Math ConceptsMath Concepts

Chemistry Chemistry

ObservationsObservations

A large part of laboratory chemistry is A large part of laboratory chemistry is making observations.making observations. Two types of observations:Two types of observations:

Qualitative observations = Qualitative observations = descriptive descriptive observations, no numbers involvedobservations, no numbers involved

Quantitative observations = Quantitative observations = observations described by a numbered observations described by a numbered measurement.measurement.

Accuracy and PrecisionAccuracy and Precision

Chemists need to have to make exact and Chemists need to have to make exact and reproducible results.reproducible results. Accuracy = Accuracy = measurements that only have measurements that only have

slight deviation from the true value.slight deviation from the true value. Depends on:Depends on:

Equipment usedEquipment used Precision = Precision = being able to reproduce a being able to reproduce a

measured value through several measured value through several experimental runs or trials.experimental runs or trials. Depends on:Depends on:

The person making the measurementsThe person making the measurements

Accuracy and PrecisionAccuracy and Precision

Accuracy and PrecisionAccuracy and Precision Experimental results:Experimental results:

Sean:Sean: 2.56g2.56g

2.37g2.37g

2.41g2.41g Morgan: 3.12gMorgan: 3.12g

2.11g2.11g

4.32g4.32g Doug: 3.22gDoug: 3.22g

3.25g3.25g

3.27g3.27g

If the true value of the If the true value of the mass is 3.10g, explain mass is 3.10g, explain each students each students measurements in measurements in terms of the words terms of the words accuracy and accuracy and precision.precision. Answer: Sean not Answer: Sean not

accurate, but preciseaccurate, but precise Morgan accurate, but Morgan accurate, but

not precisenot precise Doug: good accuracy Doug: good accuracy

and very precise.and very precise.

Why is it so important to be Why is it so important to be accurate and precise as a accurate and precise as a

chemist?chemist? Medicine – certain amounts can turn Medicine – certain amounts can turn

into lethal dosagesinto lethal dosages Work with flammable productsWork with flammable products To insure reproducible products To insure reproducible products

(cosmetics, soap, hair products…)(cosmetics, soap, hair products…) To insure quality of our environments To insure quality of our environments

(air and water quality)(air and water quality)

How can a chemist achieve How can a chemist achieve exactness in measurements?exactness in measurements?

Significant Significant Digits/figures.Digits/figures.

Sig figs = Sig figs = the the reliable numbers reliable numbers in a in a measurement measurement and at least one and at least one estimated digit.estimated digit.

Make readings for the following Make readings for the following measurements using significant measurements using significant figures.figures.

Rules for significant figuresRules for significant figures 11. All non-zero . All non-zero

numbers or digits are numbers or digits are significant. Ex: 23 gsignificant. Ex: 23 g

2. All zero in-between 2. All zero in-between 2 non-zero numbers 2 non-zero numbers are significant. Ex: are significant. Ex: 2.002g2.002g

3. When working with 3. When working with a small decimal a small decimal number, work your way number, work your way over to the right until over to the right until you get to your 1you get to your 1stst non- non-zero number - anything zero number - anything from there over is from there over is significant. Ex:significant. Ex: 0.00250g0.00250g

4. Final zeros 25.00g 4. Final zeros 25.00g are significant.are significant.

5. When working with 5. When working with large numbers (no large numbers (no decimals), look for your decimals), look for your 11stst non-zero number – non-zero number – anything from there to anything from there to the beginning of the the beginning of the number are significant. number are significant. Ex: 240100gEx: 240100g

6. A line/bar over or 6. A line/bar over or under a zero designates under a zero designates it as significant.it as significant.

7. Exact numbers = 7. Exact numbers = numbers that you are numbers that you are use to working with are use to working with are unlimited in terms of unlimited in terms of significant figs. Ex: significant figs. Ex: there are 12 men on the there are 12 men on the football field. = football field. = unlimited.unlimited.

Significant FiguresSignificant Figures An easy way to count the number of An easy way to count the number of

significant figures in any number is:significant figures in any number is:DOT LEFT – NOT RIGHTDOT LEFT – NOT RIGHT

*If there is a visible decimal, look all the *If there is a visible decimal, look all the way to the left of the value and move to way to the left of the value and move to the right. Begin counting digits after your the right. Begin counting digits after your first non-zero digit. Any numbers that first non-zero digit. Any numbers that follow a non-zero digit are significant.follow a non-zero digit are significant.

EX: 2.500 = 4 sig figsEX: 2.500 = 4 sig figs500.00 = 5 sig figs500.00 = 5 sig figs

*If there is no visible decimal, look all *If there is no visible decimal, look all the way to the right of the value and the way to the right of the value and move to the left. Begin counting digits move to the left. Begin counting digits after your first non-zero digit. Any after your first non-zero digit. Any numbers that precede a non-zero digit numbers that precede a non-zero digit are significant.are significant.

