Dimensional Analysis Problem Help

Question

A recipe for making creamy pasta sauce calls for 0.750 liters of cream. Your measuring cup only measures in cups. How many cups of cream should you use?

Answer 1

There are 4 cups in 1 quart. 4 cups = 1 qt

A liter is almost the same size as a quart, but we need to know specifically that 1 qt = 0.946 L

A rough guess of 0.750 L should be about 3/4 of a quart, which should be around 3 cups. But we can't just guess, we need to calculate it! Use the relationships we know to create conversion factors for the calculation, it should look like this:

0.750 L x (1 qt / 0.946 L) x (4 cups / 1 qt) = ? cups

Notice that the units Liters and quarts cancel out, and you are left with cups.

The math is 0.750 ÷ 0.946 x 4 = 3.17 cups (reported to 3 sig figs)

This is the same result as what the other tutor got, but step by step without creating more new and different conversions, only using the ones "we should already know". Hope that helps - good luck!

Answer 2

3.17 cups for 3/4 liter

4.22675 cups in a liter

For .750 liters, multiply (.750)(.422675) = 3.170 cups

one cup = 236.5 mL so 1 liter = 1000/236.5=4.22 liters