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Dimensional Analysis

Dimensional Analysis. Chapter 5, Section 3A. Let’s Review The Metric System. In General:. Example:. Kilometer = 1000 m Meter = base unit Decimeter = 0.1 m Centimeter = 0.01 m Millimeter = 0.001 m. Kilo = 1000 of base Deci = 0.1 of base Centi = 0.01 of base Milli = 0.001 of base.

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Dimensional Analysis

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  1. Dimensional Analysis Chapter 5, Section 3A

  2. Let’s Review The Metric System In General: Example: Kilometer = 1000 m Meter = base unit Decimeter = 0.1 m Centimeter = 0.01 m Millimeter = 0.001 m • Kilo = 1000 of base • Deci = 0.1 of base • Centi = 0.01 of base • Milli = 0.001 of base

  3. Converting units of Measurement • You convert units of measurement in your everyday life. • How would you convert from minutes to seconds? • 1 minute = 60 seconds • Doing 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: 60 seconds 1 minute

  4. Steps for converting units • Identify the unit you are starting in, and identify the unit you need to convert to. • Choose the appropriate conversion factor(s) to get from your starting unit to your ending unit. • Set-up your problem, so your units are easily compared and canceled • Multiply the top, multiply the bottom, divide the top by the bottom

  5. Minutes To Seconds How many seconds are in 5 minutes? • Starting units: minutes, ending units: seconds • Conversion factor: 60 seconds/ 1 minute • Set-up: • 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 5 minute 60 seconds 1 minute

  6. Metric conversions How many meters are in 300 centimeters? • Starting units: centimeters, Ending units: meters • Conversion factor: 0.01 m = 1 cm, or 100 cm = 1 m • Set-up: • 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 300 centimeter 1 meter 100 centimeter

  7. 2 conversion problems • 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? • Starting units: hours, Ending units: seconds • Conversion factors: 60 minutes = 1 hour, 60 seconds = 1 minute • Set-up: • 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 4.0 hours 60 minutes 60 seconds 1 hour 1 minute

  8. 2 Conversion Problems How many yards are in 250 centimeters? Hint: 1 m = 1.094 yds • Starting units: centimeters, Ending units: yards • Conversion Factors: 100 cm = 1 m, 1 m = 1.094 yds • Set-up: • 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 250.0 cm 1 m 1.094 yds 100 cm 1 m

  9. Practice Time! • Try practicing dimensional analysis on your own on the worksheet. This worksheet will be a part of your homework packet.

  10. Multi-Step Conversion Problems • 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 • Starting units: miles, Ending unit: kilometers • Conversion factors: 1 mi = 1760 yds, 1 m = 1.094 yd, 1 km= 1000 m • Set-up: • 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) 26.2 mi 1760 yd 1 m 1 km 1 mi 1.094 yd 1000 m

  11. Multi-Step Conversion How many seconds are in 25 days? • Starting unit: days, Ending unit: seconds • Conversion factors: 1 day = 24 hrs, 1 hr = 60 min, 1 min = 60 sec • Set-up: • 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 25 days 24 hrs 60 min 60 sec 1 day 1 hour 1 min

  12. What about measurements with 2 units? • 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

  13. 2 unit Conversions 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 yd • Starting units: mi/hr, Ending units: km/hr, Note: hours is the same in both • Conversion factors: 1 mi = 1760 yd, 1 m = 1.094 yd, 1000 m = 1 km • Set-up: • 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) 225 mi 1760 yd 1 m 1 km hr 1 mi 1.094 yd 1000 m

  14. 2 unit Conversions Silver has a density of 10.5 g/cm3; what is the density of silver in kg/L? • Starting units: g/cm3, Ending units: kg/L, Note: you have to convert both units • Conversion factors: Top unit: 1000 g = 1 kg, Bottom unit: 1 cm3 = 1 mL, 1000 mL = 1 L • Set-up: • 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. 10.5 g 1 kg 1 cm3 1000 mL cm3 1000 g 1 mL 1 L

  15. 2 unit conversions You are driving at 50 mi/hr; how fast are you going in m/s? Hint: 1 mi = 1760 yd, 1 m = 1.094 yds • Starting units: mi/hr, Ending units: m/s • Conversion Factors: Top unit: 1 mi = 1760 yd, 1 m = 1.094 yd, Bottom unit: 1 hr = 60 min, 1 min = 60 s • Set-up: • 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 50 mi 1760 yd 1 m 1 hr 1 min hr 1 mi 1.094 yd 60 min 60 sec

  16. Let’s Practice • 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.

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