Chapter 5, Section 3A

DIMENSIONAL ANALYSIS

In General:

Kilo = 1000 of baseDeci = 0.1 of baseCenti = 0.01 of baseMilli = 0.001 of base

Example:

Kilometer = 1000 mMeter = base unitDecimeter = 0.1 mCentimeter = 0.01 mMillimeter = 0.001 m

LET’S REVIEW THE METRIC SYSTEM

You convert units of measurement in your everyday life.How would you convert from minutes to seconds?

1 minute = 60 secondsDoing unit conversions in chemistry is no different, we just

call it dimensional analysis.Hint: Unit conversions are exact numbers, so the only sig figs

you count are the ones in your original number In chemistry, we use conversion factors, a ratio used to

convert from unit to another. I will give you non-metric conversion factors. Ex grams to pounds

As a conversion factor, minutes to seconds would be written like this:

CONVERTING UNITS OF MEASUREMENT

60 seconds

1 minute

1. Identify the unit you are starting in, and identify the unit you need to convert to.

2. Choose the appropriate conversion factor(s) to get from your starting unit to your ending unit.

3. Set-up your problem, so your units are easily compared and canceled

4. Multiply the top, multiply the bottom, divide the top by the bottom

STEPS FOR CONVERTING UNITS

How many seconds are in 5 minutes?1.Starting units: minutes, ending units: seconds2.Conversion factor: 60 seconds/ 1 minute3.Set-up:

4.Multiply top: 5 x 60 = 300, Multiply bottom: 1, Divide top by bottom: 300/1 = 300 seconds, this answer already has the correct number of sig figs

MINUTES TO SECONDS

5 minute 60 seconds

1 minute

How many meters are in 300 centimeters?1.Starting units: centimeters, Ending units: meters2.Conversion factor: 0.01 m = 1 cm, or 100 cm = 1 m3.Set-up:

4.Multiply top: 300 x 1 = 300, Multiply bottom: 100, Divide top by bottom: 300/100= 3 meters, this answer already has the correct number of sig figs

METRIC CONVERSIONS

300 centimeter 1 meter

100 centimeter

For some dimensional analysis problems you will have to use 2 conversion factors to get to an answer. But you still use the same steps! Let’s look at an example:

How many seconds are in 4 hours?1.Starting units: hours, Ending units: seconds2.Conversion factors: 60 minutes = 1 hour, 60 seconds = 1

minute3.Set-up:

4.Multiply the top: 4 x 60 x 60 = 14400, Multiply the bottom: 1 x 1 = 1, Divide top by bottom: 14400/1 = 14400 seconds, sig fig answer 14000 seconds

2 CONVERSION PROBLEMS

4.0 hours 60 minutes 60 seconds

1 hour 1 minute

How many yards are in 250 centimeters? Hint: 1 m = 1.094 yds1.Starting units: centimeters, Ending units: yards2.Conversion Factors: 100 cm = 1 m, 1 m = 1.094 yds3.Set-up:

4.Multiply the top: 250 x 1 x 1.094 = 273.5, Multiply the bottom: 100 x 1 = 100, Divide the top by the bottom: 273.5/100 = 2.735 yards, this answer already has the correct number of sig figs

2 CONVERSION PROBLEMS

250.0 cm 1 m 1.094 yds

100 cm 1 m

Try practicing dimensional analysis on your own on the worksheet. This worksheet will be a part of your homework packet.

PRACTICE TIME!

Many dimensional analysis problems will have more than 2 conversions. However, you follow the same steps

The length of a marathon is 26.2 mi. What is this distance in kilometers? Hint: 1 mi = 1760 yds, 1 m = 1.094 yd

1.Starting units: miles, Ending unit: kilometers2.Conversion factors: 1 mi = 1760 yds, 1 m = 1.094 yd, 1 km=

1000 m3.Set-up:

4.Multiply top: 26.2 mi x 1760 yd x 1 m x 1 km = 46112, Multiply bottom: 1 mi x 1.094 yd x 1000 m = 1094, Divide top by bottom: 46112/1094 = 42.1 km (correct sig figs)

MULTI-STEP CONVERSION PROBLEMS

26.2 mi 1760 yd 1 m 1 km

1 mi 1.094 yd 1000 m

How many seconds are in 25 days?1.Starting unit: days, Ending unit: seconds2.Conversion factors: 1 day = 24 hrs, 1 hr = 60 min, 1 min = 60 sec3.Set-up:

4.Multiply the top: 25 x 24 x 60 x 60 = 2160000, Multiply the bottom: 1 x 1 x 1 = 1, Divide top by the bottom: 2160000/1 = 2160000 seconds, sig fig answer: 2200000

MULTI-STEP CONVERSION

25 days 24 hrs 60 min 60 sec

1 day 1 hour 1 min

Some measurements, like density (g/mL), have two units. You can still use dimensional analysis to convert one or both of the units present.

You will still use the same steps, but your set-up will be longer and you have to be more careful about canceling your units.

For your conversion factors, I recommend separating them into the units you need to use for the top unit and the bottom unit

Let’s look at a few examples

WHAT ABOUT MEASUREMENTS WITH 2 UNITS?

Race cars routinely travel at an average speed of 225 mi/hr. What is the speed in km/hr? Hint: 1 mi = 1760 yd, 1 m = 1.094 yd1.Starting units: mi/hr, Ending units: km/hr, Note: hours is the same in both2.Conversion factors: 1 mi = 1760 yd, 1 m = 1.094 yd, 1000 m = 1 km3.Set-up:

4.Multiply top: 26.2 mi x 1760 yd x 1 m x 1 km = 46112, Multiply bottom: 1 mi x 1.094 yd x 1000 m = 1094, Divide top by bottom: 46112/1094 = 42.1 km/hr (correct sig figs)

2 UNIT CONVERSIONS

225 mi 1760 yd 1 m 1 km

hr 1 mi 1.094 yd 1000 m

Silver has a density of 10.5 g/cm3; what is the density of silver in kg/L?1.Starting units: g/cm3, Ending units: kg/L, Note: you have to convert both units2.Conversion factors: Top unit: 1000 g = 1 kg, Bottom unit: 1 cm3 = 1 mL, 1000 mL = 1 L3.Set-up:

4.Multiply the top: 10.5 x 1 x 1 x 1000 = 10500, Multiply the bottom: 1 x 1000 x 1 x 1= 1000, Divide top by the bottom: 10500/1000= 10.5 kg/L.

2 UNIT CONVERSIONS

10.5 g 1 kg 1 cm3 1000 mL

cm3 1000 g 1 mL 1 L

You are driving at 50 mi/hr; how fast are you going in m/s? Hint: 1 mi = 1760 yd, 1 m = 1.094 yds1.Starting units: mi/hr, Ending units: m/s2.Conversion Factors: Top unit: 1 mi = 1760 yd, 1 m = 1.094 yd, Bottom unit: 1 hr = 60 min, 1 min = 60 s3.Set-up:

4.Multiply the top: 50 x 1760 x 1 x 1 x 1= 88000, Multiply the bottom: 1 x 1.094 x 60 x 60= 3938.4, Divide the top by the bottom: 88000/3938.4= 22 m/s

2 UNIT CONVERSIONS

50 mi 1760 yd 1 m 1 hr 1 min

hr 1 mi 1.094 yd 60 min 60 sec

This worksheet is great practice for the skills we learned today and yesterday.

Use this worksheet to gauge your understanding of dimensional analysis

This worksheet will be a part of your homework packet due on the day of the test.

LET’S PRACTICE