Transcript Calibration of Volumetric Equipment & Thermometer Recall from last

Last week: Statistics I (average, standard deviation,
standard deviation of the mean)
This week: Statistics II (95% Confidence Interval)
&
Calibration of Volumetric Equipment & Thermometer
Recall from last week…..
The mean or average
 x =  true value,  measurements
x
i
i
n
≈  true value, finite # of measurements
Uncertainty given by standard deviation

2


x


 i
i
n 1
For finite # of measurements σ ≈ S
Standard deviation of the mean
S
Sm 
n
1. S , Sm - 2 significant figures
2. Mean (Average) expressed to most significant digit in Sm
For small number of measurements σ ≈ S is
very poor. Must use Student t value.
σ ≈ tS; where t is Student t
Usually use 95% Confidence Interval
So, 95% confident that if we make a
measurement of x it will be in the range
± t95s
Uncertainty of a SINGLE MEASUREMENT
Example
Measure 3 masses: 10.5763, 10.7397, 10.4932 grams
Average = 10.60307 grams
Std. Dev. S = .125411 = .13 grams
Sm = .125411 / 3 = .072406 = .072 grams
Then average = ?
= 10.60 grams
t95 for 3 measurments
95% C.I. = t95Sm = 4.303 * .072406 = .311563 = .31 grams
of the mean
Relative 95% C.I.of the mean = ?
= 95 % C.I. / Average = .311563/10.60307 = .029384 = .029
of the mean
Usually expressed at parts per thousands (ppt)
= .029 * 1000 parts per thousand = 29 ppt = Relative 95% C.I. of the mean
What if measure 10.5766, 10.5766, 10.5767 grams? Ave. = 10.57663; Sm = .000033
Ave. = ?
Ave. = 10.5766, not 10.57663 because limited by measurement to
.0001 grams place
Now work problems.
Sally
5 times, average value of 15.71635% ; standard deviation of 0.02587%.
Janet
7 times, average value of 15.68134% ; standard deviation of 0.03034%.
(different technique)
Express the averages and standard deviations to the correct number of significant figures.
Must use Sm.
Sally: Sm = 0.02587/5 = 1.157 x 10-2 = 1.2 x 10-2%
Janet: Sm = 0.03034/7 = 1.147 x 10-2 = 1.1 x 10-2%
Sally: 15.72%; S = 0.026%
Janet: 15.68%; S = 0.030%
Using the proper statistical parameter, whose average value is more precise?
Must use Sm.
Sm(Janet) < Sm(Sally) so Janet’s average value is more precise.
95% confidence intervals of the mean, relative 95% confidence intervals of the mean
Sally: 95% C.I. = ±t95Sm = ±2.776 (1.157 x 10-2) = ±3.21 x 10-2% = ±3.2 x 10-2%
Range = 15.69 – 15.75%
Relative 95% C.I. = 3.21 x 10-2 / 15.71635 * 1000 ppt = 2.04 = 2.0 ppt
Janet: 95% C.I. = ±t95Sm = ±2.447(1.147 x 10-2) = ±2.81 x 10-2% = ±2.8 x 10-2%
Range = 15.65 – 15.71%
Relative 95% C.I. = 2.81 x 10-2 / 15.68134 * 1000 ppt = 1.79 = 1.8 ppt
Sally
5 times, average value of 15.71635% ; standard deviation of 0.02587%.
Janet
7 times, average value of 15.68134% ; standard deviation of 0.03034%.
(different technique)
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Are the two averages in agreement at this confidence level?
Because the 95% C.I. for both measurements overlap, the two averages are in agreement
If you owned a chemical company and had to choose between Sally’s and Janet’s technique,
whose technique would you choose and why?
Choose Sally’s techniques because the uncertainty in a single measurement based on S is better
than that using Janet’s technique.
CLEANING GLASSWARE
• Do NOT rinse at de-ionized water taps –
take flask back to own sink to rinse.
• Rinsing with de-ionized water should leave no droplets.
• For open and easily rinsed containers, use a cleansing powder,
rinse with tap water and finally with de-ionized water.
• For burets, pipets, volumetric flasks, etc., use liquid detergent,
rinse with tap water and finally with de-ionized water.
NEVER use cleansing powder; it is too hard to get out and in the
case of burets it will usually score the Teflon stopcocks.
Buret
Buret Drainage Times:
Time After
Delivery
(Buret should drain within 100-120 seconds)
Volume Change After Drainage with
Different Buret Free Delivery Times
(aka time required to drain entire buret)
30 sec
100 sec
1 min
0.01 mL
0.00 mL
10 min
0.10 mL
0.02 mL
Check Duplicate Runs by Approximate Method
V
Run l
Run 2
25.15 ml
24.51 ml
W
D=V-W
24.97 g
24.36 g
0.18
0.15
Δ1 – Δ2 ≤ .03
Run l
Run 2
35.19 ml
35.03 g
0.16
34.47 ml
34.28 g
0.19
etc.
Make sure to compare the same volume from DIFFERENT runs.
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Name__________________________________ Lab Section________________
Date Report Submitted___________________
CALIBRATION OF VOLUMETRIC EQUIPMENT
1. Thermometer
Thermometric Standard, true reading (TT)
___________°C
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2. Buret
Series A:
Observed
Mass of
T(H2O), °C
Volume, Vo
Water
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(approximately 0-25mL)
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(approximately 0-35mL)
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(approximately 0-45mL)
Series B:
T(H2O), °C
__________
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Desk Thermometer, observed reading (To)
___________°C
Thermometer Correction (TT - To)
___________°C
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Series C:
(if needed)
T(H2O), °C
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Corrected
Mass
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True
Volume, VT
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Vol. Correction
VT – Vo
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Nominal buret reading
Average volume correction
0 – 25
__________
0 - 35
__________
0 - 45
__________
Archimedes’s Principle: an object immersed in a fluid is buoyed up
by a force equal to the weight of the fluid displaced.
If an object is larger in volume than the weights that balance it,
then it displaces more air and is buoyed up by a greater force.
Buoyancy Correction:
ΔB = daww[1/do – 1/dw]
DB
da
dw
do
o
ww
wo
=
=
=
=
=
=
=
=
Mass of air displaced by object
Mass of air displaced by weights
buoyancy correction
0.00115 g/cm3 (density of air at room temperature)
8.0 g/cm3 (density of calibration weights)
1.00 g/cm3 (density of water to 3 sig. fig.)
object (water)
mass read on balance (mass of weights)
actual mass of object
ww + DB
Volumetric Pipet
Uncertainty of a SINGLE MEASUREMENT
Check the highest-lowest < 0.03g
***how is this quick check like the one for the buret?
crossbar with hooks
probe
Thermometer (on side bench)
Quartz thermometer
Hang your thermometer on a hook
(count from left or right)
Should be within 0.5C
Thermometer
Stirrer
Storage of buret and pipet:
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Fill with de-ionized H20
Cork in top of buret (if old obtain a new cork)
Rubber policeman on tips
Loosen stopcock of buret slightly for
storage. Remember to retighten
when you use buret again.
Store in buret cabinet
Things to remember...
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Wear goggles, lab coat, closed-toe shoes
Backpacks on hooks
No eating, drinking, using cell phones, etc.
Make sure balances are calibrated, not
moved (check the bubble)
• Work on the wet bench side (sinks)