Molecularity: Nuts and Bolts

1 lab period; work in pairs. Complete the Preparation page before laboratory.

Goals

• To explore ways to indirectly determine the mass of a bolt that cannot be directly weighed.
• To find the mass of a bolt using these methods
• To determine the number of nuts and bolts in a sealed vial

It happens occasionally in science that a quantity of interest cannot be measured directly, and an indirect method must be developed to measure it. For example, the mass of an electron can be found indirectly from the charge and mass-to-charge ratio, but cannot be directly measured because it is much too small. In this experiment, you will use indirect methods to measure the mass of a bolt with an attached nut. The nut may not be removed from the bolt during the experiment. You will explore at least 2 methods to estimate the mass of the bolt. You will then decide which method gives the better estimate of the mass by considering the uncertainties in each method.

An experimental measurement inevitably involves uncertainty from several sources. This uncertainty must be reflected in the number of significant figures to which the desired result is reported. For example, if you were to use a double beam balance to measure the mass of a nut in this experiment, there would be an uncertainty in each reading of + 0.02 g. On the other hand, a mass measured with an analytical balance would be known to an uncertainty of only + 0.0001 g. Therefore, the mass of a nut might be 3.02 + 0.02 grams when measured with the double beam balance, and 3.0246 + 0.0001 g when measured with the analytical balance. Thus the measuring device contributes one source of uncertainty.

The estimate of the mass of a typical nut can be improved by measuring the mass of each of a number of nuts, then averaging the masses. Alternatively, the mass of a large number of nuts may be determined and divided by the number of nuts weighed. These two approaches seem quite similar, but in fact one method provides much more information than the other. Which provides more information?

In this experiment, you are not able to measure the mass of the bolt directly because it is attached to a nut. Therefore, you must estimate the mass of the bolt. We ask that you devise two different approaches to this. Each method will have associated with it a certain precision, which is a measure of the reproducibility of the reported mass. One way to indicate the reproducibility (precision) of a measurement is to report the standard deviation. Another method is to report one-half of the range of experimental values. We will use the latter in this experiment.

In the second part of the experiment, your group will use the results from the first part to measure the number of nuts and bolts contained in a sealed vial. Given only the mass of the empty vial, you will determine the number of nuts and bolts in the vial to within the uncertainty of the mass data from part 1.

1. Report the values for the mass of the bolt found from your two methods. For measured or calculated values report a standard deviation or one-half range.
2. Discuss the precision of your results in terms of the standard deviations. Do you think one of your methods gives a better estimate of the "true" mass of the bolt than the other? Why or why not?
3. Report the numbers of N and B in your unknown vial. Explain the logic involved in determining this ratio. How does the uncertainty in the mass of the nut and/or bolt affect your conclusions?
4. Can you think of other ways to carry out this experiment now that you have completed it?

• lab glassware: beakers, graduated cylinders, Erlenmeyer flasks
• balance - double beam, top loading or analytical
• bolt with nut attached
• bolts
• nuts
• sealed vial containing an unknown number of bolts and nuts

Eye protection must always be worn in the laboratory. The materials used in this experiment are not harmful; however, good lab practice requires the use of eye protection.

Record all data in your laboratory notebook.

Proper use of the balance will be demonstrated in lab. Each team will be given a bolt (B) with a nut (N) attached, and a supply of nuts and bolts similar to the nut and bolt in the combination. Devise at least 2 methods for estimating the mass of the bolt without removing the nut. Before you begin, clearly explain your method in one or two sentences and indicate what data you will need to obtain. Then carry out your methods, neatly tabulate your data, and determine the mass of the bolt.

You and your partner will be given a sealed vial of specified mass containing an unknown number of nuts and bolts. Using the results of part 1 of this experiment, determine the number of nuts and bolts in the vial.

Clean-up. When you have finished all of your work:

• Clean all glassware with Alconox and water and shake dry.
• Rinse Pasteur pipets by inserting the nozzle of your wash bottle in the top end and squirting water through. Aspirate dry.
• Return all components to the labkit.
• Return all borrowed equipment to the instructor before leaving lab.

No disposal required.

Preparation Questions