1 | P a g e

AP/IB Chemistry

Introduction

Tools of The Trade

Mr. Salter Room S106

Name: ___________________________________________ Period: ___________

Brief History of Measurement:

Up until the time of Napoleon, every country has its own measuring system usually based on a body part of

the ruling monarch (thus the term ruler). The units of length might have been based on the length of a king’s foot

(thus the measurement foot). Weight units might have been called stones for the number of equal size stones it

took to counter-balance a king on a huge balance. Not only did every country have its own measuring system, but

it might have changed every time a leader died or was replaced.

Napoleon used cannon and cannon shells to conquer most of Europe. He didn’t want to run his supply lines

too thin; therefore he wanted to use locally produced cannon balls and artillery supplies. Since every country had

different measuring systems, he found it impossible to have the conquered countries manufacture his needed

supplies. He, therefore, ordered his scientists back in Paris to come up with a measuring system that was easy to

understand and use by the people in any country he occupied. He could then have all his supplies made locally to

his specifications. The system that the French scientists came up with was the metric system based upon divisions

of 10 using the same prefixes for length, mass and volume.

Most countries today still use this system for all their measurement. The North Atlantic Treaty

Organization (NATO) uses it so every member’s weaponry is interchangeable. Example: A 60-millimerter artillery

shell means that it has a diameter, at its width, of 60 mm. This could be fired by any member country’s guns.

Why then does the United States still use the English System of measurement? Napoleon never conquered

England. The United States was mainly developed from English heritage, so it ended up with the English

measurement system. Ironically enough, the British and its Commonwealth Countries now use the metric system,

but we in the U.S. still hold out. Most of our technical measurement, however, is metric.

2 | P a g e

Unit Vocabulary

1. Word: Accuracy a. Definition:

________________________________________________________________________________________________________________________________________

b. Example: ________________________________________________________________________________________________________________________________________

2. Word: Precision a. Definition:

_______________________________________________________________________________________________________________________________________

b. Example: ________________________________________________________________________________________________________________________________________

3. Word: Random Error (indeterminate error) a. Definition:

________________________________________________________________________________________________________________________________________

b. Example: ________________________________________________________________________________________________________________________________________

4. Word: Systematic error (determinate error) a. Definition:

________________________________________________________________________________________________________________________________________

b. Example: ________________________________________________________________________________________________________________________________________

Drawing

Drawing

Drawing

Drawing

3 | P a g e

Measurements

Essential Question

What are the essential parts of a measurement?

What measurement system do chemists use?

What are the Fundamental SI units?

1. What is a measurement?

2. What measurement system do chemists use?

3. What are the Fundamental SI Units?

4. What is mass?

5. What is the difference between mass and weight?

Lecture 1

11111

4 | P a g e

6. What is Volume?

7. What is Temperature?

Volume = 1 cm X 1 cm X 1 cm = 1 cm3

Volume = 1 cm3 = 1 mL

The relationship between Kelvin

and Celsius will be very important

to know. Kelvin and Celsius are

related by the following equation:

K = °C + 273.15

Make sure that you can convert back and

forth between Kelvin and Celsius.

5 | P a g e

The Fundamental SI Units

Physical Quantity Name of Unit Abbreviation

Mass Kilogram Kg

Length meter m

Time second s

Temperature Kelvin K

Electric current ampere A

Amount of Substance mole mol

Luminous intensity candela cd

The Prefixes Used in the SI System (Those most commonly encountered in chemistry are in bold type)

Prefix Symbol Meaning Exponential Notation

Tera T Trillion (1,000,000,000,000) 1.0 X 1012

Giga G Billion (1,000,000,000) 1.0 X 109

Mega M Million (1,000,000) 1.0 X 106

Kilo k Thousand (1,000) 1.0 X 103

Hecto h Hundred (100) 1.0 X 102

Deka da Ten (10) 1.0 X 101

Base Unit One (1) 1.0 X 100

Deci d Tenth (0.1) 1.0 X 10-1

Centi c Hundredth (0.01) 1.0 X 10-2

Mili m Thousandth (0.001) 1.0 x 10-3

Micro µ Millionth (0.0000001) 1.0 X 10-6

Nano n Billionth (0.000000001) 1.0 X 10-9

Pico f Trillionth (0.000000000001) 1.0 X 10-12

Unit Relationships (Conversion Factors)