EX: 2500 = 2 sig figsEX: 2500 = 2 sig figs

50000 = 1 sig figs50000 = 1 sig figs

5001 = 4 sig figs5001 = 4 sig figs

If an exponential number, look at If an exponential number, look at coefficient only.coefficient only.

If decimal at end all numbers are If decimal at end all numbers are significant.significant.

A line over a zero indicates that zero A line over a zero indicates that zero as the last significant digit.as the last significant digit.

Use decimal Use decimal oror line, not both. line, not both. No lines over nonzero digits.No lines over nonzero digits.

ExamplesExamples How many sig How many sig

figs are in the figs are in the following:following: 20 kg20 kg

1 sig fig1 sig fig 0.0051 g0.0051 g

2 sig figs2 sig figs 11 m11 m

2 sig figs2 sig figs 0.010 s0.010 s

2 sig figs2 sig figs 90.490.4˚C˚C

3 sig figs3 sig figs 0.004 cm0.004 cm

1 sig fig1 sig fig

0.089 kg0.089 kg 2 sig figs2 sig figs

0.00900 l0.00900 l 3 sig figs3 sig figs

100.0˚C100.0˚C 4 sig figs4 sig figs

20 cars20 cars unlimitedunlimited

2.15000 cm2.15000 cm 6 sig figs6 sig figs

5310 g5310 g 3 sig figs3 sig figs

12050 m12050 m 4 sig figs4 sig figs

Calculations using sig figsCalculations using sig figs Adding or subtractingAdding or subtracting:: Look at the decimal Look at the decimal

places. Choose the given places. Choose the given information that has the information that has the least number of least number of decimal placesdecimal places. Make . Make sure to put your answers sure to put your answers in the least number of in the least number of decimals. Your decimals. Your calculator does not do calculator does not do this! this! Your final Your final measurement can not be measurement can not be more specific than your more specific than your least specific least specific measurement!measurement!

Multiplying or Multiplying or dividingdividing::

Identify sig figs for Identify sig figs for each number in your each number in your information. Your information. Your answer needs to be answer needs to be altered to the altered to the least least number of sig figs number of sig figs used used when solving when solving the problem. (for the the problem. (for the same reason)same reason)

Addition

Division

Multiplication

Subtraction

Practice:Practice:1. 1. Give the correct number of significant Give the correct number of significant

figures for: figures for: 4500 4500 45004500.. 0.00320.00320.040500.04050

2. 2. 4503 + 34.90 + 550 = ? 4503 + 34.90 + 550 = ? 3. 3. 1.367 - 1.34 = ? 1.367 - 1.34 = ? 4. (1.3 x 103)(5.724 x 104) = ? 4. (1.3 x 103)(5.724 x 104) = ? 5. 5. (6305)/(0.010) = ?(6305)/(0.010) = ?

Scientific NotationScientific Notation

Why is it that we use scientific Why is it that we use scientific notation in science?notation in science?

because many of the numbers, because many of the numbers, amount, etc. that we use are either amount, etc. that we use are either really big or very small.really big or very small.

Examples: Distance from the Earth Examples: Distance from the Earth to the Sun, size of an atom, the mass to the Sun, size of an atom, the mass of an electron, proton, or even of an electron, proton, or even neutron…..neutron…..

Scientific NotationScientific Notation If the number is large If the number is large

– you will have a – you will have a positive exponentpositive exponent

If the number is very If the number is very small – you will have a small – you will have a negative exponent.negative exponent.

Exponent decides Exponent decides which direction and which direction and how many spots you how many spots you will move the decimalwill move the decimal

EX: EX: 10000 = 1 x 1010000 = 1 x 1044 0.00044 = 4.4 x 0.00044 = 4.4 x

1010--44

Must honor sig figs Must honor sig figs in original valuein original value

Root number or Root number or coefficient is the coefficient is the only number that only number that is significant is significant (exponent does (exponent does not count)not count)

EX: 2.4327 x 10EX: 2.4327 x 1044 5 sig figs5 sig figs

7.8 x 107.8 x 10--33

2 sig figs2 sig figs

ExamplesExamples

What is the correct scientific notation What is the correct scientific notation for:for: 2500025000 .00000801 12.87.00000801 12.87

What is the correct standard notation What is the correct standard notation for:for:

1.98 x 101.98 x 103 3 2.609 x 10 2.609 x 10 -2-2

3.81 x 103.81 x 10-5-5

0.070 x 100.070 x 1055

0.005 x 100.005 x 10-3-3

Calculations with scientific Calculations with scientific notationnotation

Multiplication: Multiplication: multiply the multiply the coefficients(rootcoefficients(roots) and add your s) and add your exponentsexponents

