General Chemistry
Unit 8
Measurement
(2013-2014)
 Units of Measurement
 Accuracy and Precision
 Significant Figures
 Scientific Notation
 Unit Analysis
 Density
 Percent Error
1
Unit of Measure
Qualitative:
Quantative:
2
Accuracy and Precision:
Accuracy and Precision Activity
Lab
Equipment
Your
Reading
Volume
Reading
#1
Volume
Reading
#2
Average
Reading
Precision
Prediction
1–5
1 = best
Actual
Precision
Ranking
Actual
Accuracy
Ranking
Burette
50 mL
Graduated
Cylinder
250 mL
Beaker
250 mL
Graduated
Cylinder
250 mL
Erlenmeyer
Flask
Burette
50 mL Grad
Cylinder
250 mL
Beaker
250 mL Grad
Cylinder
250 mL
Erlenmeyer
Flask
Actual
Reading
1. Predict how precise each piece of lab equipment is by ranking them from 1-5. 1 being most
precise to 5 being least precise. Put your predictions in column 5.
2. Read the volume of water in each type of lab equipment.
3. Record your answer in column 1.
4. Record the answers of two classmates in column 2 and column 3.
5. Find the average reading for each piece of lab equipment. Record your answer in column 4.
6. Obtain the actual volume of water in each piece of equipment.
7. Determine the actual ranking of precision of each piece of equipment by comparing the actual
reading to your average reading. Record the actual precision ranking in column 6.
3
Accuracy ____________
____________
____________
Precision ____________
____________
____________
4
Significant Figures
To determine how many significant figures a number has:
Atlantic Pacific Rule:
P = Pacific = Present decimal = Start on Left
A = Atlantic = Absent decimal = Start on Right
Pass over any zeroes until you come to a non-zero digit. Count every digit starting with that digit. They are all
considered significant starting from the non-zero digit.
Examples:
5
Multiplying Sig Figs:
Multiply the numbers as you normally would. To determine the number of digits to report, calculate the number of
significant figures for each of the numbers being multiplied (decimal present or absent). The answer will have the
same number of significant figures as the number being multiplied with the lowest number of sig figs.
Example:
x
33.874 (left : 5 sig figs)
11.24 (left : 4 sig figs)
380.74376
(From the calculator), the answer is 380.74376 BUT 11.24 only has 4 sig figs, so the answer can only contain 4
sig figs.
Start counting from the left:
380.74
123 4
Look at the digit in the 5th place to see if it is a 5 or higher. If it is a 5 or higher, the 4th digit would be rounded up
by one. In this example, it is a four so no rounding will take place. The correct answer is 380.7.
Examples:
Dividing Sig Figs:
Follow the same rules for multiplication.
Examples:
6
Adding Sig Figs:
Add numbers as you would a normal addition problem.
To determine the number of digits in your answer: Look at the number of places after the decimal in each of the
original numbers. The answer will match the value that has the fewest places after the decimal.
Example:
+
44.223
11.55
55.773
(From the calculator) the answer is 55.773, but 11.55 only has 2 places after the decimal so the answer must be
reported to 2 places after the decimal
(55.77).
From the previous example if the 3 in thousandths place had been a 5 or higher, the answer would have been
reported as 55.78.
So before reporting places after the decimal, you must look at one place past the correct answer to see if that
digit is 5 or more. If it is, the last reported digit must be rounded up by one.
Example:
+
28.218
1.55
29.768
Since 1.55 only has 2 places after the decimal, the answer would be 29.76 BUT since an 8 is in the place after
the 6, the answer is reported as 29.77.
Examples:
Subtracting Sig Figs:
Follow the same rules as Addition: Look at the places after the decimal. The answer must match the number
with the fewest places.
Examples:
7
Scientific Notation
When writing a number in scientific notation, there are two parts:
1. a number equal to or greater than 1 and less than 10
1 ≤ n < 10
2. a power of 10
Example:
2.37 x 105
Writing a number in scientific notation
Example:
# of electrons in a circuit:
6,250,000,000,000,000,000
Step 1: If original # is larger than 1, the power is going to be POSITIVE!
Step 2: Put imaginary decimal point at the end of the number.
6,250,000,000,000,000,000.
