Expt: C Uncertainty In Measurements Flashcards
Measuring uncertainty, significant figures, and tolerances
Statistical analysis
Ex. Determine the mean density and standard deviation for the density of the unknown liquid using the measured values below:
Density of unknown solution: 1.59 g/mL, 1.56 g/mL, 1.55 g/mL
Step 2) Determine the standard deviation:
= 0.0208 g/mL = 0.02 g/mL
0.02 therefore, the mean density should be reported to 2 decimal places.
•Uncertainty and significant figures
Important! The number of significant figures in the absolute uncertainty of a value determines the number of significant figures in the reported value!!!
Ex. Mass = (13.057 ± 0.003) g
13.057 therefore, the mass should be reported to 3 decimal places (or 5 sig figs)
0.003 only the 1st uncertainty figure is considered, as this determines the lowest place value the measured number can be reported to
•Uncertainty describes the range of expected values for the measurement and is a measure of the random error in a measurement. Arises due to fact that every scientific measurement involves an estimation of the value of the final digit reported for the Measurement.
Uncertainties never reported to more than 1 sig fig. (+ or - 0.0001g)
•Relative uncertainty reports the magnitude of uncertainty relative to the size of the measurements, and usually reported as a percentage. Calculated as the absolute uncertainty divided by the mean.
Tolerances:
Analytical balances: + or - 0.003g.
10mL grad cylinder: + or - 0.05g
10mL vol pipette: + or - 0.04g
20mL breaker: + or -
Error in measurements
Random error – associated with our limited ability to make the same measurements multiple times. Values all over the place
Systematic error – associated with a consistent flaw in instrumentation values either too high or too low
Error = observed error- Actual value
Accuracy and precision
What does the standard deviation of a data set tell us?
How do you determine if your data set exhibits random or systematic error?
Precision – how closely clustered a data set is (related to random error)
Accuracy – how close a value matches to a true value (related to systematic error)
Reporting scientific measurements
Measurements usually done 3 or more time.
Allows for better estimate of the true measured value, and also enables the uncertainty of the measurement to be determined.
Linear regression and graphical analysis
What does the slope represent?
What should the value of the y-intercept be?
Density is a measure of the amount of matter (mass) contained in a specific volume
D (g/mL) = mass of Solution(g) / volume of Solution (mL)
It is a constant value for a substance at a constant temperature
Graphical Determination: Plot of Mass vs. Volume (y vs. x)
Y = m x + b
m = slope (will be a number and will represent density)
b is y-intercept (when y = 0)
Slope = rise/run = y/x = m(g)/V(mL) = density.
Mass is y axis
Volume is x axis
Using data from your first measurement with the 20 mL beaker, show your calculations to determine the following values. Note: you only need to show one calculation in full for each part. Be sure to include units!
a. The mass of the dispensed solution: (0.25)
b. The density of the NaCl (aq) solution: (0.5)
A. 25.269-15.863 = 9.433 g NaCl
B. D = 9.433g/ 1x10^-1 mL = 0.9433 g/mL NaCl
- Using the four trials for the 20 mL beaker, show your calculations to determine the following values. Be sure to include units!
a. The mean density of the NaCl (aq) solution: (0.75)
b. The standard deviation of the density of the NaCl (aq) solution, rounded to the correct number of significant figures: (0.75)
0.9433+ 0.9408 + 0.9338 + 0.9437 = 3.7616/4 = 0.9404 g/mL NaCl
X(line over top) = 9.433 + 9.408 + 9.338 + 9.437 / 4 = 9.404
S = square root (9.433-9.404)^2 + (9.408-9.404)^2 + (9.338-9.404)^2 + (9.437-9.404)^2 / 4-1
S = square root 0.006302/3
= square root 0.0021006667 = 0.0458330307
S = 0.05 + or - 5% g/mL NaCl
- Using the given density for the NaCl (aq) solution, determine which piece of glassware (beaker, graduated cylinder, or pipette) yielded the most accurate measurements. Base your answer on your own results. Explain your answer, and indicate whether or not y our results are consistent with the expectations for each piece of glassware. (0.75)
Based on my own results, the glassware that generated the most accurate measurements was the pipette. This is consistent with my expectations as the tolerance for the pipette is the smallest out of three. Therefore, it should produce more accurate measurements.
- Of the beaker, graduated cylinder, and pipette, which one exhibited the best precision? Base your answer on your own results. Explain your answer, and indicate whether or not your results are consistent with the expectations for each piece of glassware. (0 .75)
The pipette showed the best precision. This is consistent with my expectations, as from previous chemistry classes I’ve been told that the meniscus is easier to accurately read, yielding to higher position.
- Based on your data, did any of the pieces of glassware exhibit systematic error? Explain. (0.5)
There seemed to be a systematic error with both the 20 mL beaker and a volumetric pipette. The 20 mL beaker was consistently lower, while the pipette was consistently higher.
However, the 20 mL graduated cylinder seem to contain systematic and random error.
- Based on the data obtained for the 20 mL beaker, is it necessary (or proper) to report four digits in the answer? Explain why or why not? (0.5)
It is not proper because of the relative uncertainty for the 20 mL beaker is 5%. The significant figures are determined by the equipment uncertainty. m
Using the graph and best-fit line prepared in Question 7 to complete the following:
a. Write out the equation (in the form y = mx + b) for the best-fit line. (0.25)
b. What is the value for the slope of the best-fit line generated by the spreadsheet software? Don’t forget to include units. (0.25)
c. To which physical property of the salt solution does this slope correspond? (0.25)
d. What is the value for the y-intercept of your best-fit line? Include units. (0.25)
e. Your y-intercept should have a value very close to 0 g. Explain why this is so. (0.25)
A. Y = 0.992x + 0.17
B. The value is 0.992x g/mL NaCl
C. The slope corresponds to the density of NaCl
D. The value is 0.17 g NaCl
E. This is because x = 0, meaning the volume equals 0 mL, when it’s at the Y intercept. Therefore, if the y-intercept is when the volume equals 0 mL, then theoretically, the mass should also equal 0g.
