Chapter 1:Unit 13. Conversion Factors

Conversion Factors

A conversion factor is a ratio that specifies how one unit of measurement is related to another unit of measurement. Chemists often need to convert the value from one unit to another unit. When the equalities are written as a ratio, it becomes a conversion factor.

To convert the measured number from one unit to another unit we always take the following path
1)First we define the given quantity with number and unit and needed unit.
2)Then we set up the conversion factor as a ratio to convert from one unit to another unit. This conversion factors are measured or exact number depending upon the quantity. Always the desire unit is on the top and the unit to be cancelled is written as denominator in the ratio.
3)We multiply the the given quantity by the appropriate conversion factor and find the new value with the target unit.

1 min= 60 sec ……………………………………………this an equality

1 min or   60 sec       these two quantities are same.  ………………….this is conversion factor

60 sec         1 min

There are two sets of conversion factor for every relationship.

Conversion factor can be used within a system of units or between different units of system.

Case1: Conversion factor can be used within a system of units or between different units of system. (defined relationship)

Example problem: A lab test showed an individual’s cholesterol level to be 186 mg/dL. Convert this quantity into g/dL

given 1g= 1000mg

In order to obtain metric to metric conversion factor, the meaning of metric prefixes and their values must be known.

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Metric conversion: ladder method:

How do you use ladder method?

Example:  4km  =__________m

↑start                          ↑End

Write the abbreviation of following Metric Conversions:

1) Kilogram _____                 4) Milliliter _____                  7) Kilometer _____

2) Meter _____                       5) Millimeter _____                8) Centimeter _____

3) Gram _____                        6) Liter _____                         9) Milligram _____

Try these conversions, using the ladder method.

10) 2000 mg = _______ g      15) 5 L = _______ mL            20) 16 cm = _______ mm

11) 104 km = _______ m       16) 198 g = _______ kg          21) 2500 m = _______ km

12) 480 cm = _____ m            17) 75 mL = _____ L             22) 65 g = _____ mg

13) 5.6 kg = _____ g               18) 50 cm = _____ m             23) 6.3 cm = _____ mm

14) 8 mm = _____ cm            19) 5.6 m = _____ cm             24) 120 mg = _____ g

Compare using <, >, or =.

56 cm         6 m

7 g          698 mg

5 g         508 mg

1,500 mL         1.5 L

536 cm          53.6 dm

43 mg         5 g

3.6 m         36 cm

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Questions:

1. Convert each of the following measurements into meters?
2. 5 × 10³ mm
3. 25 μm

Ans: a. 2.5 m, b. 25E-6 m

Case 2: Metric to English conversion factors are specified with different number of significant figures. (measured relationship). They are called equalities.  For example: 1 mile= 1.61 km. mile is the English unit and kilometer (km) in the metric unit.

Example #1 : Capillaries, the microscopic vessels that carry the blood from small arteries to small veins, are on the average only 0.1cm long. What is the average length of a capillary in inches?

Given 1 inch= 2.54 cm

0.1 cm × 1 inch         =   0.0393 in= 0.04 in ( lowest 1 sig fig used in calc)
2.54 cm
Here is the table of most common metric to metric and metric to English conversion factors:

Example #2: Convert 10.8 ft to meters

Given that  12 in = 1ft,  2.54 cm= 1 inch and 100 cm = 1meter

Pathway: ft * 12 in             *  2.54 cm                  *  1 m         = meter
                          1 ft                    1 in                        100 cm

Now plug in the numbers in tis problem:

10.8 ft * 12 in    * 2.54 cm  * 1m = 3.28 m ( ans)
                 1ft *   1 in *    100cm

Example#3:  Convert 58.8 lbs to kg.

Given : 58.8 lbs,  needed  kg. conversion factor: 2.205 lbs= 1 kg

pathway:  lbs *   1kg
                              2.205lbs

now use the values given in the problem,

58.8 lbs *  1 kg  = 26.7 kg

2.205

Below is the table with common English to metric equalities.

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Questions:

1. A chemistry student weighs 83.1 kg and 1.93 m tall. What are the person’s equivalent measurements in pounds and feet?
2. What volume of water in gallons would be required to fill a 30.ml of container?
3. A person weights 110 lbs. What is the mass in kilograms?
4. What is the height in cm of a child who is 50. in tall?

Ans: 1. weight=183 lbs, height=6.33 ft

2. 0.0079 gal
3. 20. kg
4. 130 cm