Step 3: Put another imaginary decimal point in the position where the number is between 1 and 10
6.250 000 000 000 000 000.
Step 4: Move the decimal at the end of the number until it is on top of the decimal in the 6.25 position. Count the
positions as you move.
Step 5: The number of times you move is equal to the power value.
Step 6: Write the value that is now
1 ≤ n < 10
followed by
x 10
and
The number of times the decimal moved should be written as a superscript on the 10.
Add units to the answer
Answer: 6.25 x 1018 electrons/sec
To undo the scientific notation, move the decimal 18 times to the right (since the power is positive, the new value
will be larger than 10)
8
Adding / Subtracting with Scientific Notation:
If the powers are not equal then one of them must be changed to make them match before addition or subtraction
can take place:
9.42 x 109
+1.12 x 108
Since both of these powers are positive, it means as the decimal is moved to the right the answer is going to get
bigger, while the power number is going to get smaller.
Example:
9.42 x 109 = 94.2 x 108 = 942. x 107
So, changing this first number to be to the power of 8, the problem becomes:
94.2 x 108
+1.12 x 108
Now, adding them together, the answer looks like
95.32 x 108
Last step – check for places after the decimal. Limiting value is 94.2, so the answer will contain one decimal
place:
95.3 x 108
Multiplying and Dividing with sig figs:
9
Name ___________________________________
General Chemistry Worksheet
"Significant Figures"
Part 1. Determine the number of significant figures in each of the following measurements and write your
answer in the space provided.
1) 8 675 309 g
_________
4) 30 200 s
__________
2) 0.035 6 m
_________
5) 0.080 20 g __________
3) 801.50 mL
_________
6) 1000 K
__________
Part 2: Round the following quantity to the specified number of significant figures.
7) 650,000 mL to one sig fig.
____________________________
8) 0.001 342 94 g to four sig figs.
____________________________
9) 49 203.03 g to three sig figs.
____________________________
10) 48 412 g to two sig figs.
____________________________
11) 0.000 823 938 0 g to five sig figs.
12) 7600 g to one sig fig,
____________________________
____________________________
Part 3: Perform each of the following calculations and express the answer to the correct number of
significant figures.
13) 69.24 cm + 14.2 cm =
____________________________
14) 13.5 mg – 8 mg =
____________________________
15) 45.90 dam x 5.41 dam =
____________________________
16) 34.9 km / 11.169 km =
____________________________
17) 0.0023 Mg x 787 Mg =
____________________________
10
General Chemistry Worksheet
"More Practice"
Determine the number of significant figures in the following measurements:
1.) 640 cm3
_____
2.) 0.000 000 009 234 00 mL
_____
3.) 6,650.000 kg
_____
4.) 790,001 dag
_____
Perform the following calculations and express the result in the correct number of digits:
5.) 22.0 m + 5.28 m + 15.554 m =
____________
6.) 0.0050 m2 x 0.042 m =
____________
7.) 14000 kg + 8000 kg - 590kg =
____________
8.) 300.3 L / 180. sec =
____________
9.) (0.054 kg + 1.33 kg) x 5.4 m2 =
____________
10.) 13.75 mm x 10.1 mm x 0.91 mm =
____________
Express the following quantities in scientific notation:
11.) 8,800,000,000 cm =
_____________________
12.) .000 000 06 L =
_____________________
13.) 0.210 5 g =
_____________________
14.) 4813.67 hm =
_____________________
15.) 654,321.789 Gg =
_____________________
16.) 0.000 683 5 mL =
_____________________
11
Take these measurements out of scientific notation and put them into standard notation:
17.) 8.4356 x 10-4 =
_____________________
18.) 6.574839 x 103 =
_____________________
19.) 4.21 x 106 =
_____________________
20.) 9.21 x 10-7 =
_____________________
Carry out the following calculations.
