CUNY Bronx Community College Measurements and The Chemist’s Tools Lab Report fill it out for tonight before at 12 lab assignment………………………

CUNY Bronx Community College Measurements and The Chemist’s Tools Lab Report fill it out for tonight before at 12 lab assignment…………………………………………………….. CHEMISTRY 17
Experiment 1 – MEASUREMENTS AND THE CHEMIST’S TOOLS
Measurements in the laboratory need to be made with careful attention, and attention must be given not only to the object
being measured but also to the tools or instruments being used to gather the data. It is this set of tools that provides us with
the data, information, and subsequently the knowledge we will transmit to fellow-scientists and to the scientific community.
Let’s review the basic concepts involved in data gathering to help you complete this lab report.
PRECISION VERSUS ACCURACY
Accuracy refers to how closely a measured value agrees with the correct value.
Precision refers to how closely individual measurements agree with each other. This assumes the measurements were made
using the same measuring tool.
Measurements are precise, but are very far
away from the true value (target center).
Not accurate
(the average may be accurate)
not precise
Precise
not accurate
Accurate
and
precise
When making measurements, the number of significant figures is critical. The number of significant figures is the number
of digits believed to be correct based on instrument precision and the individual’s careful attention in making the
measurement. The measurement has an uncertainty in the digit furthest to the right of the decimal point. This is called the
estimated digit.
SIGNIFICANT FIGURES
There are two kinds of numbers in the world:
•
•
exact: numbers that are counted or are exact equivalents.
o example: There are exactly 12 eggs in a dozen or 23 students in a classroom.
o example: 2.54 cm. equals 1.00 inches (exactly). These numbers may have as many zeros to the right of
the decimal point as to limit the significant number only to the measured quantities.
inexact numbers:
o example: measured quantities. Measured quantities could be mass, volume, temperature, pressure, or any
value taken with any measurement tool. The significant digits will be determined by the instrument’s
precision or tool’s measurement scale used in making the measurement.
MEASURING VOLUME
Consider measuring volume in the laboratory. This can be done in many ways:
•
•
•
using a beaker with volumes marked on the side
a graduated cylinder
a graduated pipet
The precision of the volume measurement depends on the volume scale and its scale divisions. In general, one reads the
volume to one more digit than the scale divisions. The number of significant figures includes one estimated digit. So, if the
scale division is in 1/100th of a mL than one estimates the value of the thousandths place. This will give the number of
figures that are significant. Always read the volume to 1/10 or 0.1 of the smallest division. This means that the error in
reading (called the reading error) is +/-1/10 or 0.1 of the smallest division on the glassware. Let’s figure out the volume for
each one of the following illustrations and its associated error.
Before starting, we must learn how to properly read the liquid level in a graduated
cylinder. Before measuring the volume of a liquid with a graduated cylinder, it is necessary to
be able to read the scale to the closest fraction of the smallest subdivision. The value in mL
of the smallest subdivision is first determined by ascertaining a volume indicated at or
between two adjacent numbered lines. The reading of this value is then completed by
estimating how many subdivisions are contained within these same two lines. The level of the
liquid is properly read only at eye level, as illustrated in the diagram (left). The visibility of
the meniscus can be enhanced by using a white or dark paper placed behind the
cylinder. Illustration of reading liquid levels on a white or dark background are given in
the Appendix, along with some practice exercises in determining the smallest
subdivisions for graduated cylinders and other important measuring tools, such as a
rulers and thermometers.
Beaker
The smallest division is 10 mL, so we can read
the volume to +/-1/10 of 10 mL or +/-1 mL. The
volume we read from the beaker has a reading
error of +/-1 mL.
The volume in this beaker is 32 +/-1 mL.
There are two significant figures in this
measurement. The 3 is certain, while the units
place, the number 2, is an estimate.
Graduated
Cylinder
At the liquid/air interface, the liquid level has a
curvature called a meniscus. The cause of this is
because water molecules are attracted to each
other as well as to the glass surface. The volume
of the liquid is measured at the bottom of the
meniscus.
The smallest division of this graduated cylinder
is 1 mL. Therefore, the reading error will be +/0.1 mL or 1/10 of the smallest division. An
appropriate reading of the volume is 36.5 +/-0.1
mL. An equally precise value would be 36.6 mL
or 36.4 mL. There are three significant figures
in this measurement.
Graduated
Pipet
The smallest division in this pipet is 0.1 mL.
Therefore, the uncertainty in the measurement is
+/- 0.01 mL. A good volume reading is 1.08 +/0.01 mL. An equally precise answer would be
1.07 mL or 1.09 mL.
