Problem Solving Using Conversions and Dimensional Analysis

Unit 5: Chemical Quantities and Calculations                                                                                     GIA 5-2
Chapter 3                                                                                                                       NAME:_________________

Using the units to help you solve problems in science is a benefit to the presence of units associated with numbers in science.  Often a measurement can be in a unit that is of a different dimension than another measurement.  In this case the measurement has to be converted.  By learning what various prefixes mean, such as “kilo” and “milli” or “mega,” you can use the relationship of this prefix with the standard unit to establish a conversion factor.  For example, there are 1000 m in one 1 km.  Therefore, I can state a relationship between these as 1000 m = 1 km.  The numbers of these two are not equal but the measurement is.  I can build a conversion factor between a meter and kilometer by writing this equation as a ratio of 1000 m/ 1 km or 1 km/ 1000 m.  I can use this ratio is either form to convert between km and m.  In this worksheet you will practice converting units using single and then multiple conversion factors.  Then you will be given relationships between two otherwise unrelated units and be able to use that ratio as a conversion factor in a dimensional analysis method of solving certain problems.

Part I: Converting Using Conversion Factors

1.  What conversion factor would you use to convert the following:

a.  years to days                                   a.  ___________

b.  liters to mL                                      b.  ___________

c.  kilograms to grams                           c.  ___________

d.  minutes to hours                               d.  ___________

e.  nm to m                                           e.  ___________

f.  moles (mol) to millimoles (mmol)       f.   ___________

To make the conversion, use the identities from above as ratios to convert as requested.  The key is to cancel the unit you are converting from and leave the unit you are converting to.  In this case in your conversion factor the unit you convert from is on the bottom of the ratio.  The unit you convert is on the top of the ratio.

2.      Make the following conversions, using the information above.  Use scientific notation as necessary.

a.       484 days to years

b.      125 mL to liters

c.       5 x 10³ kg to grams

d.      0.12 hrs to min.

e.       1.35 nm to meters

f.        25.3 mmol to mol

3.      Make the following two step conversions. 

a.       25,400 mm to megameters

b.      8.3 x 10⁴ ns to milliseconds

c.       18.7 x 10³ mg to decigrams

Part II: Solving Problems with Dimensional Analysis

Units that represent a ratio like “mph” miles per(/) hour can be used as a conversion factor.  Sometimes these values are given to you sometimes they involve constants and other times they are what you derive.  In solving problems that involve several steps and conversion factors remember the canceling principle, take one conversion at a time and use the number with a single dimension to start with.

4.      The density of a liquid is 0.821 g/mL.  What is the volume of 71.3 g of this liquid?

5.      How many seconds are there in one week?

6.      A 100. gram sample of iron ore was found to contain 44 g of iron.  How many grams of iron are in a 450. gram sample of the ore?

7.      A radio wave travels 186,000 miles per second.  How many kilometers will the wave travel in one microsecond?  (1 mile = 1.61 km) 

8.      If a car goes 30.0 miles per gallon of gasoline, how many kilometers could it travel on 1 liter of gasoline?  (1.61 km = 1 mile; 1 gal = 4 qt; and 1.06 qt = 1.0 L)