Temperature Scales and Conversions 0°C 233.15 K 273.15 K 373.15 K - 40°F - 40°C 212°F 32°F 100°C 0 K - 273.15°C - 459.67°F Boiling point of water freezing.

Temperature Scales and Conversions

0°C

233.15 K

273.15 K

373.15 K

- 40°F- 40°C

212°F

32°F

100°C

0 K - 273.15°C - 459.67°F

Boiling point of water

freezing point of water

Absolute zero

Kelvin CelsiusT(°C) = T(K) – 273.15T(°C) = (T(°F) – 32)

FahrenheitT(°F) = T(°C) + 32

Converting T(°F) to T(K)

Convert body temperature 98.6°F to kelvin.

T(

98.6°F = 37°C

98.6°F = 310. K, or T = 310. K

Density =

Mass and volume are extensive, physical properties.

Density is an intensive physical property, the value of which changes with temperature.SI units of density are kg/m3.Commonly used units of density are g/cm3.

The density of water at 25°C is 1.00 g/cm3.Materials with densities greater than water will sink

in water (e.g. Au, density 19.32 g/cm3).Materials with densities less than water will float on

water (balsa wood, density 0.16 g/cm3).

massvolume

• I measure the mass of a chunk of metal and find it to be 26.113 g. I measure its volume by displacement and find it to be 10.0 mL. What is the density of the metal?

density = 26.113 g 10.0 mL

density = 26.113 g 0.14061 cm3

• I measure the mass of a cube of metal and find it to be 26.113 g. I measure one of its sides and find it to be 0.52 cm. What is the density of the metal?

volume of a cube = (0.52 cm)3 = 0.14061 cm3

= 2.61 g/cm3= 26.113 g 10.0 cm3

= 1.9 x 102 g/cm3

1 mL = 1 cm3

Density = massvolume

Density is used to convert mass to volume.How many milliliters will 15.0 g of ethanol occupy when

its density is 0.79 g/cm3?

15.0 g x conversion factor = volume in mL

Density is used to convert volume to mass.What is the mass of 100.0 cm3 of ethanol?

100.0 cm3 x 0.79 g = 79 g cm3

100.0 cm3 x conversion factor = mass in g

Remember:0.79 g = 0.79 g cm3 mL

15.0 g x mL = 19 mL 0.79 g

Density = massvolume

Density

The red liquid is water with food color. What can be said about the density of the yellow liquid?

The Scientific Method and Measured Data Central to the scientific method is the accumulation and

study of measured data. A measurement consists of two parts: a number and a unit. Both must be reported correctly. A systematic set of units (SI units and the metric prefixes)

allows scientists from different areas to communicate easily. A systematic way to report the number measured (by using

the correct number of significant figures) communicates how good you think your measurements are.

Types of Numbers (Data)

Exact numbers (data) obtained from counting some conversions (e.g. 2.54 cm = 1 inch, exactly)

Inexact most measured data

Significant figures apply to inexact numbers!

Uncertainty in Measured Data

Measured data is written to convey two (2) things!the magnitude of the measurementthe extent of its reliability

The more significant figures a measurement has, the more certain it is.

Worker #1 reports a mass of 12 g

Worker #2 reports a mass of 12.0142 g

12 g means 12 ± 1 g

12.0142 g means 12.0142 ±0.0001 g

12 g has 2 significant figures.

12.0142 g has 6 significant figures. 12.0142 g is the more certain (reliable) number.

Measured Values: Accuracy vs. Precision

• Accuracy is how close your measured value is to the right value (can be shown by % error).

• Precision is how well you can reproduce your measurement (can be shown by standard deviation).

accurate and

precise

precise but not accurate

not accurate not precise

Recording Data to the Correct Number of Significant Figures

23°C

22°C

21°C

recorded value = 21.6°C

23°C

22°C

21°C

recorded value = 21.68°C

The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit.

Making Measurements in the Lab: Recording Volumetric Data to the Correct Number of Significant Figures - Glassware with Graduations

20 mL

30 mL

30-mL beaker: the volume you write in your lab report should

be 13 mL

0 mL

1 mL

2 mL

Buret marked in 0.1 mL: you record volume as

0.67 mL

1. If the glassware is marked every 10 mLs, the volume you record should be in mLs. (Example A)

2. If the glassware is marked every 1 mL, the volume you record should be in tenths of mLs.

3. If the glassware is marked every 0.1 mL, the volume you record should be in hundredths of mLs. (Example B)

10 mL

Example A

Example B

Making Measurements in the Lab: Recording Volumetric Data to the Correct Number of Significant Figures - Volumetric Glassware

On this volumetric flask is written 500mL ± 0.2 mL. You would

record the volume of the liquid in this flask as 500.0 mL.

Look on the glassware for written indication of the precision of the volumetric flask or pipet.

Making Measurements in the Lab: Recording Masses to the Correct Number of Significant Figures

This one is easy: record EVERY number (especially zeros) that appears on the

display of the electronic balance.

Trailing zeros MUST be recorded.

How to Count Significant Figures All nonzero digits are significant (1.23 has 3 SFs).

All zeros between nonzero digits are significant (1.003 has 4 SFs).

