Exercise: Measurements, Standards and Values

Image above: The current standard for the kilogram. (Image from Japan's Agency of Industrial Science and Technology -Ministry of International Trade and Industry.)

Refer to: C&EN May 26, 2008 .pdf and Wired, January 7, 2013 and Physics Today, July 2014 .pdf and C&EN August 25, 2014 .pdf

Measurements are an important part of science, commerce and our day-to-day life. The science of standards and measurres is refered to as metrology. The question of "how much?" can relate to anything, and the answer can vary depending on what is being referred to and in what country the question is being asked. Countries can use very different units to refer to the same quantity, for example the mile vs. the kilometer to measure driving distance or length. In chemistry, international SI "base" and "derived" units are commmonly used with minor variations. Complete Parts I, II, and III. Record the information in your own Lab Manual's form.

Part I:
 

The anwers to the following questions can be found in one or more of the Web references, your course text or handouts. Quickly peruse the questions and the Web sites.  A) Identify the SI unit for the following base measurements:  Length Temperature Time Mass (Chemical) Amount of a substance B) Define the measurement standard currently used to define each of the following measures, for example the  meter is the unit of length determined by the speed of light in a vacuum. Provide brief descriptions for the remaining units. Length: meter (m), determined by the speed of light in a vacuum Temperature Time Mass (Chemical) Amount of a substance C) What is the composition of the object under the jars in the above image?    D) What is the main difference in the Mass standard from the other standards?

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Part II:

The image below is a caliper measuring the diameter of a sphere. The value in this trial is recorded as 22.0 mm.

 

A) If in three separate measurements, the following values were recorded: 21.8 mm, 22.0 and 21.8 mm.  What single value should be reported for the diameter? B) What value should be recorded for the length of the side of the cube in the following image using the caliper's scale in the illustration?

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Part III:
• Check out 1 caliper and 1 ruler from the stockroom for the Group and obtain an unknown metal cylinder from Dr. R.
• Follow the instructions in the Table below. (Weighings are to be done on a Mettler Analytical Balance to four decimal places, 1/10 of a milligram. (Dr. R. will provide instuctions on the use and care of the Balance.). Each of you in the group is to weigh the object and perform the measurements independently, recording the results on the Lab Manual's form on pages 5-6.
 

In the chemistry laboratory, variations of the International SI units are commmonly used: centimeters or millimeters, grams and milliliters. Perform the following processes as precisely and accurately as possible using a unit that provides the most reasonable numerical value. eg. 1.2345 cm vs. 0.012345 m. A)  1) Record the unknown cylinder's reference number, which is on the bottom of the cylinder. 2) Measure and record the cylinder's length as accurately and precisely as possible. 3) Measure and record the cylinder's diameter as accurately and precisely as possible. 4) Weigh and record the mass of the cylinder as accurately and precisely as possible. Although the cylinder is weighed directly, the most common way of measuring the mass of a chemical is "by difference". This means that you first measure the mass of an empty container such as a beaker, flask or vial and record its mass. (This is referred to as the tare or tared weight.) The chemical is then added to the container and it is weighed again. The mass of the chemical is found by subtracting the mass of the empty container from the mass of the container plus the substance.  B) Complete the following table (Lab Manual page 6) using the data: A DEA forensic laboratory technician weighed an empty vial. It weighed 45.6783 g.  An amount of an unknown substance, reference # 08-21-00-1, which was thought to be [1R-(exo,exo)]-3-(Benzoyloxy)-8-methyl-8-azabicyclo[3.2.1]octane-2-carboxylic acid methyl ester, was added to the vial. The vial was re-weighed. It weighed 47.9834 g.   Table Unknown Sample Reference # Mass of container + substance  Mass of container    Mass of substance      Always use the same balance throughout an experiment because if there is any constant error in the balance it will not present itself in your determination. A container is used for two reasons. First, no chemical is ever put directly on the balance pan and second since it can cause serious damage to the instrument, and secondly, the container is convenient for transporting the substance to and from the balance room. In those experiments where a substance is heated before weighing, it is allowed to cool to room temperature before weighing. This is because an object which is warmer than the balance heats the air above the balance pan more than below it. This creates a buoyancy problem which causes the balance to give incorrect readings.   You will sometimes be instructed, for example, to weigh about 5 g of a substance to the nearest 0.001 or 0.0001 g. Such an instruction may seem to be contradictory, but it means that it is not important that the exact amount of substance weighed be 5.000 g or 5.0000 g. However, it is important that it be close to 5 g and that you know exactly how much you have, for example 4.856 g or 5.0738 g. It is a complete waste of your time to try to make the sample weigh exactly 5.000 g.  Keep these issues in mind for future experiments.     C) Equations:  (1) Write the algebraic formula (equation) for calculating the volume of a sphere. (2) Write the algebraic formula (equation) for calculating the volume of a cylinder. (3) Write the algebraic formula (equation) for calculating the volume of a cube. (4) Write the algebraic formula (equation) for calculating the volume of a rectangular block. You will most likely have to consult another reference if you don't remember the formulas, a math book or the CRC Chemical Handbook are two possibilities. The CRC Handbook can be checked out of the stockroom The formulas will be used in the next experiment.