21.) 2.48 x 102 kg + 9.17 x103 kg + 7.2 x 101 kg =
_____________________
22.) 4.07 x10-5 mg + 3.966 x 10-4 mg + 7.1 x 10-2 mg =
_____________________
23.) 3.890 x 108 km / 1.97 x 103 s =
_____________________
24.) 1.111 1 x 105 cm x 5.82 x 104 cm =
_____________________
Without using a calculator, solve the following problems:
25.) 2.000 x 10120 mL x 3.0 x 1044 mL =
_____________________
26.) 5.000 x 10341 g / 5.00 x 10141 mL =
_____________________
12
Name ___________________________________
General Chemistry Worksheet
"Scientific Notation"
Change the following numbers to proper scientific notation:
1. 65.7 g
2. 0.005 45 g
3. 22 450 000 g
4. 3 450 678 001 g
5. 679.3 g
6. 0.0803 g
Change the following numbers to standard notation:
7.
6.5 x 10-2 g
8.
9.75 x 106 g
9.
3.4009 x 10-5 g
10.
1.847 x 102 g
11.
8.85 x 10-1 g
Addition / Subtraction Problems:
12. 2.367 x 10-3 mL + 5.4 x 10-2 mL
13. 6.50 x 101 mL
+ 4.321 x 102 mL
14. 4.89 x 10-3 mL
+ 2.17 x 10-6 mL
15. 9.875 x 102 mL
- 2.343x101 mL
13
Multiplication Problems (Make sure the answer is in scientific notation form):
16. (2.87 x 105 mL) x (3.514 x 109 mL)
17. (5.0 x 10-2 mL) x (7.85 x 104 mL)
18. (1.042 x 10-1 mL) x (4.002 x 10-5 mL )
19. (2.21 x 105 mL) x (1.807 x 10-7 mL)
Division Problems (Make sure the answer is in scientific notation form and has the right number of
sig figs.:
20. (9.4 x 107 mL) / (1.24 x 105 mL)
21. (2.4 x 106 mL) / 5.49 x 109 mL)
22. (1.92 x 10-2 mL) / (2.3 x 106 mL)
23. (9.2 x 10-3) / (6.3 x 10-5)
14
Name ___________________________________
General Chemistry Worksheet
"Significant Figures and Scientific Notation"
Part 1: Determine the number of significant figures in each of the following measurements and write your answer in the
space provided.
1) 8 675 309 g
________
4) 30200 s
________
2) 0.0356 m
________
5) 0.080 20 g
________
3) 801.50 mL
________
6) 1 000 000 K
________
Part 2: Round the following quantity to the specified number of significant figures.
Standard Notation
7)
695,900 mL to three sig. figs.
8)
0.001 342 94 g to four sig. figs.
9)
49 203.03 g to three sig. figs.
Scientific Notation
10) 0.000 000 775 2 mg to two sig. figs.
11) 0.000 293 749 0 in to four sig. figs.
12) 3400 kg to one sig. fig.
Part 3: Perform each of the following calculations and express the answer to the correct number of significant figures.
Standard Notation
Scientific Notation
9)
69.24 dm + 144. 2 dm =
10) 13.5 mg – 8 mg =
11) 245.90 dam x 9.41 dam =
12) 34 km2 / 1581.169 km =
13) 0.0023 Mg x 77 Mg =
14) 5.44 cm x 31 cm x 0.0984 cm =
15) 0.043 kg / 452.1 kg/mL =
16) 300 ft x 9.7600 ft =
15
Factor Label Method
(Notes on how to convert using conversion factors)
I.
Conversion Factor: a ratio that can be used to convert from one unit to
another.
 The numerator and the denominator are equal to each other
 The denominator’s unit should be the same as the given numbers
unit
 The numerator’s unit will be the unit you want to convert to
Example of a conversion factor:
4 quarters or
1 dollar
12 eggs
1 dozen
II.
Factor Label Method Procedure:
1. Write the given number and unit
2. Set up a conversion factor (fraction used to convert one unit to
another)
3. Place the given unit as denominator of conversion factor
4. Place desired unit as numerator
5. Cancel units
6. Solve Problem
III.