There are 3 significant figures in this
measurement.
Note that the numbers get larger as one goes down the
pipet. A pipet will expel a volume of liquid, while a beaker
or graduated cylinder contains a given volume.
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RULES FOR WORKING WITH SIGNIFICANT FIGURES
Identification of Significant Figures:
Example: 12.697
all digits are significant.
1. Leading zeros, or zeros to the left of the first significant digit are never significant.
Example: 0.00682
3 sig figs
6.82 x 10-3
2. Zeros between two non-zero digits are always significant
Example: 111.045
6 sig figs
1.11045 x 102
3. Trailing zeros are significant when a decimal point is included in the number.
Examples: 6500
2 sig figs
6.5 x 102
8000
1 sig figs
8 x 103
8000.
4 sig figs
8.000 x 103
CALCULATIONS WITH SIGNIFICANT NUMBERS
1.
Addition or Subtraction:
The final answer may not exceed the precision of the least precise value. Stated another way, the answer will
have the same number of digits to the right of the decimal as the single value with the least number of
significant figures to the right of its decimal.
400.2 1 digit to the right of the decimal
2.5608
+ 15.92
418.6808 calculator answer
–
2.
2.5608
1.592
1.0688 calculator answer
Rounded Answer: 418.7 1 digit to the right of the
decimal. The number 400.2 is least precise.
Therefore, one may only report the answer to the
tenths place.
Rounded Answer: 1.069
The number 1.592 is least precise. Therefore,
one may only report the answer to the
thousandths place.
Multiplication or Division:
The answer contains no more significant figures than the least accurately known value.
56.3813
x 1.8
101.48634 calculator answer
Rounded Answer: 1.0 x 102 easily written in scientific
notation. Note: by writing this value in long form
would give a value of 100 and is ambiguous. Generally
trailing zeros would be considered insignificant. This
poses a problem for scientists that is easily rectified
using scientific notation.
Rounding Process
When rounding off numbers to a certain number of significant figures, if the number to the right of the last significant digit
is a 5 or greater, the number is rounded up.
 example: Round to 2 significant figures: 475281 (Answer: 480000; NOT 48)
 example: Round to 3 significant figures:.0.0054367 (Answer: 0.00544)
 example: Round to 2 significant figures: 8.01629 (Answer: 8.0)
SCIENTIFIC NOTATION
Scientific notation is the way that scientists manage very small numbers or very large numbers. The method allows for easy
estimation of a calculated answer.
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Consider the scientific notation value 7.64 x 10-9. The significant term is 7.64, while the value 10-9 is the power of ten or
the order of magnitude and is often referred to as the exponential term.
Examples of scientific notation:
10000 = 1 x 105
10000 = 1 x 104
1000 = 1 x 103
100 = 1 x 102
10 = 1 x 101
1 = 100
1/10 = 0.1 = 1 x 10-1
1/100 = 0.01 = 1 x 10-2
1/1000 = 0.001 = 1 x 10-3
/10000 = 0.0001 = 1 x 10-4
1
689705= 6.89705 x 105
43819 = 4.3189 x 104
3658 = 3.658 x 103
718 = 7.18 x 102
94 = 9.4 x 101
6.8 x 100 = 6.8
0.32 = 3.2 x 10-1
0.053 = 5.3 x 10-2
0.0078 = 7.8 x 10-3
0.00044 = 4.4 x 10-4
Upon review of the above examples, one notices that the power of 10 is the number of places the decimal point must be
shifted to return the number to its original form in standard notation.
A positive exponent indicates the number of decimal places to the right one must move the decimal point to return the
number to its original form. A positive exponent also indicates a number greater than one (1).
A negative exponent indicates the number of decimal places to the left one must move the decimal point to return the
number to its original form. A negative exponent also indicates a number less than one (1), but greater than zero (0).
In scientific notation, the significant term indicates the number of significant figures in the number while the exponential
term only indicates the order of magnitude and where the decimal point is placed to return the number to its original form.
Note that the placement of the decimal is ALWAYS between the 1st and 2nd non-zero digit of the significant term, which is
then followed by the power of ten.
As an example, 0.0000567 = 5.67 x 10-5
This number has 3 significant figures. The zeros are not significant; they are only holding a place. The decimal is
placed between the 5 and the 6.
Another example, 8973000 = 8.973 x 106
This number has 4 significant figures. The zeros are place holders. The decimal is placed between the 8 and the 9.
USING YOUR SCIENTIFIC CALCULATOR
To put a number in scientific notation into your calculator correctly is important..
Read the directions for your particular calculator.
