Chapter11 Measurement and data processing
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Transcript Chapter11 Measurement and data processing
11.1 Uncertainty and error in measurement
11.2 Uncertainties in calculated results
11.3Graphic techniques
Uncertainty in analogue
instruments
For example, graduated
cylinder, pipette, burette, or
alcohol thermometer
The uncertainty of an
analogue scale is +half the
smallest division.
Uncertainty in digital
instruments
For example, analytical
balance
The uncertainty of a digital
scale is + the smallest scale
division.
Scientific Notation
Express the following in standard notation:
a. 0.04g
b. 222mL c. 0.0030g
d. 30˚C
Significant Figures
What is the number of significant figures in each of the
following?
a. 15.50L b. 150s
c. 0.00123g d. 150g
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
Systematic errors
Examples include the
following:
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.
Accuracy refers to how
close the reading are to the
true value.
The smaller the systematic
error, the greater is the
accuracy.
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.
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
=?
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
= ?
D= 2.2g/mL
Total mass= 51g
when adding or subtracting
measurements, the
uncertainty is the sum of
the absolute uncertainties.
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.
Percentage uncertainty=
(absolute
uncertainty/measured
value) × 100%
Percentage error =
(accepted value –
experimental
value/accepted vale) ×
100%
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.
Step1: number of moles=concentration × volume
=1.00mol/L × 0.01L=0.0100mol
Step2: % uncertainty in concentration=0.05/1.00 ×100
=5%
Step3: % uncertainty in Volume=0.1/10.0 ×100 =1%
Step4: % uncertainty in number of moles= 5% + 1% = 6%
Step5: absolute uncertainty in number of moles
= 6% × 0.0100 = 0.0006
Number of moles = 0.0100+ 0.0006mol/L