A. Conversion Factors
Measurements made during a chemical experiment are often used to calculate another property. Frequently it is necessary to change measurements from one unit to another - inches to feet, meters to centimeters, or hours to seconds. A relationship between two units that measure the same quantity is a conversion factor. For example, the conversion factor between feet and yards is:

3 ft = 1 yd

A conversion factor relates two measurements of the same sample. The measurements may be of the same property (in 3 ft = 1 yd, both measurements are of length) or of different properties of the same sample. In saying that 3 mL alcohol weigh 2.4 g, we are considering two different properties of the same sample - volume and mass. Together these measurements express a conversion factor, for they refer to the same sample and show a relationship between its volume and its mass.

Conversion factors are so named because they offer a way of converting a measurement made in one dimension to another dimension. They do not change the original property, only how it is measured. Table 2.1 listed many conversion factors within the metric system and between the metric and English systems.

Conversion factors that define relationships, such as 3 ft = 1 yd or 1 L = 1000 mL, are said to be infinitely significant. This statement means that the number of figures in these factors does not affect the number of significant figures in the answer to the problem.

B. Problem Solving by Unit Analysis
Problem solving by unit analysis (or dimensional analysis) is based on the premise that, in an arithmetic operation, units as well as numbers can be canceled. The idea may be new to you but the method is familiar. For example, if you were asked how many inches are in 6 feet, you would reply without hesitation that 6 feet equals 72 inches. In doing this calculation, you would be using a familiar relationship, or conversion factor, between inches and feet - namely, 12 in. = 1 ft. This relationship can be written as a conversion factor or as a ratio (fraction). Both are equal to 1 because they measure the same distance:

To convert 6 feet to inches, you would use the conversion factor on the left because it allows you to cancel the unit (dimension) you do not want (feet) and arrive at an answer with the unit you do want (inches).

Note that only the units cancel; the numerical values remain.

Problem solving by unit analysis can be divided into the following steps:

1. Determine what quantity is wanted and in what units.

2. Determine what quantity is given and in what units.

3. Determine what conversion factor (or factors) relates the units given to the units wanted.

4. Determine how the quantity and units given and the appropriate conversion factors can be combined into a mathematical equation in which the unwanted units cancel and only the wanted units remain.

5. Perform the mathematical calculations and express the answer using the proper number of significant figures. Next look at the equation again and estimate the answer. If your estimate is close to the calculated answer, all is probably well; if it is quite different, check your calculations. Be sure that you performed all operations correctly and that you properly placed the decimal point.

Many problems require two or more conversion factors to arrive at the units wanted.

Problem solving by unit analysis is a straight forward method by which you can organize your thinking and approach problems in a systematic way. We will use this method and these same five steps for all the numerical problems that follow.