Equalities

• Equalities are set of numbers which are mathematically equal, but expressed in different units. For example, 12 inches = 1 foot. 1 m = ____ cm 1 km = ____ m 1 mm = ____ m 1 L = ____ mL

Prefixes and Equalities:Problems

• Fill in the blanks with the correct numerical value: Kilogram = _____ grams Millisecond = _____ second Deciliter = _____ Liter


• Complete the following list of metric equlaities: 1 L = _____ dL 1 km = _____ m 1 m = _____ cm 1 cm3 = _____ mL


• Write the abbreviation for each of the following units: Milligram Deciliter Kilometer Kilogram microliter


• Write the complete name for each of the following units: cm kg dL Gm mg


• Write the complete name (prefix + unit) for the following numerical values: 0.10 g 0.000 001 g 1000 g 1/100 g 0.001 g


• Complete the following relationships 1 kg = _____ g 1 mL = _____ L 1 g = _____ kg 1 g = _____ mg


• Which is the smaller unit?– mg or g– Centimeter or millimeter– mm or km– mL or µL

Writing Conversion Factors

• I have a half-dozen eggs, how many is that? • We’ve been in here for about X hours, how many

minutes is that? • We are going to learn how to convert between the

metric and US customary units, and also converting within the metric system. The process is the same as converting between hours and minutes


• For any conversion, we use a conversion factor which relates the current units to the desired units.

• The conversion factor comes from the equalities that you just practiced writing.

Common Conversion FactorsLength

2.54 cm = 1 in (exact) 1 yd = 0.9144 m = 3 ft (exact)1 mi = 1609 m 1 mi = 5280 ft (exact)

Mass1 kg = 2.2046 lb 1 lb = 16 oz (exact) 1 lb = 453.6 g 1 oz = 28.35 g

Volume1 mL = 1 cm3 (exact) 1 gal = 3.786 L 1 qt = 0.9464 L 4 qt = 1 gal (exact)

Energy1 BTU = 1055 J 1 cal = 4.184 J

TemperatureT(K) = T(°C)+ 273.15 T(°F) = 1.8 x T(°C) + 32


1 dozen 12 units 1 dozen

12 units

12 units

1 dozen

1000 mL 1 L 1000 mL

1 L

1 L

1000 mL

1 lb 454 g 1 lb

454 g

454 g

1 lb

5% acid by mass 5 g acid

100 g solution

100 g solution

5 g acid

• Write conversion factors for the relationship for the following pairs of units: milligrams and grams quarts and milliliters

Writing Conversion Factors: Problems

• Write the conversion factors for each of the following statements: There are 325 mg of asprin in 1 tablet One kilogram of bananas costs $1.25 A cyclist rides at the average speed of 62.2 km/hr A 100 g sample of silver has a volume of 9.48 cm3


• Write a numerical relationship and conversion factors for each of the following statements: One gallon is 4 quarts At the store, oranges are $1.29 per 1b There are 7 days in a week One dollar has four quarters A ring contains 58% by mass gold


• Write the numerical relationship and conversion factors for the following pairs of units: centimeters and meters milligrams and grams liters and milliliters Deciliters and milliliters


• Write the numerical relationship and conversion factors for the following pairs of units: Centimeters and inches Pounds and kilograms Pounds and grams Quarts and milliliters


Problem Solving Strategies

• Given/Need• Plan• Equalities/Conversion Factors• Set Up Problem

Example with Multiple Unit FactorsThe density of ethanol is 0.789 g/mL. What is it in lb/gal?

Step 1: Collect unit factors

1 lb = 453.6 g & 1 gal = 3.786 L & 1000 mL = 1 L

Step 2: Write desired quantity on left & known on right

...mL 1

g 0.789gal lb d

Step 3: Set up unit factors to cancel unwanted units

gal 1L 3.786

L 1mL 1000

g 453.6lb 1

mL 1g 0.789

gal lb d

Step 4: Complete calculation

gal lb

59.6453.6

)786.3 1000 (0.789

• A container holds 0.750 qt of liquid. How many milliliters of lemonade will it hold?

• In England, a person is weighed in stones. If one stone has a weight of 14.0 lb, what is the mass in kilograms of a person who weighs 11.8 stones?

Conversion Factors: Examples

• How many inches thick is an arterial wall that measures 0.50 μm?

• The femur, or thighbone, is the longest bone in the body. In a 6-foot tall person, the femur is19.5 inches long. What is the length of that femur in millimeters?

Conversion Factors: Examples

Solve Problems without FormulasMy crazy in-laws drove their camper and boat from Bellingham to Fairbanks (5100 mile round trip) to fish for salmon. Their rig gets 7.0 miles per gallon, with most of their fuel purchased in Canada at 1.20$Cdn per liter (the exchange rate was 1$US = 1.10$Cdn).

How much did they spend on fuel in $US? If they caught 9 salmon with an average

weight of 11 lb, what was the fuel cost per lb of salmon?

If Marmota Monax can move 17.0 lb of wood in a day, how many cords of wood could it move in a year?

1 cord = 128 ft3

density of stacked wood = 45.0 lb/ft3

Find the answer to the question.

Solve Problems without Formulas

Solve Problems without Formulas

The sun is 93 million miles from earth.

The speed of light is 2.998 x 108 m/s.

How many years does it take for sunlight to reach earth from the sun?

Thickness of Aluminum Foil

A sample of aluminum foil has the following characteristics.