Length Mass Volume

1,000,000,000 nm = 1 m 1,000,000,000 ng = 1 g 1,000,000,000 nL = 1 L

1,000,000 μm = 1m 1,000,000 μg = 1 g 1,000,000 μL = 1 L

1000 mm = 1 m 1000 mg = 1 g 1000 mL = 1 L

100 cm = 1 m 100 cg = 1 g 100 cL = 1 L

10 dm = 1 m 10 dg = 1 g 10 dL = 1 L

1000 m = 1 Km 1000 g = 1 kg 1000 L = 1 kL

1L = 1 dm3 1 mL = 1 cm3 1 L = 1000 cm3 2.54 cm = 1 in 1 kg = 2.2 lb 1 L = 1.06 qt

Each type of measurement has a

base unit- the meter (m) for length;

the gram (g) for mass; the liter (L)

for volume; the second for time.

All other units are related to the

base unit by powers of 10

The prefix of the unit name

indicates it the unit is larger or

smaller than the base unit.

6 | P a g e

Unit Conversion

Essential Question

What are Unit Relationships or Conversion Factors?

How is dimensional analysis used to convert units?

1. What are unit relationships?

2. What are the unit relationships for the following:

a) g and mg?

b) m and km?

c) ml and cm3?

d) L and dm3?

e) μg and g?

3. How is dimensional analysis used to convert units?

Now we will do some conversions involving just the metric system. There is only one correct way

to set up these problems. In fact this method will be very valuable throughout this course and for

physics and other sciences as well. Even if you think you can do the problem easier, or in your

head DON’T. This process, called dimensional analysis or factor-label method is the only way to

succeed.

Ex. 1: Covert 4.75 g to milligrams (mg)

Lecture 2

11111

7 | P a g e

Ex. 2: Convert 89.43 liters (L) to nanoliters (nL)

Ex 3: Convert 3.44 x 104 sec to kiloseconds (ksec)

Ex 4: Convert 55.82 micrometers (μm) to kilometers (km) [takes two steps]

Ex 5: Convert 0.0075 dg to mg

Ex 6: Convert 8.774 km to cm

Notice that working problems that involve only the metric system, the number of sig. figs. In the answer

will depend only on the original data given since all the conversion factors are definitions and therefore

have an infinite number of sig. figs.

Since we are living in a country that hasn’t seen fit to go completely metric, it is necessary to make

conversions between the two systems. There are many, many conversion factors that are available for

conversions between the two systems that it would be impossible to list them all. There are only three

conversions that are necessary. These need to be learned and are found at the bottom of page 5 in these

unit notes.

8 | P a g e

Ex. 7: Convert a 7 ft 4 in basketball player’s height into meters.

Ex. 8: Convert the mass of a very large wrestler (355 lbs) into kg

Ex. 9: Convert 1.00 gallons into liters

Ex. 10: The average velocity of an oxygen molecule at room temperature is 4.0 x 104 cm/sec. Find this

velocity in mi/hr. This problem requires two conversions. One from cm to mi. (both length units) and

one from sec to hr. (both time units)

Ex. 11: The volume of a room is 278 m3. Find the volume in in3.

9 | P a g e

Lecture 3

Uncertainty and Error in Measurements Essential Question

What are the differences between precision and accuracy?

What are the major sources of error in experimental measurements?

How can sources of error in experimental measurements be reduced?

1. What are the differences between precision and accuracy?

Two important concepts to understand are the differences between accuracy and precision.

___________________ refers to how closely individual measurements agree with the

generally accepted (correct value) or literature value. ____________________ is indicated

how many significant figures there are in a measurement. The more significant figures

(decimal points) that can be recorded for a measurement the more precise your measurement

is.

Example: The normal boiling point of water is 100°C. A mercury thermometer could measure

the normal boiling temperature of water as 99.5°C (+/- 0.5°C) whereas a data probe recorded it

as 98.15°C (+/- 0.05°C). In this case the mercury thermometer is more accurate whereas the

data probe is more precise.