For scientific calculators:
1.
2.
3.
Punch the significant number into your calculator.
Push the EE or EXP button. Do NOT use the x (times) button!!
Enter the exponent number. Use the +/- button to change its sign. This step may be reversed on some calculators,
so the +/- is the first button followed by the exponent number.
Addition and Subtraction:
All numbers are converted to the same power of 10, and the significant terms are added or subtracted.
 Example: (6.897 x 10-3) + (4.8 x 10-4) = (6.897 x 10-3) + (0.48 x 10-3) = 7.38 x 10-3
 Example: (6.897 x 10-3) – (4.8 x 10-4) = (6.897 x 10-3) + (0.48 x 10-3) = 6.42 x 10-3
Multiplication:
 The numbers are entered into the calculator including the exponents and the result is then rounded.


Example: (4.2 x 105)x(5.1 x 103) = (4.2)x(5.1) x 10(5+3) = 21.42 x 108 = 2.1 x 109 2 significant figures
Example: (6.483 x 10-8)x(2.26 x 103) = (6.483)x(2.26) x 10(-8+3) = 14.65158 x 10-5 = 1.47 x 10-4 3 significant
figures
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Division:
 The digit terms are divided in the normal way and the exponents are subtracted. The quotient is changed (if
necessary) so that there is only one nonzero digit to the left of the decimal.


Example: (6.4 x 106) ÷ (8.9 x 102) = (6.4) ÷ (8.9) x 10(6-2) = 0.719 x 104 = 7.2 x 103 2 significant figures
Example: (3.2 x 103) ÷ (5.7 x 10-2) = (3.2) ÷ (5.7) x 103-(-2) = 0.561 x 105 = 5.6 x 104 2 significant figures
Powers of Exponentials:
•
•
The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the
power.
Example: (6.4 x 104)3 = (6.4)3 x 10(4×3) = 262.144 x 1012 = 2.62144 x 1014
(to 4 significant figures)
The Deliverable for This Experiment
After reading the information presented above, you will be ready to complete the Prelab
Assignments on pages 6 and 7, and the Measurements Answer Sheet on Page 8 that
corresponds to all the illustrations in the Appendix. View the illustration of the several
measurements and estimate the values to the correct number of significant figures.
Transfer your values to the Measurements Answer Sheet. By the agreed method, submit
to your instructor only the completed pages 6, 7, and 8 of this virtual lab experiment. Be
sure to include your name on each pages.
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Name ________________________________
PRELAB ASSIGNMENT I – SCIENTIFIC NOTATION
Question 1
Write in scientific notation: 0.000123 and 64000000
Question 2
Express 7.23 x 10-3 as a number in standard notation.
Question 3
(5.8 x 10-16) x (7.8 x 105) =?
Question 4
(7.1 x 105) ÷ (1.9 x 10-3) = ?
Question 5
(6.54 x 10-4)3 =?
Question 6
The sixth root of 7.20 x 1038 =?
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Name ________________________________
PRELAB ASSIGNMENT II – SIGNIFICANT FIGURES AND ROUNDING
Question 1
Give the correct number of significant figures for 2500, 2500. , 0.0043, 0.06050
Question 2
Give the answer to the correct number of significant figures:
7964 + 86.94 + 760 =?
Question 3
Give the answer to the correct number of significant figures:
4.596 – 2.81 =?
Question 4
Give the answer to the correct number of significant figures:
(4.58 x 106) x (4.3198 x 10-19) = ?
Question 5
Give the answer in scientific notation and to the correct number of significant figures:
(7860) / (0.00001) =?
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Name ________________________________
MEASUREMENTS ANSWER SHEET
Reading a Graduated Cylinder 1.
Value in mL of the smallest subdivision __________
Measurement in mL of the volume __________
Reading a Graduated Cylinder 2.
Value in mL of the smallest subdivision __________
Measurement in mL of the volume __________
Reading a Graduated Cylinder 3.
Value in mL of the smallest subdivision __________
Measurement in mL of the volume __________
Volumetric Measurements 1
Volumetric Measurements 2
a.
____________ mL
d.
____________ mL
b.
____________ mL
e.
____________ mL
c.
____________ mL
f.
____________ mL
Linear Measurements 1
Linear Measurements 2
g.
____________ mL
j.
____________ mL
h.
____________ mL
k.
____________ mL
i.
____________ mL
l.
____________ mL
Temperature Measurements
m. ____________ mL
n.
____________ mL
o.
____________ mL
p.
____________ mL
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APPENDIX
MEASUREMENTS AND THE CHEMIST’S TOOLS
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