This experiment is designed to give you an opportunity to collect and analyze both gravimetric (mass) and volumetric (volume) data.  The data will be analyzed to discuss the precision and accuracy of laboratory glassware. The first part of this exercise involves the use of the top-loading (bench-top) analytical balance and a 25-mL graduated cylinder to reproducibly measure the mass of an assigned aliquot (sample or portion) of water.  Balances are frequently used laboratory tools for measuring mass and it is important to be thoroughly familiar with them. Be sure to read the procedures carefully so you know what to do when you come to the laboratory. The second part of the experiment is to use a 10-mL volumetric pipet to measure the aliquots of water while still using the top-loading balance to measure the mass. The third part of this exercise involves the use of a graduated pipet to measure varying amounts of water and correlating the volume to mass (Density??).

Example Procedures

1. Use a 25-mL Graduated Cylinder to measure four 10.00 mL aliquots of water into a 50-mL beaker.
2. Weigh the beaker empty and after each addition.
3. Repeat steps 1 and 2 using a 10-mL Volumetric Pipet instead of the Graduated Cylinder.
4. Use a 10-mL Graduated Pipet to measure four aliquots of water at 3, 5, 7, and 9 mL into a 50-mL beaker.
5. Weigh the beaker empty and after each addition.
6. Record the temperature of water, density of water, reference for the density, and balance numbers.

Calculations and Questions (COPY/RE-WRITE and COMPLETE in sequential order, the items in BLUE in your Notebook)

Data Given in “Excel for Expt 1 Measurements F21.xlsx” — see above for file

1. PRECISION of a measuring device relates to how consistently identical measurements can be made. Consider your measurements of the mass of 10.00 mL of water in Tables 1 and 2.
• Standard Deviation: Standard deviation is a statistical quantity used to give a range within which the correct value for a measured quantity may be found.  The smaller the standard deviation, the more precise the measurements and hopefully the more accurate.  Standard deviation values are expressed with the same number of decimal places as the measured values and is calculated using the following formula:

Where xavg  is the mean (average) value, xi are the individual values and n is the number of measurements taken.

Calculate, using the formula above, the Standard Deviation of the 4 masses of water from the 25-mL graduated cylinder. Show a sample set up for the calculation with your numbers.  Your answer should have the same number of decimal places, and units, as your original data. Also calculate the Standard Deviation for the 4 masses of water from the 10-mL Volumetric pipet, but you do not need to show the sample calculation.

Standard Deviation of the masses of water from the 25-mL grad. cyl: ________________

Standard Deviation of the masses of water from the 10-mL Vol. Pipet: _______________

Excel can also be used to do calculations. In the Excel spreadsheet in the Experiment 1 module “Excel for Expt 1 Measurements F21.xlsx” notice that the calculations are now complete. If you click on a cell, you can see the calculation formula in the Formula Bar. Notice the Mass of Water was calculated using a subtraction “=D9-C9”, whereas the average was calculated using “=AVERAGE(E9:E12)”. You can display different number of decimal places by formatting the cell. Also notice the Standard Deviation was calculated using “=STDEV.S(E9:E12)” which is the Sample Standard Deviation of the four aliquots of water and should match your answer to 1 above.

Which device (cylinder or pipet) is more precise for you? _____________________.

Generally, the Standard Deviation will start to show uncertainty (imprecision) in the same decimal place as the least precise measurement linked to the data. Even the best chemists would have Standard Deviations of 0.10 to 0.50 g using the graduated cylinder and 0.01 g to 0.05 g using the Volumetric pipet.

Since the balance is very precise, what is the major difference between the two volumetric devices that makes the pipet approximately ten times more precise? Briefly explain why.

1. ACCURACY relates to how closely a measurement compares to an accepted standard.
• Using only the average mass for your aliquots of water, and the density of water (see spreadsheet) at your temperature, calculate the average volume of water. (show one calculation with units)

Average volume of water using 25-mL Grad. Cyl.:_______________

Average volume of water using 10-mL Vol. Pipet:_______________

(Note: These are truly the volumes you measured!!! These are “Accepted” values)

• Percent Error (always positive) is a measure of accuracy and can be calculated using the equation below. The 10.00 mL readings from the devices would have been your experimental volumes recorded, but the true volume of water was determined from the mass of water (above).
• Use your answer above in 2 as the Accepted Volume, and use 10.00 mL (average volume reading) as your Experimental Volume to calculate the Percent Error. (Show one sample calc)

????????????????????????????????????????????????=|????????????????−????????????????????????????????|????????????????????????????????????100%PercentError=|Expt−Accepted|Acceptedx100%

% Error for 25-mL Grad.Cyl. =___________________________     High or Low?

(High means the Experimental value is Higher than the Accepted)

% Error for 10-mL Vol.Pipet =___________________________      High or Low?

Which Device is more Accurate for you dispensing 10.00 mL of water? _______________

What does “TC” on a graduated cylinder mean? ___________________________

What does “TD” on a Volumetric pipet mean? _____________________________

Knowing the Graduated Cylinder is a TC device, would you expect a Percent Error for the graduated cylinder to be High or Low? Briefly explain. (High/Low does not mean Big/Small)

1. The Excel file also generated a new Table #4 which shows the mass and volume data for the 0, 3, 5, 7, and 9 mL of Water aliquots. Use Excel to make a graph of the data obtained from the 10-mL Graduated Pipet (Table 4). There is a handout/screen recording on Canvas that briefly explains how to use Excel to make a graph. Put the Volume of Water as the x-axis (the independent variable) and the Mass of Water as the y-axis (the dependent variable).  Note that we have a (0,0) data point since you weighed the empty beaker correlating to zero mL.  Use the “Insert Trendline” option to show the best straight line through the data points. Select the option to show the equation of the line and the R-squared value on the chart.
• Save the Excel file with the spreadsheet and labeled full size, landscape graph (with title and axis labels). Print a copy of the spreadsheet and graph and staple into your notebook.  Again, this should be on the left-hand page opposite the data section. .
• What are the units for the slope? __________
• What Physical Property of Water does the value for the slope actually represent? _________________________________

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