Accuracy Precision

Single Data

Point

A single data point is accurate if it is close the

literature value

A single data point is

precise if it has many

decimal places/significant

figures. Meaning, you

used a very precise tool or

method for measuring the

value.

Set of Data

Points

A set of data points are accurate if the average or

mean is close to the literature value. This is the

reason we do multiple trials. Any random errors

cancel out when the average is taken, thus

random error is reduced.

A set of data points are

precise if they are all very

close together. This

definition refers to the

consistency of the data.

10 | P a g e

2. Analyze the accuracy and precision of each set of data

Example

Student A’s density

measurements

g/mL

Student B’s density

measurements

g/mL

Student C’s density

measurements

g/mL

Student D’s density

measurements

g/mL

Trial 1 5.423 5.20 4.20 3.9

Trial 2 9.000 5.24 4.18 6.5

Trial 3 1.203 5.22 4.21 7.2

Average 5.21 5.22 4.20 5.87

Actual value: 5.2 g/mL

3. What are the major sources of experimental error?

In experimental sciences such as chemistry, the results of experiments are never completely

reliable as there are always experimental errors and uncertainties involved. It is therefore

important to be able to assess the magnitude of these and their effect on the reliability of the

final results. You will need to become very comfortable with identifying, analyzing, and

evaluating experimental error. A big part of your lab report will consist of evaluating sources

of experimental error and how to avoid these errors in the future.

__________________________, arise mostly form limitations in the instruments

____________________ and can lead to readings being above or below the ‘true’ value. Note

random error will always accrue for any measurement. This is because the last digit of any

measurement is __________________. You can decrease random error by making careful

measurements, using a more precise instrument (more decimal points), and repeating an

experiment a number of times (3 to 5 times) and then averaging your results.

11 | P a g e

The random error is equivalent to the uncertainty in measurement. This is usually given by the

manufacturer of the equipment and expressed as ± a certain value. If this information is not

available, a good guideline is:

a) Analogue equipment the uncertainty is ± half the smallest hash marks.

b) Digital equipment the uncertainty is ± the smallest measure (the least count)

Note when the uncertainty is recorded, it should be to the same number of significant figures as the measured value. For example a balance reading to 53.457g ± 0.001

_______________________________ occurs in the same direction each time; it is either always

high or always low, always deviating from the ____________________ (accuracy of the

experiment). They arise from flaws or defects in the instrument or from poor experimental

design or procedure. Systematic errors can in principle be eliminated or at least reduced by

making modifications to the experimental design. Systematic error cannot be reduced by

repeating the experiment.

Experimental Errors

12 | P a g e

Lecture 4

Significant Figures Essential Question

Why are Significant Figures so Significant?

1. Why do we need to worry about significant figures (Sig Figs)?

Random Error exists in every measurement. This is because there are limitations in every

instrument that you use to measure something. A limitation in the instrument affects the

precision of that instrument or the number of possible digits that can be recorded for that

measurement.

The possible digits that can be recorded for any measurement are known as Significant Figures or

Sig Figs for short. Each measurement includes all the certain digits that everyone will agree on and

one uncertain or estimated digits. These digits make up a measurement’s significant figures.

2. How many digits in a measurement can be estimated?

13 | P a g e

SIGNIFICANT FIGURE RULES

1. All non-zero digits are significant

For example, 123 g has three significant digits

2. If the zeros precede the first non-zero digit, they are not significant

For example, 0.00012 m has two significant figures, and 0.01 has one significant figure

3. If the zeros are between non-zero digits, they are significant

For example, 40.103 kg has five significant figures, and 0.0503 has three significant figures

4. If the zeros follow non-zero digits, they are significant only if a decimal point is given

For example, 400. mL has three significant figures, but 400 mL only has one significant figure

5. For multiplication and division, an answer can only be as accurate as the measurement with the

least number of significant figures that goes into its calculation.

6. For addition and subtraction, the answer should contain no more digits to the right of the decimal

point than the measured value with the least number of decimal places that goes into its

calculation.