Factor Label Method Procedure (Metric to Metric):
1. Write the given number and unit
2. Set up a conversion factor (fraction used to convert one unit to
another)
3. Place the given unit as denominator of conversion factor
4. Place desired unit as numerator
5. Place a “1” in front of the larger unit
6. Determine the number of smaller units needed to make “1” of the
larger unit
7. Cancel units
8. Solve Problem
16
Metric System Units
(Number of base units
needed to make one)
Grand
Giga
G
1,000,000,000
Master
Mega
M
1,000,000
King
Kilo
K
1,000
Henry
Hecto
H
100
Died
Deka
Da
10
By
Base Unit
Liter, Meter, Gram
(Number needed to make
one base unit)
Drinking
Deci
d
10
Chocolate
Centi
c
100
Milk
Milli
m
1,000
Monday
Micro
μ
1,000,000
Night
Nano
n
1,000,000,000
Other Important Conversions:
12 in. = 1ft
2 pt = 1 qt
1 lb = 454 g
1 in = 2.54 cm
3 ft = 1 yd
4 qt = 1 gal
1 lb = 16 oz
1 m = 39 in
5280 ft = 1 mi
1 qt = 0.946 L
1 metric ton = 2200 lb
1 mi = 1.61 Km
1760 ft = 1 mi
1 qt = 32 fl oz
17
Metric Conversions Practice Worksheet
Complete the following problems using UNIT ANALYSIS (must show work). Remember to
have your answer to the proper number of significant figures.
(b = base and units are grams or liters or meters)
G _ _ M _ _ k h da b d c m _ _ μ _ _ n
1. 550.0 millimeters (mm) = ? meters (m)
2. 9.50 dekaseconds (das) = ? deciseconds (ds)
3. 2500 centigrams (cg) = ? kilograms (kg)
4. 5.30 centimeters (cm) = ? millimeters (mm)
5. 462.55 Gigaliters (GL) = ? hectoliters (hL)
18
6. 77.1 micrograms (μg) =? grams (g)
7. 21000 millimeters (mm) = ? kilometers (km)
8. 500.88 Megaliters (ML) = ? kiloliters (kL)
9. 442.6 decimeters (dm) = ? nanometers (nm)
10. 34.5 Gigagrams (Gg) = ? nanograms (ng)
19
Unit Analysis Practice
You must show all of your work. Your answer should be reported to the
correct number of sig figs.
G _ _ M _ _ k h da b d c m _ _ μ _ _ n
1) Convert 62 km to centimeters
2) Convert 198.50 micrograms to dekagrams
3) Convert 15.00 ft to meters
4) 5.00 meters to inches (you should have a hint memorized!!)
5) Change 64 hours to seconds
20
6) Change 1,314,000 minutes to years
7) Convert 3.0 liters to quarts (hints: 1 gallon = 4 qts, 1 liter = 1.0567 qts)
8) Change $8.25 / hour to dollars per year
9) Change 220 feet per second to miles per hour (hint: 1 mile = 5280 ft)
10)
Suppose you plan to visit Mammoth Caves in Kentucky. You want
to take the three-mile walking tour. At home you pace yourself and
find out that you stroll 90 feet per minute. Use unit analysis to
determine how many hours it will take you to walk the 3 miles. (hint: 1
mile = 5280 ft)
21
Factor Label Problems
1 mile = 1.61 km
2.54 centimeters (cm) = 1 inch
1 cup = 236.59 milliliters (mL)
5280 feet = 1 mile
1) 1254.50 inches = ? feet
2) 15.8 miles = ? kilometers
3) 459.75 mL = ? cups
4) 62.88 inches = ? cm
5) 42 hours = ? days
6) 400. minutes = ? hours
22
7) 3.0 miles = ? inches
8) 9.000 weeks = ? minutes
9) 4590 seconds = ? days
10)
43.0 cups = ? Liters
11)
14.75 μm (micrometers) = ? yards
12)
65 miles/hour = ? meters/sec
13)
80.50 kilometers /year = ? centimeters/sec
23
Reading Lab Equipment Correctly
Must always report one digit past what is given on the scale of that piece of equipment.
This last digit is called the uncertainty digit…you are estimating it as best as you can.
Examples:
24
25
26
27
Measurement Lab Activity
There are eight lab stations set up and each will ask you to answer a question related to measurement. Please
record your values (a complete value requires UNITS AND UNCERTAINTY!!!) and answer the follow-up question
in a complete sentence.
Station 1:
Temperature of beaker A: __________
Temperature of Beaker B: ___________
Convert both temperatures into the appropriate SI unit, which for temperature is: ________________.