Leading zeros are NEVER significant (0.01 has 1 SF).

Trailing zeros WHEN A DECIMAL POINT IS PRESENT are significant (0.0780 has 3 SFs and 180. has 3 SFs.)

Trailing zeros WHEN NO DECIMAL POINT IS SHOWN are not significant. (180 has 2 SFs.)

Scientific NotationAn unambiguous way to show the number of

significant figures (SFs) in your dataNumbers are written as the product of a number

greater than or equal to 1 and less than 10 and a power of 10.

Measurement in scientific notation #SFs

186282 mi/s0.0051900 m512.1 x 101 g

1.86282 x 105 mi/s5.1900 x 10-3 m5.121 x 103 g

654

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

Multiplication/Division: The answer contains the same number of SFs as the measurement with the fewest SFs.

25.2 x 6.1 = 153.72 (but only 2 SFs are allowed) = 1.5 x 102 (correct answer)

25.2 x 6.1 = 44.604747 (on my calculator)3.44627

25.2 = 7.3122535 (on my calculator)3.44627 = 7.31 (correct answer)

= 45 (correct answer)

Addition/Subtraction: The answer contains the same number of digits to the right of the decimal as that of the measurement with the fewest number of decimal places.

3.14159+ 25.2 28.34159

28.3 (correct answer)

3 SFs

33.14159 - 33.04 0.10159

0.10 (correct answer)

2 SFs

Calculators do NOT know these rules. It’s up to you to apply them!

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

Addition/Subtraction: Dealing with numbers with no decimal places. Convert both numbers to exponential notation with the same power of ten, and then use the decimal place rule.

286.4 x 105 - 8.1 x 103 = ?

286.4 x 105

- 0.081 x 105

286.319 x 105

286.3 x 105 (correct answer)

4 SFs

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

Addition/Subtraction: Dealing with numbers with no decimal places. Write out the numbers and underline uncertain digit.

286.4 x 105 - 8.1 x 103 = ?

28,640,000 (uncertain in 10,000 place) - 8,100 (uncertain in 100 place)

28,631,900 (take the uncertain digit farthest to the left)

28,630,000 or 2.863 x 107

4 SFs

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

Combined operations: Do the add/subtract first, carrying all digits, then do the multiply/divide. The only time you round is at the very end of the calculation.

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

% difference = 100 x (your value - accepted value)

accepted value

an exact number…it does not affect SFs

Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data

% difference = 100 x (3.015 - 3.025)

3.025

Find the percent difference between 3.015 and an accepted value of 3.025.

First, subtract 3.025 from 3.015: 3.015

- 3.025

result has 2 SFs - 0.010

Second, multiply by 100 and divide by 3.025 (4 SFs)

(in either order): - 0.3305785

Finally, round to 2 SFs: - 0.33 %

Converting Measurements Using Dimensional Analysis

Helps ensure that the answers to problems have the proper units.

Uses conversion factors to reach the proper units.A conversion factor is a fraction whose numerator and

denominator are the same quantity expressed in different units.

2.54 cm 1 inch and are conversion factors.1 inch 2.54 cm

2.54 cm = 1 inch (2.54 cm and 1 inch are the same length.)

Convert 0.8474 liters to cubic meters (m3).

3.785 L16.7 gal x = 63.2 L

1 gal

Convert 16.7 gallons to liters.

Converting Measurements Using Dimensional Analysis

OR

The density of air at ordinary atmospheric pressure and 25°C is 1.19 g/L. What is the mass, in pounds, of the air in a room that measures 12.5ft x 15.5ft x 8.0ft?

The volume of the room is (V = l w h):

12.5 ft x 15.5 ft x 8.0 ft = 1550 ft3 (We treat sig figs at the end.)

The temptation is to start with the density. But density has units in the numerator AND denominator:

Our answer should only contain a unit of mass (lbs).

Density Problem - Where to start?

The density of air at ordinary atmospheric pressure and 25°C is 1.19 g/L. What is the mass, in pounds, of the air in a room that measures 12.5ft x 15.5ft x 8.0ft?

Start with the volume (it has units only in the numerator).

Clearly, we need to change g to lbs and L to ft3.

Density Problem - pay attention to units!

The density 1.19 g/L is in metric units (a close cousin to SI units), but lbs (pounds) and cubic feet are English units.

For length, a good conversion factor is 1 in = 2.54 cm.

Since volume comes from the cube of a length, we have to cube the conversion factor:

Density Problem - Using conversion factors

If we stopped here, we would have a mass. But the units would be grams, not lbs. One final conversion is needed: 1 lb = 453.6 g (For a conversion that looks like this, the “1” is treated as exact, so the number of sig figs here would be 4.)

This is the calculation in dimensional analysis form (aka complete dimensional analysis form). As you work more problems, you might change the order of the conversion factors.

Density Problem - Dimension Analysis Form

With the conversion factors rearranged, it is clear what units have canceled each other:

You may then get the answer by, on your calculator, entering 1550 x 123 x 2.543 x 1.19 / 1000 / 453.6 =

115 lbs. Since we are allowed only 2 SFs, 120 lbs

Density Problem - Using your calculator to avoid rounding errors and expessing your final answer

with the correct number of SFs