26.46 This has the least digits to the right of the decimal point (2)

+ 4.123

30.583 rounds off to 30.58 has 4 significant figures

2.61

x 1.2 This has the smaller number of significant figures (2)

3.132 rounds off to 3.1 has 2 significant figures

The last digit of any measured quantity is

uncertain and must be estimated. All of

the digits, including the uncertain one,

are called significant digits or, more

commonly, significant figures.

14 | P a g e

3. How do we apply the significant figure rules to a measurement(s)?

Ex 1: How many significant figures are in:

a) 29.43 ______ b) 507.2 ______ c) 0.0034 ______

d) 245,000 ______ e) 0.00008760 ______ f) 345,876.00 ______ g) 3 eggs ____

Ex 2: What is the area of a room that measures 8.3 m x 4.83 m?

Ex 3: Add the following measurements and give the answer to the proper number of significant

figures: 12.52 cm, 8 cm, and 72.3 cm.

Ex 4: Multiply 2.45 x 108 by 3.478 x 10-4. Show the answer to the proper number of sig. figs.

Ex. 5: Multiply 5.67 x 10-4 by 0.023 and divide the answer by 3.88 x 1012. Write the problem in a

single expression, calculate and show the answer to the proper number of sig. figs.

4. Determine the measured amount of water in each of the following volumes. Show the answer to

the proper number of sig. figs. Do all these measuring tools have the same precision? Explain.

15 | P a g e

Lecture 5

Uncertainties in Calculated Results Essential Question

How do you determine the uncertainty of a measurement in a calculated result?

1. What is the difference between the absolute uncertainty and the percent uncertainty?

2. How do we determine the uncertainties for measurements that are added or subtracted?

Ex. 1: A student took to temperature measurements during an experiment, the Initial and final temperatures. Use the student’s data below and calculate the change in temperature and record the answer with the correct calculated uncertainty.

Initial temperature = 20.1 ± 0.1 C°

Final temperature = 27.9 ± 0.1C°

Ex. 2: Consider two burette readings: Initial reading: 15.05 ± 0.05 cm3 Final reading: 37.20 ± 0.05 cm3 What value should be reported for the volume delivered?

16 | P a g e

3. How do we determine the uncertainties for measurements that are multiplied or divided?

Ex. 3: Use the calculated temperature change in Ex. 1 and the following equation to determine the

amount of heat released during the student experiment.

Heat Released = mass x specific heat x change in temperature

Mass reading: 5.456g ± 0.001

Specific Heat: 4.18 J/gC°

Ex. 4: Calculate the density (mass/volume) of an object using the following data:

Mass Reading: 24.0 ± 0.5 g

Volume Reading: 2.0 ± 0.1 cm3

4. How do we determine the accuracy of our experimental values?

Experimental value – Accepted value

Percent Error = X 100

Accepted Value

17 | P a g e

Lecture 6

Recording Experimental Data Essential Question

How should you organize your experimental data in a table?

1. What types of data should be recorded during an experiment?

2. How do you organize your data in a table?

Title of Data Table:

Independent Variable (Units and Uncertainty)

Dependent Variable (Units and Uncertainty) Trial 1 Trial 2 Trial 3

Leave room here to write qualitative data

The table for raw data is constructed prior to beginning data collection.

The independent variable is recorded in the leftmost column (by convention).

The dependent variable (that you measure) with the different trials is in the next columns.

The data table is given a descriptive title which makes it clear which experiment it represents.

Each column of the data table is labeled with the name of the variable it contains.

Below (or to the side of) each variable name is the name of the unit of measurement (or its symbol) in parentheses along with the measurements uncertainty.

Data is recorded to an appropriate number of decimal places as determined by the precision of the measuring device or the measuring technique (Use correct significant digits).

Raw data is recorded in ink. Data that you think is "bad" is not destroyed. It is noted but kept in case it is needed for future use.

Collect both qualitative and quantitative data. Plan ahead and leave space for your required qualitative data.

Calculations are not to be put in data tables.

