Unit Analysis

Unit analysis or dimensional analysis is a method for converting from one system of measure to another. In this technique, all measurements are written with their units and conversion factors are written as ratios such that units cancel, top to bottom, like common factors in fractions.

For example, convert 67 inches from English inches to metric meters.

Conversion factors: 1 inch = 2.54 cm and 100 cm = 1m.

67in=1.7m

In this case, the answer is rounded to two significant figures because the original measurement had two significant figures. The other values are exact numbers. The conversion between inches and centimeters is an unusual example of a definition between two totally different measurement systems.

Concept Check: The there are two values for the gas law constant, R: 0.08206 ^{L atm}/_{mol
K}and 8.314^J/_{mol K}. These two values are the same quantity but use different units. Show this to be the case. You may need to see the previous page for the derived units.

Answer: From the table on the previous page, we know that a joule can be reduced to SI base units. We need to convert liters and atmospheres into base units; the moles and degrees Kelvin are fine. One milliliter is the same as a cubic centimeter. A cubic meter is a cube with each side 100 centimeters long, or 1x10⁶ cm³. Setting up conversion factors as ratios such that the units cancel top to bottom gives us:

1L=0.001cubic meters

So we have a new conversion factor: 1L = 0.001 m³. If we convert atmospheres to pascals, we can find SI base units. Using the conversion for atmospheres to kilopascals, knowing that there are 1000 pascals in a kilopascal, and using the definitions of the pascal and the joule we get:

So, 1 atm = 1.01325x10⁵ J/m³. Note that the meters units do not cancel. We have cubic meters in the denominator. We can use these conversions to convert the gas law constant:

This is close enough to the accepted value to prove the point. Now we need to think a bit about the significant figures. The original constant, 0.08206, has four significant figures. The atmosphere to kilopascals conversion has six significant figures. All of the other conversions are exact, because they are based on metric system definitions rather than measurements. The result is rounded to four significant figures by the multiplication/division rule.

This site was last updated 08/01/06