Division: divide Division: divide the the coefficients(rootcoefficients(roots) and subtract s) and subtract your exponentsyour exponents

Add or subtract: Add or subtract: Change your Change your exponents to equal exponents to equal (largest one), then (largest one), then add and put back add and put back into correct into correct scientific notation. scientific notation. OR put your OR put your numbers in standard numbers in standard notation +/- and notation +/- and then place back into then place back into scientific notationscientific notation

Practice:Practice: (2.68 x 10(2.68 x 10-5-5) x (4.40 x 10) x (4.40 x 10-8-8)) (2.95 x 10(2.95 x 1077) ÷ (6.28 x 10) ÷ (6.28 x 101515)) (8.41 x 10(8.41 x 1066) x (5.02 x 10) x (5.02 x 101212)) (9.21 x 10(9.21 x 10-4-4) ÷ (7.60 x 10) ÷ (7.60 x 1055)) (4.52 x 10(4.52 x 10-5-5) + (1.24 x 10) + (1.24 x 10-2-2) + (3.70 x 10) + (3.70 x 10-4-4) )

+ (1.74 x 10+ (1.74 x 10-3-3) ) (2.71 x 10(2.71 x 1066) - (5.00 x 10) - (5.00 x 1044) ) (4.56 x 10(4.56 x 1066) + (2.98 x 10) + (2.98 x 1055) + (3.65 x 10) + (3.65 x 1044) + ) +

(7.21 x 10(7.21 x 1033)) (3.05 x 10(3.05 x 1066) x (4.55 x 10) x (4.55 x 10-10-10))

How can you decide if your How can you decide if your experiments are experiments are accurate/precise?accurate/precise?

Percent error = calculations that will Percent error = calculations that will give you a percent deviation from give you a percent deviation from the true value.the true value.

Formula: Formula: l True – experimental ll True – experimental l x x

100100

TrueTrue

ExampleExample

A student measured the density of an A student measured the density of an object to be 2.889 g/ml, the true density of object to be 2.889 g/ml, the true density of the object is 2.699g/ml. What is the the object is 2.699g/ml. What is the percent error of the experiment? Is the percent error of the experiment? Is the student accurate?student accurate?

ANSWER: 7.000% error, anything ANSWER: 7.000% error, anything below 10% is acceptable as accurate. below 10% is acceptable as accurate. The closer to 0% the better!The closer to 0% the better!

Metric SystemMetric System The Metric system was developed in The Metric system was developed in

France during the Napoleonic reign of France during the Napoleonic reign of France in the 1790's. France in the 1790's.

The metric system has several The metric system has several advantages over the English system advantages over the English system which is still in place in the U.S. which is still in place in the U.S.

However the scientific community has However the scientific community has adopted the metric system almost from adopted the metric system almost from its inception. its inception.

The advantages of the Metric system The advantages of the Metric system are: are: 1. It is based on a decimal system 1. It is based on a decimal system (powers of ten). (powers of ten). 2. It simplifies calculations by using a 2. It simplifies calculations by using a set of prefixes. set of prefixes. 3. In order to move from one prefix to 3. In order to move from one prefix to another you simply move the decimal.another you simply move the decimal.4. It provides a standard measurement 4. It provides a standard measurement system that is used by the scientific system that is used by the scientific community. (SI Base Units)community. (SI Base Units)

Prefix Prefix Decimal equivalent Decimal equivalent ExponentExponent

Pico Pico 0.000000000001 0.000000000001 1010-12-12

Nano Nano 0.000000001 0.000000001 1010-9-9

Micro Micro 0.000001 0.000001 1010-6-6

Milli Milli 0.001 0.001 1010-3-3

Centi Centi 0.01 0.01 1010-2-2

Deci Deci 0.1 0.1 1010-1-1

no prefix no prefix 1.0 1.0 101000

Deka Deka 10.0 10.0 101011

Hecto Hecto 100.0 100.0 101022

Kilo Kilo 1000.0 1000.0 101033

Mega Mega 1,000,000. 1,000,000. 101066

Giga Giga 1,000,000,000. 1,000,000,000. 101099

SI Base UnitsSI Base Units Table 1. Table 1. Base quantityBase quantity NameName Symbol Symbol

SI base unitsSI base units

LengthLength metermeter mmMassMass kilogramkilogram kgkgTimeTime secondsecond sselectric currentelectric current ampereampere AAtemperature      temperature       kelvinkelvin KKamount of substanceamount of substance molemole molmol

Common Base UnitsCommon Base Units

The SI Base Units are standard for The SI Base Units are standard for Scientific Reports.Scientific Reports.

