Measurements and Calculations

Chemistry Chapter 2 1

Measurements and Calculations

Chapter 2


Scientific Method

A logical approach to solving problems by:Observing and collecting dataFormulating hypothesesTesting hypotheses, andFormulating theories that are supported by data


Observing

Using the five senses to gather information

Often involves making measurements and collecting data


Qualitative data

DescriptiveNot numericalExample – the sky is blue


Quantitative data

NumericalMeasurable or countableExample – the temperature of the water

went up 1 °C


System

A specific portion of matter in a given region of spaceHas been selected for study during an

experiment or observationMust be defined by the experimenter


Formulating hypotheses

Hypothesis – testable statementGeneralizations about dataBasis for making predictions and

designing experimentsUsually if-then statements


Testing hypotheses

Doing experimentsYou must be ready to reject a hypothesis

that is proven wrong


Theorizing

Model – an explanation of how phenomena occur and how data or events are relatedMay include a physical object or drawingMay be visual, verbal, or mathematical

Theory – a broad generalization that explains a body of facts or phenomenaMust predict to be successful


Discuss

Section ReviewPage 31


Quantity

Something that has magnitude, size, or amount.


SI Measurement

Le Système International d’UnitésMetric systemSeven base units – the rest are derived


Standards of measurement

Objects or phenomena that are of constant value, easy to preserve and reproduce, and practical in size.

Note – ten thousand is written 10 000, not 10,000. Some countries use the comma as a decimal point.


Mass

Measure of the quantity of matterKilogram is base unitkgYour textbook has a mass of about 1 kgA paper clip has a mass of about 1 g, or

1/1000 of a kg


Mass vs. weight

Weight is the measure of the gravitational pull on matter.

The weight of an object on the moon is 1/6 its weight on earth, but its mass is the same.


Length

MetermAbout 39 inches – width of a doorway1 km = 1000 m1 m = 100 cm


Other base units

Time – seconds – sTemperature – kelvin – KAmount of substance – mole – molElectric current – ampere – ALuminous intensity – candela – cd


Prefixes

Used to indicate multiples of 10See table 2-2 on page 35


Derived SI units

Combinations of base unitsCan also use prefixes


Volume

Amount of space occupied by an object.SI unit is cubic meters, or m3

We often use cubic centimeters, or cm3

Important – 1 cm3 = 1 mL1 m3 = 1 000 000 cm3

We also use the liter, or LEqual to 1 cubic dm, or dm3

There are 1000 mL in 1 L


Density

The ratio of mass to volume

volumemassdensity

VmD


Density

SI unit is kg/m3

We often use g/mL or g/cm3 in Chemistryg/L or kg/m3 might be used for gases

massdensityvolume


Conversion factors

Used to convert from one unit to anotherA ratio derived from equality


Example

How many seconds are in 1 day?


Example

How many centigrams are there in 6.25 kg?


Units

When doing conversions, keep track of your units.

They should cancel out to get units you want at the end.


Examples using table

Convert 10 cm to m.Convert 25 mL to L.Convert 50 mg to kg.Convert 33 cm3 to mm3.


Discuss

Section ReviewPage 42


Accuracy vs. Precision

Accuracy – closeness to correct or accepted value

Precision – closeness of a set of measurements of the same quantity made the same way

See page 44, figure 2-3


Percent error

Finds accuracy of a single value or an average value.

See sample problem 2-3 on page 45

100

accepted

alexperimentacceptederrorpercent


Reading instruments

Estimate the last digit.Example – a ruler is marked to a tenth of

a centimeter.Your measurement should be to the nearest

hundredth of a centimeter.Example – a thermometer is marked to

the nearest degree.Your measurement should be to the nearest

tenth of a degree


Significant Figures

All the digits known in a measurement, plus one that is somewhat uncertain.

All nonzero digits are significant Zeros are governed by four rules1. Zeros between nonzero digits are

significant 203 has 3 sig figs 5.0279 has 5 sig figs


Significant Figures

2. Zeros in front of all nonzero digits are not significant

0.0035 has 2 sig figs 0.0008 has 1 sig fig

3. Zeros at the end of a number and after the decimal point are significant.

75.000 has 5 sig figs 0.000800 has 3 sig figs


Significant Figures

4. Zeros at the end of a number but before the decimal point may or may not be significant.

If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show all

zeros are significant, use a decimal point. To show some are, use scientific notation (tomorrow) 2000 has 1 sig fig 2000. has 4 sig figs


How many sig figs?

2.52 sig figs

2.503 sig figs

2502 sig figs

2.50 x 102

3 sig figs

250.04 sig figs

0.00252 sig figs

0.002503 sig figs

0.0025014 sig figs


Rounding

If the next digit is less than five, round down.3.044 → 3.04

If the next digit is more than five, round up.3.046 → 3.05

If the next digit is a five and there are nonzero digits after it, round up3.0452 → 3.05

If the next digit is a five and not followed by nonzero digits round to the even number3.045 → 3.043.035 → 3.04


Adding or subtracting with sig figs

The answer must have the same number of digits after the decimal point as there are in the measurement with the fewest digits after the decimal point.


Example

Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Round the answer to 1.253

25342.121342.0040.1


Multiplication and Division

The result should have the same number of significant figures as the least number of significant figures in any factor.


Example

Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would round our answer to 1.6

608.12.134.1


Conversion factors

Are not considered when finding the number of significant figures.

Are exact


Discuss

How do you round a number that ends in a five if you are rounding to the place before the five?

What is the difference between accuracy and precision?

How many significant figures are in the answer when you multiply? When you subtract?


Scientific Notation

Useful when writing very small or very large numbers

696 000 000 m = 6.96 x 108 m4 000 000 km = 4 x 106 km0.012 kg = 1.2 x 10-2 kg0.000 000 000 567 s = 5.67 x 10-10 s


Scientific notation

The mantissa (number in front) is greater than or equal to 1 but less than 10.

Only significant figures are shown.All digits shown are significant figures.

2000 has 1 sig fig2000. has 4 sig figs2.0 x 103 has 2 sig figs2.00 x 103 has 3 sig figs


Multiplying in Scientific Notation

Multiply the mantissas.Multiply the units.Add the exponents.


Example

m 100.6m 100.2m 100.3 999

327 m 1036

326 m 106.3

3999 m 100.60.20.3


Dividing in scientific notation

Divide the mantissas.Divide the unitsSubtract the exponents.


Example

31

3

m 1050.1kg 10635.7

313

mkg10

50.1635.7

32

mkg1009.5


Addition and subtraction

If the exponents (and units) are the same, you can simply add or subtract the mantissas and keep the exponents and units the same.

If the exponents are different, do it on your calculator.Your book shows you how, but most people don’t like to

do it that way.If the units are different, you can’t add or

subtract.


Direct proportions

Two quantities are directly proportional if dividing one by the other gives a constant.

Graph is a straight line that passes through the origin

General forms of the equation:

kxy

kxy


Inverse proportions

Two quantities are inversely proportional if their product is constant.

Graph is a hyperbola (see page 57)General forms of the equation:

kxy

xky

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Measurements and Calculations

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