Exactly how “good” is a measured number?

Pre-Lab Assignments:

Before doing this lab you should have completed the following prelab tutorials or taken the corresponding fast-track quizzes demonstrating your proficiency.

Measurements and Units

Significant Figures

Student Learning Outcomes:

How to properly make and record measurements taken with both analog and digital measurement devices with the maximum precision.

The rules for the use and importance of significant figures.

How the choice of measurement device affects the quality of measurements.

Review calculations of volumes of regularly shaped objects from their dimensions.

Familiarity with the concept of density. Should know how it is used to identify samples qualitatively and should be able to use it the interconvert between mass and volume.

How to properly use a volumetric pipette.

Define accuracy and precision.

Determine the accuracy and precision of different types of laboratory glassware so that in future labs you can select the appropriate glassware for a particular application.

Experimental Goals:

The goal of the first part of this experiment is to determine the densities of a number of cylinders, and gain an understanding of how different measurement techniques can affect the reliability of experimental results. In the second part of the experiment, you will measure the volume of water delivered by several different types of volumetric glassware, and determine the relative precision of their measurements.

Introduction:

Measurements are important in all areas of our lives. A great deal of effort goes into making sure that the measurements we base our decisions on are accurate, but much of that effort is hidden from our day-to-day experience.

What are some measurements made by you or others that affect you as a consumer? What are some measurements that would be made by someone in a profession that you are interested in pursuing? In both of these cases, what might the consequences be if those measurements are off by 5%, 10 % or 25%?

In this lab, you will develop skills for measuring and recording measurements with the maximum attainable precision, distinguish between accuracy and precision, and develop some insight into what is required to make measurements that are truly accurate and precise. You will also learn some tools for gauging the precision (and to a lesser extent, the accuracy) of a measurement.

You will be required to choose appropriate glassware for future lab exercises based on what you learn from this lab. Make sure you understand how the choice of glassware and the proper use of significant figures affect the quality of experimental results.

Determining Volume from the Dimensions of an Object

The volume (V) of a cuboid (or rectangular prism), a box-like 6-sided shape with all angles being right angles, is calculated from its length (l), width (w), and height (h) by the equation

V = l w h

For any regular shape (cuboid, cylinder, or prism) in which the area (A) of a face can be easily calculated, this simplifies to

V = l A

For a cylinder, the face is a circle. Since the area of a circle is πr2 or π(½D)2 (where r is the radius and D is the diameter), the volume of a cylinder is πr2l [or π(½D)2l].

Determining Volume by Displacement of a Liquid

Another way to determine the volume of a solid is to measure the volume of a liquid that is displaced by the solid. This is particularly useful for irregularly shaped objects. This type of measurement is usually done in a graduated cylinder. (See Figure 1.) The solid object must fit in the graduated cylinder, and be denser than the liquid.

(a) (b)

Figure 1. Measuring the volume of a cylinder by displacement of water. The volume of water in the cylinder in 1a is 35.5 mL1, and the volume of water in the cylinder in 1b is 47.8 mL, therefore, the volume of the metal cylinder is 12.3 mL.

Enough liquid to completely