During your chemistry experience, you During your chemistry experience, you will use these common base units:will use these common base units:

-temperature -temperature Celcius Celcius °C°C

-length-length centimeter centimeter cmcm

-mass-mass gram gram gg

Common PrefixesCommon Prefixes

Converting Between Units of Converting Between Units of MetricMetric

EX: Convert 500.0 mm EX: Convert 500.0 mm m mStep 1: Identify the prefixes in the given Step 1: Identify the prefixes in the given

values.values.Step 2: Refer to the order of prefixes:Step 2: Refer to the order of prefixes:

K h D m(base unit) d c mK h D m(base unit) d c mStep 3: Find the direction that you will Step 3: Find the direction that you will

need to move the decimal to achieve need to move the decimal to achieve your new prefix.your new prefix.

Step 4: Move the decimal in that direction, Step 4: Move the decimal in that direction, the same number of times.the same number of times.

Step 5: Express new value with correct unit Step 5: Express new value with correct unit and sig fig. and sig fig.

500.0 500.0 mmmm mm

Step 1: (milli) (base unit of Step 1: (milli) (base unit of metermeter

so no prefix)so no prefix)

Step 2: K h D Base Unit d c mStep 2: K h D Base Unit d c m

Step 3: Step 3:

Step 4: 500.0Step 4: 500.0

Step 5: 0.5000 mStep 5: 0.5000 m

EX: Convert 7.500 L EX: Convert 7.500 L cL cL

Step 1: (liters is (centi)Step 1: (liters is (centi)

base unit)base unit)

Step 2: K h D Base Unit d c mStep 2: K h D Base Unit d c m

Step 3: Step 3:

Step 4: 7.500Step 4: 7.500

Step 5: 750.0 cLStep 5: 750.0 cL

Practice:Practice:• 5000 mg 5000 mg g g• 0.0076 km 0.0076 km m m• 1.000 hL 1.000 hL L L• 250000 mm 250000 mm km km• 50.0 cg 50.0 cg mg mg• 3.0 cm 3.0 cm dm dm• 1.0 kg 1.0 kg mg mg

Density and TemperatureDensity and Temperature

MassMass Mass = amount of matter that an object contains. Mass = amount of matter that an object contains.

This is a physical property of matterThis is a physical property of matter Golf ball or tennis ball?Golf ball or tennis ball?

Golf ball is solid therefore has more mass, tennis Golf ball is solid therefore has more mass, tennis ball is made of empty space.ball is made of empty space.

Lab instrument and unit?Lab instrument and unit?Scale and grams (g)Scale and grams (g)

VolumeVolume

Volume = The amount of space an Volume = The amount of space an object occupies. This is also a physical object occupies. This is also a physical property of matterproperty of matter 1. Volume of a 1. Volume of a regular shapedregular shaped

object like a cube, uses the formula:object like a cube, uses the formula: V = L x W x HV = L x W x H

What lab instrument would be used What lab instrument would be used to find and its unit?to find and its unit?Ruler and cubic centimeters (cmRuler and cubic centimeters (cm33))

VolumeVolume

2. 2. Volume by displacementVolume by displacement Used when you have an irregular Used when you have an irregular

shaped object. Ex: Marble or rockshaped object. Ex: Marble or rock Lab instrument and unit?Lab instrument and unit?

Graduated cylinder and milliliters Graduated cylinder and milliliters (mL)(mL)

How do you perform?How do you perform?

DensityDensity Both mass and Both mass and

volume make up volume make up density, it is the density, it is the relationship relationship between the two.between the two.

Density is also a Density is also a physical propertyphysical property of matterof matter

Formula = D = m/v Formula = D = m/v M= massM= mass V = volumeV = volume

DensityDensity

Units for density are:Units for density are: 1. g/mL1. g/mL 2. g/cm2. g/cm33

Question: A piece of Question: A piece of metal has a mass of 40 metal has a mass of 40 grams and a volume of 80 grams and a volume of 80 milliliters, what is its milliliters, what is its density?density? D= D= mm = = 40g 40g = =

v 80 ml v 80 ml

0.5g/mL0.5g/mL

DensityDensity

A piece of wood has a density of 45 A piece of wood has a density of 45 g/cmg/cm33, its mass is 5.0 grams. What , its mass is 5.0 grams. What is its volume?is its volume?

New formula: m/D = vNew formula: m/D = v 5.0 grams5.0 grams = 0.11 cm = 0.11 cm33

45g/cm45g/cm33

TemperatureTemperature A measurement which describes the A measurement which describes the

hotness or coldness of a substance.hotness or coldness of a substance. Instrument used = Instrument used = thermometerthermometer We will commonly use We will commonly use ˚C in labs, but SI ˚C in labs, but SI

unit is K = unit is K = KelvinsKelvins Formulas:Formulas:

˚F = (˚c x 1.8) + 32˚F = (˚c x 1.8) + 32 ˚C = (˚F – 32) ÷ 1.8˚C = (˚F – 32) ÷ 1.8 ˚C = K – 273˚C = K – 273 K = ˚C + 273K = ˚C + 273