Purpose

• Measure different quantities and report the measurements using SI units.
• Familiarize yourself with the use of laboratory glassware and other measuring equipment.

Expected Learning Outcomes

• Report results of measurements and calculated values with the correct number of significant figures. (Lo 3)
• Calculate the percent error for a particular measurement. (LO 4)
• Use various pieces of glassware to measure the volume of a liquid sample. (LO 3)
• Determine the densities of liquid samples. (LO 3, 4)
• Compare the accuracy associated with using different glassware for measuring volume. (LO 4)
• Compare the volumes of mixtures and the constituent pure liquids. (LO 3, 4)

Textbook Reference

Tro, Chemistry: Structures and Properties, 2nd Ed, Chapter E.2, E.3, and E.5

Introduction

Significant Figures

When we make measurements and perform calculations, you can display a lot of digits (or add zeros incessantly). However, in reality you can only be certain of the answer to a particular level.

Therefore, it is necessary to express answers to reflect the degree to which you know a particular measurement. In Chemistry, the convention is that you know with certainty all digits that are marked on the measuring device. In addition, you can estimate, with some certainty, the quantity to an additional decimal place.  All of these are considered significant figures.

Measuring Volumes: Dealing with the Meniscus

For liquids in any container, there will typically be a curved surface rather than a flat surface.^[1] The meniscus needs to be read such that the the level of liquid read is the bottom of the meniscus (the curved surface).

One particularly important feature of a buret is that the graduations go downwards.  The 0 mL mark is at the top and the 50 mL mark is at the bottom.  This enables us to report the volume delivered as

 volume delivered = final volume – initial volume

Accuracy and Precision

We use accuracy and precision to characterize the quality of measurements.  It is important to realize that it is impossible to measure anything completely accurately or precisely; however, especially in analytical chemistry, it is very important that we try our best to be as accurate and precise as possible.

Accuracy

Accuracy refers to how close measurements compare to the true (accepted) value. To do this, we measure a quantity for which we know the accepted value. A common measure of the accuracy of the measurement is given by the percent error:^[2]

[latex]\text{% error} = \frac{\text{measured value} - \text{true value}}{\text{true value}} \times 100\%[/latex]

Note that the percent error can be positive or negative. In this course, the sign for the percent error is often kept to indicate the possible direction of any systematic error.^[3]

Precision

Precision refers to how close a set of measured results are to each other. A numerical measure of the precision of a measurement is given by its standard deviation, which, for a sample containing n values [latex]x_1, x_2, \cdots, x_n[/latex], is given by

[latex]s = \sqrt{\frac{\sum\limits_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}[/latex]

where [latex]\bar{x}[/latex] is the mean. The larger the standard deviation, the lower the precision. This is often easily calculated by typing in the numbers into Excel and having Excel solve for the standard deviation using the STDEV function.

Density

The density of a particular homogeneous substance (pure substance or mixture) is the mass per unit volume.

[latex]\mbox{density} = \frac{\mbox{mass}}{\mbox{volume}}[/latex]

In many cases, for liquids, the density is measured in grams per milliliter (g/mL). In this case, the mass is measured in grams and the volume is measured in milliliters. An identical unit (more commonly used for solids) is grams per cubic centimeter} [latex]\left(\frac{\mbox{g}}{\mbox{cm}^3}\right)[/latex]. For gases, grams per liter (g/L) is more commonly used.

Density is an intensive property – it doesn’t depend on the amount of substance present. Therefore, we will get the same value if we measure the density of teaspoon of water or a tanker truck full of water.

Procedures

Special Equipment Needed

The following equipment will be needed:

• 50/100 mL beaker.
• Three 100 mL graduated cylinders.
• buret
• 10 mL volumetric pipet

Chemicals Needed

You will need about 55 mL of your assigned organic liquid for the part The Volume of a Water:Organic Mixture.

Measurement of the Density of Water

In this part, you will determine the density of water and an unknown liquid. You will also evaluate the accuracy and precision associated with using each type of glassware.

The idea here is to measure out a certain volume of deionized water and determine its mass. From this information, we will be able to determine the density of water measured using the different methods.

Determining the Temperature of Water

In this part, you will determine the temperature of water.  From this, you will be able to look up the exact density of water from tables like this.

1. Fill a 400 or 600 mL beaker with approximately 300 mL of deionized water, and determine the temperature of this water.
   1. The volume here is just approximate.  We aren’t even measuring
   2. Also, it may be easier to get this straight from the deionized water tap rather than from the wash-bottle.

Using a Medicine Dropper to Measure the Volume of Water

A useful rule of thumb is that 20 drops from a medicine dropper is about 1 mL. To determine if this is a good rule of thumb, we will determine the mass of 20 drops of water.

2. Obtain an empty, dry 50 or 100 mL small beaker and determine its mass.
3. Using a medicine dropper, place 40 drops of deionized water into this beaker and determine the combined mass of the water and the beaker.  Calculate the volume of the water assuming that 20 drops is exactly 1 mL.
4. Empty and dry the beaker with a paper towel.
5. Repeat steps 2-4 two more times.

