Download MEASUREMENT IN CHEMISTRY 1- Accuracy: It is the agreement

MEASUREMENT IN CHEMISTRY
1-
Accuracy:
It is the agreement between the measured quantity and the accepted value. In other words it is how close a measurement comes
to the actual dimension or true value of whatever is measured. For example, a student takes three measurements of an object,
and he/she calculates the average. If the average corresponds to the accepted value, then we can say that the average
measurement is accurate.
Accuracy often depends on the quality of the measuring device. The measuring device has to be well calibrated, and has to be
periodically checked against a standard to ensure its accuracy.
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Precision:
Precision is the agreement between measurements of the same quantity. It is concerned with the reproducibility or the
reliability of the measurement. In the above example, if the three measurements are close to one another, then we can say that
the measurements are precise.
Precision depends mostly on the skill (or technique) of the person making the measurement. In order for the measurements to
be precise, the experimenter must use the proper technique, such as measuring the volume of a liquid in a cylinder at eye level,
and he/she must be able to repeat the same technique each time.
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Uncertainty:
No measurement is 100 % accurate, since there is always some uncertainty. There are two exceptions to this:
ex:
1) Numbers obtained by counting are exact.
28 students in a class, and not 27.29 or 28.32...
2) Numbers obtained by definition are exact.
ex:
12 objects = 1 dozen
1 m = 100 cm
These exceptions contain an infinite number of significant digits.
All other measurement contains a degree of uncertainty.
We can write a measurement using the following format:
10.60 ± 0.02 cm


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where 10.60 = average which determines the accuracy
0.02 = uncertainty which determines the precision
If the average is close to the accepted or true value, we can say that the measurement is accurate.
If the uncertainty is small, the measurements are said to be precise.
Percent Error:
When the accepted or true value of a measurement is known, it is possible to calculate the percent error. The percent error is
another way of determining the accuracy of a measurement. The smaller the percent error, the greater the accuracy.
Example: A student measures the mass of a sulfur sample and finds it to be 5.3 g. If the accepted value is 5.2 g, find the
percent error of his/her measurement.
% error
= {|accepted value - experimental value|  accepted value } x 100 %
= {| 5.2 g - 5.3 g |  5.2 g } x 100 %
= { 0.1 g  5.2 g } x 100 %
= 2%
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Significant Digits:
Scientists record the accuracy of a measurement in significant digits.
Ex:
65.12  more accurate than 65.1
The number of significant digits in a measurement can be defined as all digits that are known accurately plus the first one
that is uncertain or estimated.
Ex:
65.12  4 sig. fig. (2 is uncertain)
65.1  3 sig. fig. (1 is uncertain)
Examples of taking measurements with the right number of significant figures.
SIGNIFICANT FIGURES
1) All digits other than 0 are significant.
96  2 sig.fig.
61.4  3 sig.fig.
2) Zeros between two other significant digits are significant.
5.029  4 sig.fig.
120.008  6 sig.fig.
3) Final zeros to the right of the decimal are significant.
4.270 0  5 sig.fig.
60.0  3 sig.fig.
4) Zeros which are used only to indicate where the decimal should be are not significant
7 000  1 sig.fig.
5) Zeros to the right of the decimal but to the left of a non-zero digit are not significant.
0.007 83  3 sig.fig.
0.004 800  4 sig.fig.
6) The following numbers are exact and contain an infinite number of significant digits:
a) numbers obtained by counting whole objects:
28 students = 28.000 000 000 000... students
b) numbers obtained by definition:
1 m = 100 cm
1.000 000 000... m = 100.000 000 000... cm
RULES FOR ROUNDING OFF
a) If the first digit to be dropped is less than 5, the preceding digit stays the same..
2.622  2.6 (rounded to 2 sig.fig.)
b) If the first digit to be dropped is greater than 5, the preceding digit is increased by 1..
2.697  2.7 (rounded to 2 sig.fig.)
c) If the first digit to be dropped is 5, the preceding digit stays the same if it is even, and increases by one if it is
odd This is called rounding off to the nearest even number, and is used only when dropping a 5 which is not
followed by non-zero digits.
2.65  2.6 to 2 sig.fig.
2.75  2.8 to 2 sig.fig.
but
2.654  2.7 to 2 sig.fig.
2.655  2.7 to 2 sig.fig.
2.751  2.8 to 2 sig.fig.
2.7561  2.8 to 2 sig.fig.
CALCULATIONS WITH SIGNIFICANT FIGURES
a) addition and subtraction:
 the answer should not be more accurate than the least accurate measurement
677
(the least accurate)
39.0
+
6.243
¯¯¯¯¯¯¯
722.243  722
65 000
(the least accurate)