18 | P a g e

Ex.1:

Table 2. Solubility Data Table for Sodium Acetate Trihydrate

Subsequent calculations are usually clearer if data is arranged in columns instead of rows

such as Ex. 2. This would also be a good table to use if there is not a clear independent

variable but a list of different measurements that need to be taken.

All calculations should be in a Results Table that should be similar to the table in Ex. 2.

Ex. 2:

Table 3: Determination of the Mass of 50 Drops of Water Delivered from a Dropping Pipette

Trial 1 Trial 2 Trial 3

Mass of beaker with water / g (±0.01 g)

58.33 58.45 58.42

Mass of empty beaker / g (±0.01 g)

56.31 56.40 56.38

Mass of Sodium Acetate Trihydrate per 10 mL of water

(g ± 0.1)

Temperature (°C ± 0.2) Trial 1 Trial 2 Trial 3

Leave room here to write qualitative data

19 | P a g e

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 100 200 300 400 500

Vo

lum

e, L

Temperature, K

The volume of 1.33 g O2 gas (P = 1atm) of varying temperatures (K)

Series1

Linear (Series1)

Lecture 6

Graphing Data Essential Question

Why is it important to graph your experimental data?

What steps should you take to create a graph of your experimental data?

1. Why are graphs important?

Once data is collected, it is necessary to determine the relationship between the independent and dependent variables in the experiment. You will construct a graph (or sometimes a series of graphs) from your data table in order to determine the relationship between the two variables. Graphs are also used to predict or estimate data that are difficult to determine experimentally. A graph is a pictorial diagram of experimental data. For each relationship that is being

investigated in your experiment, you should prepare the appropriate graph. In general your graphs

in chemistry are of a type known as scatter graphs. The graphs will be used to give you a

conceptual understanding of the relationship between the variables, and will usually also be used

to help you formulate a mathematical statement which describes that relationship.

2. What Steps should you take to create a graph of your experimental data?

Ex. 1: Graphs should include each of the elements described below:

Figure 1: Graph showing the volume (in liters) of 1.33 g O2 gas (P = 1 atm) at varying temperatures (K)

Dependent

Variable

Independent Variable

Best Fit Line

Title of Graph

Includes at Least 5 Data Points

Short description or explanation of graph

20 | P a g e

Step 1 Determine the independent and dependent variables

Step 2 Place the independent variable on the x-axes and the dependent variable on the y-axes.

Step 3 Scale the axes

1. Decide how many divisions are needed on the x-axis.

2. Divide the largest value from the data table for the independent variable by the

number of divisions you have chosen.

3. Find the closest whole number value that is a multiple of 1, 2, 5, or 10

4. Repeat for the y-axis

Step 4 Label the axes with the right units

Step 5 Plot the data

Step 6 Draw the line or curve that best fits the data

Step 7 Title your graph

Step 8 Interpret the graph (determine the relationship between the two variables)

Step 9 State a mathematical equation for the type of graph

Step 10 Interpolate and extrapolate the graph

Use the computer to graph the following data sets.

1.) A chemist measured the pressure of a gas in atmospheres at different temperatures in °C. Graph data. Predict the

temperature at which the pressure would equal zero from the graph.

Temp (°C) -136 -25 0 25 100 273

Pressure (atm) 0.50 0.91 1.00 1.09 1.37 2.00

2.) The solubility of potassium dichromate in grams per 100 grams of water was measured at different temperatures in °C.

Graph the data. Predict the solubility at 110 C.

Temp (°C) 0 20 30 45 60 70 100

Solubility 5 14 20 28 41 54 104

(g/100 g H2O)

3.) The following data was obtained when water was introduced into a vacuum chamber until some liquid was seen in the

chamber. The pressure in mbar was then measured at different temperatures in °C. Graph the data.

Temp ( ) 5 8 12 14 18 23 27 35 50 70

Pressure ( ) 8.7 10.7 14.0 16.0 20.6 28.1 35.6 56.2 123 312

4.) The pressure of a gas was measured in atmospheres as the volume in liters was varied. The following data was obtained.

Graph the data set.

Pressure (atmospheres) 2.0 4.0 6.0 8.0 10.0 12.0

Volume ( ) 0.0060 0.0030 0.0020 0.0015 0.0012 0.0010