University:
University of Arkansas
Course:
CHEM 1053 | Chemistry in the Modern World
Academic year:

2023
Views:

283

Pages:

1
Author:

madeleinejames20

In this example, we'll use dimensional analysis to solve a problem involving density and cubic units. Our problem states: find the mass in pounds of one meter cubed of corn syrup, whose density is 1.38 grams per cubic centimeter. We're given the hint that one kilogram equals 2.20462 pounds. First, we can create a map of how we'll solve the problem. We can begin with meters cubed and convert to cubic centimeters using the conversion factor: 1 meter equals 100 centimeters. Then, we can convert from cubic centimeters to grams using the density. We can convert from grams to kilograms using the conversion factor: 1 kilogram equals 1,000 grams. Finally, we can convert from kilograms to pounds using the conversion factor given in the hint. To set up our dimensional analysis, we'll begin with one meter cubed. To convert to cubic centimeters, we'll use the conversion factor: 1 meter equals 100 centimeters. If we only use this conversion factor once, only one of our meters will cancel, so our current units would be meters squared centimeters. Therefore, we'll need to use this conversion factor two more times. Now, the three meters on the bottom will cancel the meters cubed, and we'll be left with cubic centimeters. Next, we can convert from cubic centimeters to grams using the density. We only need to use the density once because the density already has units of cubic centimeters, which will cancel our cubic centimeters on top. After that, we can convert into kilograms by using the conversion factor: 1 kilogram is equal to 1,000 grams. This will cancel grams, and we'll be left with kilograms. Finally, our last conversion factor we'll use is the one given in the hint. This will cancel kilograms so that we're left with pounds. If we multiply these numbers out in our calculator, we should come up with the answer: 3.04 * 10^3 pounds.