Measuring the Volume of Water Using a 50 mL Beaker

6. Check to make sure there are graduations on the beaker. If not, get another beaker.
7. Determine the mass of the empty, dry 50 mL beaker.
8. Measure out about 20 mL of deionized water using the beaker. Estimate the volume of this water to the correct number of significant figures.

9. Ensure that the outside of the beaker is completely dry, and determine the mass of the beaker containing this water.
10. Empty and dry the beaker with a paper towel.
11. Repeat steps 7-10 two more times.

Measuring the Volume of Water Using a 50 mL Graduated Cylinder

12. Accurately weigh a clean, dry 50 mL graduated cylinder.
13. Fill the graduated cylinder up to the 20 mL mark with deionized water, using a disposable pipet to get the volume as close as possible to exactly 20 mL (but don’t worry if it’s not perfect). Report the actual volume of the water to the appropriate number of significant figures. Hint: the last digit you report should NOT be 0 unless you are one of the rare people who was able to measure out exactly 20 mL.
14. Weigh the graduated cylinder containing the water.
15. Empty the graduated cylinder, and shake out all excess water. Make sure no beads of water remain.
16. Repeat steps 12 to 15 two more times.

Measuring the Volume of Water Using a Buret

17. Rinse the buret 2-3 times with a 10 mL portion of deionized water. You may wish to hold the buret approximately horizontally and then rotate the buret to do this. Try and ensure that there are no water droplets on the walls of the buret.
18. Clamp the buret to a stand using a buret clamp. Ensure that the buret is completely vertical and held in place in the clamp. Seek help from your instructor if you have difficulties.
19. Fill the buret to approximately the 10 mL mark and release water into a waste beaker until all air bubbles are removed from the buret.
20. Determine the mass of a clean, dry 50 or 100 mL beaker.
21. Record the liquid level on the buret at this time; this is the initial volume. Make sure that this is recorded to the correct number of significant figures.
22. Place the beaker under the buret and open the stopcock and allow a bit more than 10.00 mL of water to flow through. Record the volume of the buret at this point to the correct number of significant figures; this is the final volume. Hint: the final volume you record should be a bit more than 10 mL greater than the initial volume you recorded.
23. Wipe the outside of the beaker to ensure it is dry and measure the mass of the beaker and the water.
24. Empty and dry the beaker with a paper towel.
25. Repeat steps 20-24 two more times. If you have insufficient water in the buret for the next addition, then you will need to refill the buret; however, if there is sufficient water already present, you can just start from the water already present in the buret.

Measuring the Volume of Water Using a Pipet

26. Obtain about 40-45 mL of deionized water and put this in a clean, dry 100 mL (or larger) beaker or Erlenmeyer flask.
27. Half-fill the pipet with deionized water and rinse the pipet by holding it horizontally and rotating it, similar to how you rinsed the buret earlier in step 17.
28. Determine the mass of a clean, dry 50 or 100 mL beaker.
29. Pipet 10.00 mL of deionized water and dispense this into the small beaker that you weighed earlier (remember touch the tip of the pipet to the wall of the beaker while dispensing the water, but do NOT to expel the last bit of liquid stuck in the tip of the pipet). Record the volume as 10.00 mL – volumetric pipets typically are accurate to four significant figures^[5]
30. Determine the mass of the beaker containing water delivered by the pipet.
31. Empty and towel-dry the beaker.
32. Repeat steps 28-31 two more times.

The Volume of a Water:Organic Mixture

In this part, we will examine the volume of a water:organic compound mixture with varying compositions.

33. Your instructor will assign one of the organic compounds for you to mix with water in this experiment.
34. You will have a number of 50 mL graduated cylinders. If there is a mix of TC and TD graduated cylinders:
    • Use the TC (to contain) graduated cylinder for the final volume.
    • Use TD (to deliver) graduated cylinders for the volumes to be mixed into the final graduated cylinder.
35. Pour out slightly more than 75 mL of your assigned organic compound into an Erlenmeyer flask.
36. Make each of the mixtures from the table below as follows:
    1. Measure out the volume of water required in one graduated cylinder to the correct number of significant figures, and then, using a separate graduated cylinder, measure out the volume of your assigned organic liquid. Try to get as close to the listed volumes as possible, but don’t worry if it’s not exactly the desired volume.
    2. Mix the two liquids together and measure the final volume of the mixture (which may or may not be the same as the sum of the two volumes you added together).  One way of mixing the chemicals is to cover the graduated cylinder with a small piece of Parafilm and invert the graduated cylinder multiple times until mixed well. If you have never used parafilm before, be sure to ask your instructor how to do this as the correct way to use it is not intuitive.

Data Analysis

Follow the directions on the report form. Most of the theory is outlined in the introduction section above with references to your textbook. Include the volume of the pure liquids as well.

You will want to review the guidelines on graph plotting (using graph paper) before plotting the graph required for the second part. You will plot the density of the mixture as a function of the volume of the organic liquid. After you plot the data points, join the points with a smooth curve. Check with your instructor if you are unsure how to do this as it is hard to describe but easy to show.

Acknowledgment

This experiment is based on similar experiments for CHEM 105 and CHEM 120L at Fort Hays State University, as well as an experiment presented by Benvenuto, M. et al from University of Detroit Mercy.