120
¯¯¯¯¯¯¯
64 880  65 000
b) multiplication and division:
 the answer must have as many sig. fig. as there are in the least accurate measurement
49.600 0  47.40 = 1.046 413 5...
(6 sig.fig.) (4 sig.fig.)
 1.046
(4 sig.fig.)
c) combined operations:

by convention, multiplications and divisions are performed before additions and subtractions (most
calculators use this convention!)

do not round intermediate answers, but keep track of the rightmost digit that would be retained after
rounding (shown by an underline or an overline)
4.18  58.16 x 3.38  3.014 =
=
=
=
4.18  (58.16 x 3.38)  3.014
4.18  196.5808  3.014
 195.4148
 195
PRACTICE: SIGNIFICANT FIGURES
1.
How many significant figures are there in the following measurements?
a) 3 500
b) 17.505
c) 41.400
e) 0.000 573
f) 0.009 00
g) 41.50 x 10-4
-8
7
i) 123 400 x 10
j) 0.000 410 0 x 10
k) 100.005 000 000
d) 0.51
h) 0.007 160 x 105
l) 89 400
2.
Round off:
a) 4.954 93 to 5 sig.fig. b) 4.954 93 to 4 sig.fig. c) 4.954 93 to 3 sig.fig. d) 4.954 93 to 2 sig.fig.
e) 0.005 06 to 2 sig.fig. f) 95 147.2 to 3 sig.fig. g) 0.449 99 to 1 sig.fig. h) 0.005 945 to 3 sig.fig.
3.
Rewrite the following numbers in scientific notation and rounded off to 3 significant figures.
a) 35 700
b) 0.005 167
c) 45.05
d) 175 400.4
e) - 0.547 36
f) 453.052 x 106
g) - 0.004 495
h) 650 002 000
4.
Calculate the following and give your answer in scientific notation with the appropriate number of significant
figures.
a) 24.4 + 12.692 + 14.79 f)
0.3914 x 1.076  4.98 + 8.921
b) 2.229  0.571 0
g) 95.99  4.9 + 88.2
c) 10.6 x 6.9
h) 43 438 x 8.264  976 + 61.00
d) (9.93 x 1023) (6.9 x 102)
i) 54.32  23.45 x 1.39  25.15
e) 4.31 x 5.0  2.153
j) 123.470 + 90.245 x 78.12  4.102
SUPPLEMENTARY EXERCISES WITH SIGNIFICANT FIGURES
1.
How many significant figures are in each measurement? Which one is the most accurate?
a) 133.31 g
b) 0.02 g
c) 24.6 cm3
d) 109.945 7 mL
e) 29 marbles
2.
Calculate the following and round off your result to the appropriate number of significant figures.
a) 73.000  36.9
d) 12 + 0.12 + 0.012
b) 150 + 2.39 + 0.012
e) [25 x 720]  5.2
c) 0.137 + 0.0022 + 0.011
f) 25.0 x 4 x 2.88
3.
Circle the significant figures:
a) 6.29
b) 0.099 0
6
1.81 x 10
e) 1.772 x 1010
h) 1.0023
i) 40.00
d)
c) 42 000 (or 4.2 x 104)
f) 51
j) 0.005
4.
Correct the following according to SI conventions:
a) 25 gs
b) 10 grams/cm3
c) fifteen milligrams
d) 65 km
e) 80 mg per millilitre
5.
Round off to 2 sig.fig, and then to 1 sig.fig.
a) 36.4
b) 729
e) 0.001 07
f) 6.022 x 1023
6.
c) 0.145
g) 0.0210
d) 8.357
Calculate the following and round off your result to the appropriate number of significant figures.
a) 4.31 x 5.0  2.153
b) 8.92  4.002 + 1.246
c) 66.045  4.2  100.9
d) 184 x 60 + 8
e) 433.214 + 800.9  91