Measurement and Calculation

Unit 2

The Fundamental SI Units (le Système International, SI)

Physical Quantity Name Abbreviation

MassLength

Time

Temperature

Electric Current

Amount of Substance

Luminous Intensity

kilogram

meter

second

Kelvin

Ampere

mole

candela

kg

ms

K

A

mol

cd

SI Units

SI PrefixesCommon to Chemistry

Base unit1

100

Deci (d)1/1010-1

Centi (c)1/10010-2

Milli (m)1/1000

10-3

Micro (μ)1/1000000

10-6

Nano (n)10-9

Pico (p)10-12

Kilo (k)1,000103

Mega (M)1,000,000

106

Giga (G)109

Dimensional Analysis• A simple mathematical approach to converting

between units.• Involves conversion factors (fractions).• Follows simple math functions (x/÷)• We can use conversion factors for metric conversions

as well as other conversions.• Dim. analysis can be used to convert from 1 unit to

another.One step or several steps.

• Each conversion factor represents a math function – treat it as such.

Dimensional analysis

• Set up: looking for

given

Example: 25 cm = ? mm

1 cm = 10 mm; cm is given, mm is looking for

Conversion factor: 10 mm = 1cm

25 cm x 10 mm = 250 mm

1 cm

Unit conversions

• Practice:

1. What is the volume of a 250-mL beaker in L?

2. What is the mass of a 9.5 g sugar cube in mg?

3. A car travels 74,000 meters. How many km is this trip?

Accuracy vs. Precision

• Accuracy refers to how close a measurement is to the true or actual value.

• Precision refers to how close a series of measurements are to one another.

Accuracy vs. PrecisionAre the following pictures illustrating accuracy, precision,

neither, or both?

Accuracy vs. PrecisionA class of chemistry students determined the mass of a quarter to be 5.200 g. To confirm this, several students reported their “massing” 4 times. The following data was collected. Classify these students results as precise, accurate, neither, or both.

STUDENT MASS (g)A 5.240 5.242 5.239 5.240B 5.200 5.205 5.199 5.200C 5.251 5.100 5.105 5.244D 5.201 5.100 5.300 5.205

Reporting Measurements

• To indicate the uncertainty of a single measurement scientists use a system called significant figures

• Our data can only be as precise as the least precise measuring tool/instrument

• The last digit on any measurement is estimated by the reporter

How HOT are you??

• Heat (energy) cannot be measured directly.• We can measure heat transfer by change in

temperature.• We define temperature as the average

kinetic energy of a system.movement within a substance

• Measure temperature with a thermometer.

Temperature Scales• Fahrenheit Scale, °F

Relative scale• Celsius Scale, °C

Relative scaleWater’s freezing point = 0°C, boiling point = 100°C

• Kelvin Scale, KAbsolute scaleWater’s freezing point = 273 K, boiling point = 373 K

• oC = K - 273 K = oC + 273

Temperature Conversion Practice

• Convert the following from oC to K:1. 55oC2. 173oC3. -28oC4. -215oC5. 88oC

• Convert the following from K to oC:1. 15 K2. 295 K3. 415 K4. 63 K5. 186 K

Graphing

1. Determine the variables.- Independent x-axes- Dependent y-axes

2. Determine the range of values.

3. Utilize all of 1 side of the graph paper.- usually start at ‘0’ but NOT ALWAYS

4. Makes scales easy & keep consistent

Graphing

5. Label both axes (include unit).

- draw axes with a straight edge

6. Give your graph an appropriate title.

- dependent vs. independent

7. Titles, axes, & labels must be in INK!

8. Plot data with ‘x’ not ‘•’ (may be in pencil)

9. Draw “best-fit” line through your data

Graphing

10. You may be asked to use your graph to

draw conclusions & make predictions.

• Two examples would include:Interpolation – within the limits of the dataExtrapolation – beyond the limits of the data

“Best-Fit” Line

                                                

                                                

                                                

                                                

                                                

                                                

Distance vs. Time for Freefall

Scientific Notation

• A shorthand method of expressing large and small numbers using exponents.

• Expresses values to the precision of the instrument.

M x 10n

M = any number between 1 & 10n = any integer (including 0)

• Example: 2.34 x 104

6.001 x 10-4

Scientific Notation

• Identify the correct scientific notations:• 3 x 102

• 4.5• 6.7 x 10-3

• 0.573 x 105

• 12 x 10-2

Scientific Notation

• Express the following in scientific notation:1. 2,300,0002. 0.004013. 5.0500

• Express the following in long-hand form:1. 6.1 x 102

2. 6.01 x 103

3. 6.6 x 101

4. 6.01 x 10-4

Scientific Notation

• Perform the following calculations, expressing your answer in scientific notation.

1. (6.0 x 104) (2.0 x 105)

2. (4.0 x 104) (2.0 x 10-6)

3. (8.0 x 103) / (2.0 x 106)

4. (2.0 x 10-3) / (4.0 x 10-8)

Rules for Counting Significant Figures

1. Nonzero integers are always significant

Ex. 46.3 m 3 sig. figs.

6.295 g 4 sig. figs

2. ‘0’ between nonzero digits are significant.

Ex. 40.7 L 3 sig. figs.

87009 km 5 sig. figs.

Significant Figures

3. ‘0’ in front of nonzero digits are not significant.

Ex. 0.009587 m 4 sig. figs.

0.0009 kg 1 sig. fig.

*The zeros in these cases are ‘placeholders’; they are used for spacing.

Significant Figures

4. Zeros are the end of a number and to the right of a decimal are significant.

Ex. 85.00 4 sig. figs. 9.070000000 10 sig. figs.

5. A decimal point placed after zeros indicates that the zeros are significant.

Ex. 2000. 4 sig. figs 2000 1 sig. fig.

Significant Figures• Do NOT count sig. figs. in the following

numbers:

1. Counting numbers

2. Constants

3. Conversion factors

Practice: Give the SigFigs• 54.9• 0.0023• 1000.5• 2.4 x 105

• 0.0970 x 10-3

• 8500.• 8500

Adding/Subtracting Numbers with Significant Figures

• When adding/subtracting, look for the LEAST DECIMAL measurement to determine the correct number of sig. figs. (the least precise)

• Round answer to the same decimal place

Ex. 54 g + 108.6 g + .0004 g =

55.24 mL – 2.1 mL =

Multiplication/Division with Significant Figures

• Result has the same number of significant figures as the measurement with the smallest number of significant figures

• Count the number of significant figures in each measurement

• Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures

4.5 cm x 0.200 cm = 0.90 cm2

2 sig figs 3 sig figs 2 sig figs

Practice: give the SigFigs

• 87.9 + 156.098 + 40• 63.7 – 56.987• 62.4 x 3.1• 587 / 6.247• 3.567 x π

Density• Density is a property of matter representing the mass

per unit volume• For equal volumes, denser object has larger mass• For equal masses, denser object has small volume

VolumeMass

Density

Density

• Solids = g/cm3

1 cm3 (length x width x height) = 1 mL• Liquids = g/mL

1 mL of H2O = 1 g at 4oC• Gases = g/L• Volume of a solid can be determined by water

displacement

Using Density in Calculations

VolumeMass

Density

DensityMass

Volume

Volume Density Mass

Example

• A piece of lead has a mass of 127 g and a volume of 11.2 cm3. Calculate the density.

• Density = 127 g / 11.2 cm3 = 11.3 g/cm3.

Practice

• Methanol has a density of 0.792 g/mL. What is the mass of 22.3 mL methanol?