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11.1 Uncertainty and error in measurement
11.2 Uncertainties in calculated results
11.3Graphic techniques
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Uncertainty in analogue
instruments
For example, graduated
cylinder, pipette, burette, or
alcohol thermometer
The uncertainty of an
analogue scale is +half the
smallest division.
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Uncertainty in digital
instruments
For example, analytical
balance
The uncertainty of a digital
scale is + the smallest scale
division.
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Scientific Notation
Express the following in standard notation:
a. 0.04g
b. 222mL c. 0.0030g
d. 30˚C
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Significant Figures
What is the number of significant figures in each of the
following?
a. 15.50L b. 150s
c. 0.00123g d. 150g
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Random errors
caused by:
1. the readability of the
measuring instrument
2. the effects of changes in the
surroundings
3. insufficient data
4. the observer misinterpreting
the reading
Can be reduced through
repeated measurements
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Systematic errors
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Examples include the
following:
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1. Measuring the V of water from
the top of the meniscus rather
than the bottom
2. Overshooting the V of a liquid
delivered in a titration
both lead to V which are too
high
3. Heat losses in an exothermic
reaction will lead to smaller T
changes.
can be reduced by careful
experimental design.
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Accuracy refers to how
close the reading are to the
true value.
The smaller the systematic
error, the greater is the
accuracy.
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Precision refers to how
close several experimental
measurements of the same
quantity are to each other.
The smaller the random
error, the greater is the
precision.
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Multiplication and division
The answer should be
rounded to the same
number of S.F. as the least
precise data.
EX.
Density=5.00g/2.3mL
=?
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Addition and subtraction
The answer should be
rounded to the same
number of decimal places
as the least precise value.
Ex.
Total mass= 50g+1.00g
= ?
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D= 2.2g/mL
Total mass= 51g
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when adding or subtracting
measurements, the
uncertainty is the sum of
the absolute uncertainties.
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When multiplying or
dividing measurements, the
total percentage uncertainty
is the sum of the individual
percentage uncertainties.
The absolute uncertainty
can then be calculated from
the percentage uncertainty.
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Percentage uncertainty=
(absolute
uncertainty/measured
value) × 100%
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Percentage error =
(accepted value –
experimental
value/accepted vale) ×
100%
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The concentration of a solution of HCl =1.00+0.05mol/L and
the volume = 10.0+0.1mL. Calculate the number of moles
and give the absolute uncertainty.
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Step1: number of moles=concentration × volume
=1.00mol/L × 0.01L=0.0100mol
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Step2: % uncertainty in concentration=0.05/1.00 ×100
=5%
Step3: % uncertainty in Volume=0.1/10.0 ×100 =1%
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Step4: % uncertainty in number of moles= 5% + 1% = 6%
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Step5: absolute uncertainty in number of moles
= 6% × 0.0100 = 0.0006
Number of moles = 0.0100+ 0.0006mol/L