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  • Sometimes it requires more than one conversion factor to solve a problem using Dimensional

  • Analysis. The basic approach is the same. Please watch our first Unit Conversion video

  • for the introduction to this method of problem solving. Remember the general strategy is

  • to look at the units you start with, look at the units you want to end up with, and

  • use one or more conversion factors to get there.

  • starting unit x conversion factor = ending unit

  • The conversion factor looks like this: ending unit over starting unit.

  • So the starting units cancel, leaving the ending unit.

  • Here are some more complicated problems, that require at least a couple of conversion factors:

  • Here’s our first example. Convert 24.5 g/cm3 to kilograms per liter.

  • Remember, put what you know on the left, and what you want to end up with on the right.

  • Leave lots of room for your work.

  • 24.5 g/cm3 =some number of kg/liter

  • We know we want to go from g to kg, and from cm3 to liters. We can look up those conversion

  • factors and then well have to think about the right way to use them.

  • There are 1000g in 1 kg. So you could write 1000g over 1kg - that’s a fraction equal to 1.

  • You could also write 1kg over 1000 g. That’s also a fraction equal to 1.

  • and there are 1000 cm3 in 1 liter. Again, you can write this as a fraction equal to

  • 1. 1000 cm3 / 1L = 1, and 1 L/ 1000 cm3 equals 1.

  • Here’s where we have to be really careful. Which way do we write these conversion factors

  • so the units cancel in our problem?

  • 24.5 g/cm3 (1kg/1000 g) g has to go on the bottom to cancel.

  • 24.5 g/cm3 (1kg/1000g) (1000 cm3 / 1L) next, cm3 has to go on top. Check to make sure all

  • your units cancel, and you will be left with kg/L .

  • Multiply all the way across on the top, and multiply all the way across on the bottom.

  • 24.5 kg/L

  • Here’s another example: You exhale 20.0 mL of CO2 with every breath. If you breathe

  • 15 times per minute, how many liters of CO2 do you produce each month? Assume 30 days

  • per month. Were starting with 20.0 mL/breath and we

  • want to end up with L/month. That’s going to require a lot of conversion factors, so

  • leave a big space. 20.0 mL/1 breath (15 breaths/1 minute)

  • (60 minutes/1 hr) ( 24hr/1 day) ( 30 day/1 month)( 1L/1000 mL) = some number of L/month

  • Make sure your units cancel. Multiply the top all the way across, and multiply

  • the bottom all the way across. Don’t forget to check your significant figures.

  • There was a measurement of 3 significant figures in the problem: 20.0 mL, so well state

  • our answer with 3 significant figures.

  • 12,960,000/1000 = 12,960 - let’s put this in scientific notation to easily see 3 significant

  • figures. Count over 1, 2, 3, 4 decimal places. 1.296 x 10^4 L /month

  • Now round to 3 significant figures - 1.30 x 10^4 L /month

Sometimes it requires more than one conversion factor to solve a problem using Dimensional

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B1 conversion unit cancel month multiply significant

Chemistry: Introduction to Unit Conversion / Dimensional Analysis (Part 2) | Homework Tutor

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    林宜悉 posted on 2020/03/06
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