Temperature A: ___________
Temperature B: _______________
What is the accuracy of the scale on the thermometer?
This means that you should read your measurement and estimate a value in the _________ place.
When measuring the temperature of a liquid, what procedural error must you avoid? Explain.
Station 2:
Determine which graduated cylinder would be most accurate for measuring the following:
a) A volume of 13 mL___________
b) A volume of 31 mL ___________
When reading the graduated cylinder, you must remember to read the ____________ of the __________.
What is the accuracy of the scale on each graduated cylinder?
10 mL ______ 25 mL _________
50 mL_________
100 mL __________
This means that you should read your measurement and estimate a value in what place?
10 mL ______ 25 mL _________
50 mL_________
100 mL __________
Station 3:
Determine the accuracy of the 10 mL mark on the beaker. If it is not accurate, state whether it is over or under
and by how much.
Should you use a beaker or a graduated cylinder to measure volumes? Why?
28
Station 4:
Determine the accuracy of the 50 mL and the 75 mL marks on the Erlenmeyer flask are accurate. If they are not
accurate, state whether it is over or under and by how much.
Should you use a graduated cylinder or an Erlenmeyer flask to measure volumes? Why?
Station 5:
If this buret was originally filled to the 0 mL mark, how much liquid has been removed?
What is the accuracy of the scale on the buret?
This means that you should read your measurement and estimate a value in the _________ place.
Based on the design on the buret, what is its purpose? Be clear about your answer.
Station 6:
What is the length of each of the pieces of string?
Short ____________
Long _______________
What is the accuracy of the scale on the meter stick and ruler?
This means that you should read your measurement and estimate a value in the _________ place.
Station 7:
What is the mass of each of these samples?
A:__________ B:_____________
C:_____________
What is the accuracy of the balance you used? Can you estimate a final digit on the electronic balances?
Station 8:
Use the equipment provided to determine the density of the irregular object. Show your density calculations
and explain how each value was determined.
29
Answer the following questions on density and experimental error. Put your answers on the lines provided.
____________ 1. Cerium sulfate has a density of 3.17 grams per cubic centimeter. What is the volume of .54 grams of this
substance?
____________ 2. Cerium sulfate has a density of 3.17 grams per cubic centimeter. What is the volume of 1.25 grams of
this substance?
____________ 3. What is the mass of a piece of aluminum having a volume of 15.12 cubic centimeters and a density of
2.70 grams per cubic centimeter.
____________ 4. What is the density of a gold nugget having a volume of 2.39 cubic centimeters and a mass of 45.58
grams? Your answer must have the correct number of significant digits.
____________ 5 What is the density of a brick if 51.21 g occupy 31.32 cubic centimeters?
____________ 6. What is the density of a cardboard if 6.2 g occupy 8.56 cubic centimeters?
____________ 7. Tin has a density of 7.28 grams per cubic centimeter. What is the volume of 11.2 grams of this substance?
30
Density:
Density and Experimental Error:
1a. __________ Your measurement of the volume of tap water is 9.6 mL, 9.52 mL and 9.553 mL using 3 different graduates.
What is the average volume of the tap water?
1b. __________ The average mass of this tap water is 9.2 g, what is the density?
2. __________ The standard density of water is 1.00 g/mL, what is your experimental error for the problem above?
3. __________ What is your percentage error for the above problem?
31
Layered Solutions Activity
Objective:
To create a column of distinct layers of different solutions.
Procedure:
1. In five different cups, place the following ingredients:
Chart 1: Ingredients for layered solution
Cup Number
Salt (g)
Warm water (mL)
3.40
6.00
0.00
8.00
7.60
60.0
40.0
50.0
40.0
70.0
Calculated Density
(g/mL)
2. Once you have added all of the necessary materials, stir each one with a spoon for at least one
minute until all of the salt is completely dissolved.
3. Using sig figs, calculate the density for each cup and record the density in the last column of Chart
1.
4. Using the balance and 10 mL of each solution you just made, measure the density of each solution.
Record these values for density in Table 1 on the back of this sheet.
5. Determine the order to put the liquids into the graduated cylinder. Which one should go in first,
the least dense or the most dense?
