Subject: Using density to solve a dimensional analysis problem.
Dimensional analysis is a procedure for solving problems using a conversion
factor that compares units. Density is a conversion factor that comparing
the mass of a specific volume for a specific substance. YIKES! This sounds
so very complicated, but it really isn’t. Let me give you an example:
Problem 1: What is the volume of 38.64 grams of gold?
Think:
1. The conversion factor that compares grams of gold to volume (cm^3) is the density of gold, which is 19.32 g/1cm^3
2. Restate the Problem: 38.64 g = ?cm^3
3. Solve by dimensional analysis using the density of gold as the conversion factor.
38.64 g x 1 cm^3/ 19.32 g = 2.00 cm^3
Note: The conversion factor (density) was inverted so that the gram unit is canceled out and only the unit of volume, cm^3 remains.
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Problem 2: Determine the mass of 2.00 cm^3 gold using
dimensional analysis, then the calculations would look like this:
2.00 cm^3 x 19.32 g/ 1 cm^3 = 32.64 g
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Let me know if you need more help with this.
