A quick and dirty guide to dimensional analysis
First and foremost, dimensional analysis (along with the majority of chemistry) is just
clever application of algebra. To be successful in using dimensional analysis, students must be
competent in addition/subtraction, multiplication/division, powers, and parentheses. Basically,
PEMDAS is back and will actively be put to use.
Dimensional Analysis is the analysis of relationships between different physical
quantities, by first identifying unifying base qualities of the measurements in question.
Effectively, if given a measurement and you don't like the units given, how do you change the
units without changing the quantity? Can we convert miles per hour to meters per second? The
velocity will remain unchanged, but the measurement will. Dimensional Analysis can be used to
convert between compounds in a chemical reaction by utilizing any quantitative measurement of
one, and relating it to another via a balanced reaction.
The steps to solving a dimensional analysis problem are as follows:
1. Identify the measurement you are given. What is it? Is it a distance? An amount of
something? Time? The velocity of a car on the highway, the mass of a compound
consumed in a reaction, all are valid.
2. Identify what unit(s) you are trying to obtain. What is the question asking for?
3. Outline how to convert one unit to another. Are there intermediate units that you can
use to convert one to another? What conversions are you given? If I was given
kilometers and wanted centimeters, are there intermediate units that I can convert to
each? Often, you must make a unit conversion form a balanced reaction or from the
periodic table itself. If you are given a measurement that has two different base qualities
such as (amount/mass), (distance/time), make two outlines for each base quality.
4. Assemble your equation. List your given and add your conversions as you outlined in
step 3.
5. Ensure that every unit cancels out, excluding the desired units. Remember that
equal values in numerators and denominators effectively cancel out, the same principle
applies to units. A ratio of values with the same unit becomes a unitless ratio.
6. Solve the algebraic expression that you created. Multiply numerators, divide
denominators. Write the remaining units which should exactly match your desired units.
Don’t forget to track significant figures!