6. Add food coloring to create a rainbow effect with the different layers.
7. Using your pipette, carefully transfer 20 mL from each cup into the 100 mL graduated cylinder.
Observations:
Table 1: Data from the Layered Solution Activity
Cup
Number
Measured Density from
solutions made
(g/mL)
Projected order to fill
graduated cylinder
The best layers will win a prize!!!
32
Lab: Graphing and Density
Name:________________________
Purpose: -Determine the density of a liquid from a graph of mass and volume.
-Determine the layering order of three liquids if poured together into a
graduated cylinder.
Problem: Are density and the layering order of liquids in a graduated cylinder
related?
Hypothesis: (If…,then…)
Experiment:
Materials:
25mL graduated cylinder
balance
rubbing alcohol
water
dropper
calculator
Procedure:
1) Determine the mass of 5mL of water and record this in the data table.
a. Place the empty graduated cylinder on the balance and record this mass below:
i. Mass of empty cylinder:_____________g
b. Place the 5mL of water in the cylinder and carefully place it on the balance.
c. Subtract the mass of the empty cylinder.
d. Record the mass in the data table.
2) Repeat step 1 for 15mL and 25mL of water.
3) Repeat step 1 for 5mL, 15mL, and 25mL of rubbing alcohol.
a. Use the beaker of rubbing alcohol that is at your table. Return the alcohol to the beaker
when finished for the next class to use!!
4) We will not be measuring the values for silicone oil because it is too messy. The data has already
been given to you in the data table.
5) Graph the data on the provided graph under the data table.
a. Use a different colored pencil for each line.
b. Provide a key to identify each color.
c. Make a title for the graph.
d. Make a best-fit line for each color. The line must go through 0,0.
e. Determine the slope of each line and show your work.
Data:
Volume (mL)
Water (g)
Rubbing
Alcohol (g)
5.0
Silicone
Oil (g)
4.60
15.0
13.70
25.0
23.10
33
___________________________________
Use slope determination of each line to calculate the density of each liquid: (You MUST show your work!
Remember to put units with your work and answer.) Circle your answer.
Water:
Rubbing alcohol:
Silicone oil:
Given your results, how will the liquids be layered if poured carefully into a graduated cylinder? Make
sketch show which liquid would form the bottom… will be in the middle, and … will be on top.
34
Density Graphing Pre-test Activity
1. Graph the following data on a sheet of graph paper.
What variable goes on the x-axis? __________
What variable goes on the y-axis? __________
2. Make sure to include all “graph” features
Volume, mL
0.0
2.0
5.0
10.0
15.0
Mass, g
0.00
5.40
12.50
27.30
40.50
3. Determine the slope of your line – use (0,0) as one of your data points. Please show all of your
work below:
4. How are the slope of the line from the graph and density related? Explain.
5. Based on the density you calculated and the table below – determine the name of the
substance represented in the graph!
Unknown Substance = ___________________
Substance
Methanol
Glycerin
Carbon Tetrachloride
Aluminum
Lead
Density (g/mL)
0.97
1.26
1.58
2.70
11.3
35
Name:_______________________________
Density Lab
Data:
Mass of Unknown
Mass of Unknown
Color: __________
Color: ___________
Mass(g)
Volume (mL)
Mass(g)
Volume(mL)
0.0
0.0
Period:_____
Mass of Unknown
Color: ___________
Mass(g)
Volume (mL)
0.0
1) Use the excel template graph from the teacher’s outbox to input your data and it will plot the lines for
you; make sure you save this to your directory.
-Change the color heading to your actual color in the data area.
-Put your name in the parenthesis after the title.
-Print the excel document with your graph on the same page.
2) Using the printed graph, calculate the slope of each line and show your work below:
Color_________________:
Color ________________:
Color_________________:
Density of various substances (g/mL)
0.77
Maple
0.90
Polypropylene
1.03
Polystyrene
1.15
Polyamide (Nylon)
1.17
Acrylic
1.23
1.32
1.37
2.20
2.71
Polyurethane
Phenolic
Polyvinylchloride (PVC)
PTFE (Teflon)
Aluminum
3) Using the data table above, identify the substance for each color:
4) Calculate the % error for each color and show your work below:
36