Dimensions: 10. cm x 10. cm

Mass: 0.4405 g

If the density of aluminum is 2.70 g/cm3, find the thickness of the foil in µm.

How many atoms thick is the foil? (X-ray crystallography shows the distance between Al atoms in a solid is 250 pm.)

Suppose you dump a 5-lb sack of sugar into Bellingham Bay.

Assume the sugar disperses uniformly throughout all of the world’s oceans.

Estimate how many molecules of sucrose would be found in each liter of sea water.

Earth’s surface is 70.8% ocean

Earth’s diameter is 12,750 km

Average depth of ocean is 3790 m

Molecular weight of sucrose = 342 g/mole

1 lb = 453.6 g 1 m3 = 1000 L 1 km = 1000 m Surface area of sphere =

(diameter)2

1 mole = 6.023 x 1023 molecules

States of Matter

• Matter can exist in different states• In this class we will discuss 3 different states

matter can exist in– Gas– Liquid– Solid

Gas

• No definite shape• No definite volume• Expand to fill whatever container they are in• Highly compressible• Essentially no attractive forces between gas

particles• Particles move very, very quickly

Liquids

• No definite shape• Have definite volume• Slightly compressible• Particles move slowly• Some attractive forces between particles

Solids

• Have definite shape and volume• Essentially incompressible• Move very, very slowly• Strong attractive forces between particles

Properties of Matter

• “Physical” properties: what is the physical nature of the matter? For example: color, odor, physical state (liquid, gas, solid), melting/boiling point, tensile strength, density...

• “Chemical” properties: what is the “reactivity” of the matter (e.g. flammability, oxidizing agent, etc.)

Density• Density is the relationship between mass and

volume of an object:

• What does it mean to have a high density?– Examples are bricks, lead, fishing weights.

• What does it mean to have a low density?– Examples are sponges, feathers, balsa wood.

• Density is usually expressed in g/mL or g/cm3.

Density mass

volume

Density

• Density is a conversion factor.

• It is an equality or relationship between mass and volume, so it can be used to convert from mass to volume or vice versa.

• The only way to convert between mass and volume

Density of Water

The density of liquid water is defined as exactly 1 g/mL at 4 ºC.

At other temperatures between 0 and 100 ºC the density of liquid water is very close to 1 g/mL.

Density

Matter with lesser density than water will float

Matter with greater density than water will sink,

Density Calculations

• How many liters of ethanol contain 1.5 kg of alcohol?

• How many grams of mercury are present in a barometer that holds 6.5 mL of mercury?


• A sculptor has prepared a mold for casting a bronze figure. The figure has a volume of 225 mL. If bronze has a density of 7.8 g/mL, how many ounces of bronze are needed in the preparation of the bronze figure?

• How many kilograms of gasoline fill as 12.0 gallon gas tank? (1 gallon = 4 qt)

Density Calculations• Determine the denisty (g/mL) for each of the

following: A plastic material that weighs 2.68 lb and has a

volume of 2.5 L A 10.00 L sample of oxygen gas that has a mass of

0.014 kg.

• A graduated cylinder contains 28.0 mL of water. What is the new water level after 35.6 g of silver metal is submerged in the water?

• A cannon ball made of iron has a volume of 115 cm3. If iron has a density of 7.86 g/cm3, what is the mass in kilograms of the cannon ball?


• The mass of an empty container is 88.25 g. The mass of the container and a liquid with a density of 0.758 g/mL is 150.50 g. What is the volume (mL) of the liquid in the container?


Specific Gravity

sp gr density of sample

density of water

• Specific gravity is related to density and is used in the health fields to test urine. Specific gravity is calculated by dividing the density of an object by the density of water, which is 1.00 g/mL. Make sure the sample density is expressed in the same units as the density of water (g/mL).• What are the units for specific gravity?

• Energy is defined as the ability to do _____. Examples of work: – Walking– Talking– Running– Metabolizing

Energy

• We will discuss two types of energy in this class– Potential Energy

– Kinetic Energy

Energy

• Stored Energy

• Examples include:– Water at the top of a dam– Food

Potential Energy

The energy of motion

Examples:◦ Running◦ Walking◦ Water falling over a dam◦ Food in your body

Problem 2.4 page 59

Kinetic Energy

• Heat is a specific type of energy associated with molecular/atomic motion.

• Atoms are constantly in motion. ________ motion is associated with a greater amount of heat.

• Putting heat into a system causes the molecules to move ________.

Heat

• Energy used in Chemistry

• Heat will always flow from a warmer object to a cooler one

• 2 units of heat– Joule– calorie– 1 cal = 4.184 J

Heat

• The nutritional Calorie (Cal) is equal to 1 kcal.

• (Calorimeter is used to measure calories in food.)

Energy and Nutrition

• Specific heat is the amount of heat necessary to raise the temperature of 1 gram of an object by 1C. Every type of substance has a characteristic specific heat.

• Specific heat has units of J/gC or cal/gC. It can be calculated.

• Table 1.4 page 22 (note the high specific heat of water.)

• Problem 1.9 page 24• Problem 1.10 page 24• Problem 1.11 page 25

Specific Heat (SH)

• Specific heat is used to perform calculations on how hot an object will get if it is exposed to a certain amount of heat, or how much heat is necessary to raise the temperature of an object by a certain amount.

Specific Heat

Documents

Chapter 1 Matter, Energy and Measurement. Scientific Method The Scientific Method is the systematic investigation of natural phenomena where: Observations