Measurement in Chemistry Factor-Label Method

The Factor-Label Method At the conclusion of our time together, you should be able to: 1.Recognize a problem that can be solved with the factor label method 2.Transform a statement of equality into a conversion factor 3.Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol, etc. To use this we need: 1) given quantity 2) desired quantity 3) conversion factors Conversion factors are valid relationships or equalities expressed as a fraction and equal to one! The Factor label Method

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units. Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Conversion Factors Conversion factors for 1 ft = 12 in There are almost an infinite number of conversion factors that include meters:

The Steps to Follow Now we are ready to solve problems using the factor label method. The steps involved are: Write down the given quantity Determine what conversion factors you will use to turn the given label into the needed label Set up the conversion factor Given unit in the denominator Desired unit in the numerator Complete the math

How many kilometers are in 47.0 miles? (note: 1 km = miles) Factor label Example

The Steps to Follow Now we are ready to solve problems using the factor label method. The steps involved are: Complete the math with no rounding Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end Don’t forget the order of operations when you complete the math: “Please Excuse My Dear Aunt Sally”!

How many kilometers are in 47.0 miles? (note: 1 km = miles) The final answer is 75.7 km # km = 47.0 x 1 km = 75.7 km Factor label Example

Summary The previous problem was not that hard In other words, you probably could have done it faster using a different method However, for harder problems the factor label method is easiest

Converting Metric to Metric Steps Steps 1. Write the given quantity 2. Set up units in the conversion factor 1. Larger unit gets a 1 2. Determine what goes in front of smaller unit 3. Cancel units 4. Complete the math

An Easier Way G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

Converting Metric to Metric A rattlesnake is 2.44 m long. How long is the snake in cm?

Measurement in Chemistry Factor-Label Method Part 2

The Factor-Label Method At the conclusion of our time together, you should be able to: 1.Recognize a problem that can be solved by moving the decimal point. 2.Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

Convert km/h to m/s km x 1000 m x 1 h___ = h 1 km 3600 s h 1 km 3600 s m/s Dealing with Two Units

Dealing with Two Units, Your Turn If your pace on a treadmill is 65 meters per minute, what is your rate in km per hour

What about Square and Cubic units? Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! Best way: Square or cube the Entire conversion factor Example: Convert 4.3 cm 3 to mm cm 3 10 mm 3 1 cm 1 cm ( ) = 4.3 cm mm cm cm 3 = 4300 mm 3

Learning Check A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

Solution 1000 cm 3 1 dm 3 10 cm 10 cm ( ) = 1 dm 3 So, a dm 3 is the same as a Liter! A cm 3 is the same as a milliliter.

A person’s blood contains 185 mg of cholesterol per deciliter of blood. How many grams of cholesterol are there in 1 liter of this blood? A g B g C.1.85 g D.18.5 g E.1850 g Learning Check Learning Check