Math Skills

INTRODUCTION

The student must be able to use and manipulate units in the study of chemistry.  Students in math classes learn how to manipulate numbers, but often do not have to consider units or how to handle them.  This is necessary in chemistry.

The importance of using units can be demonstrated by considering something as simple as the following recipe for biscuits.
2 sifted flour
1/2 salt
1/2 soda
1/4 shortening
1 buttermilk

This recipe makes no sense without units.  A number alone is not enough but must have a unit to indicate amount, i.e. 2 cups of flour, ½ teaspoon of salt, etc.

Units commonly used in the United States (English System) are:
length: inches, feet, yards, and miles
weight: ounces, pounds, tons
volume: teaspoons, tablespoons, liquid cup, pint, quart, gallon, barrels.
See Wikipedia for a complete list of English units, but don’t expect to see them used in this class.

Chemistry uses the International System of Units (SI)  system units of measure.

The SI system has seven basic units  and several derived units.

Don’t let this intimidate you because we will be using predominately units of grams for mass, liters for volume and meters for length. Additional units will be introduced at appropriate times.

In this class, you will have to think in units and always give a unit when expressing quantities.

CONVERSION OF UNITS

Converting from one unit to another is a must in chemistry.  Although you may have done this in the past, many students who take chemistry have difficulty with unit conversions.  Converting between units is not difficult and there is a procedure that always works and can be expanded to allow for conversion between several units.  This method is referred to as the Conversion Factor Method.

The first step is to know the equality between the units being converted.  From this equality, conversion factors can be determined.  An example is the conversion of a length in inches to a length in feet.

We know there are twelve inches (in) in one foot (ft) which can be expressed as the equalities:

12 in = 1 ft   or   1 ft = 12 in

This equality will result in two conversion factors as shown below.

Following steps learned in Algebra, divide both sides of the left equality by 12 in.

12 in/12 in = 1 ft/12in

The numerical value of left side of the equality becomes one.  From Algebra, any number divided by itself is one.  Likewise if a unit is the same in the numerator as in the denominator, it is also equals one. The equality then becomes:

       1 =1 ft/12 in

and the conversion factor becomes:

         1 ft/12 in

 

We could also divide both sides of the equality by 1 ft to get:

 12 in/1 ft = 1 ft/ 1 ft

In this situation, the 1 ft in the numerator and denominator will calculate to 1 with the result:

 12 in/1 ft = 1

 

and the conversion factor becomes:

              12 in/1 ft

The two conversion factors are:

 

                   1 ft/12 in and 12 in/1 ft

When converting between units, there will be two conversion factors that are the inverse of each other.  The following examples will show how to select the correct conversion factor.

Example 1.
Convert 30 in to ft.

In this example, the beginning unit is inches and the ending unit is ft.  Since we want the inch unit to cancel and leave the foot unit, the correct conversion factor used in this conversion is 1 ft/12 in. Expressed in math form, the following is the correct way to perform the calculation.

Conversion Example 1

Stated in words.  The 30 inches is multiplied by the conversion factor which can be re-written as one fraction.  The inches (in) will cancel and go to one and the foot (ft) unit remains.   30 divided by 12 equals 2.5 which give the answer 2.5 ft.

Example 2
Convert 3.5 ft to inches.

In this case, we are converting from feet to inches. So the correct conversion factor would be 12 in/1 ft.  The inverse of Example 1.

Conversion Example 2

Expressed in math form, the following is the correct way to perform the calculation.
Stated in words.  3.5 multiplied by 12 equals 42.  The foot (ft) unit goes to 1 and the inches(in) units remains.

 

Example 3
A city block is 300 ft long.  How long is this block in miles?

Step 1:  Determine the equality between the two units.

1 mile (mi) = 5280 feet (ft)

Step 2: Determine the conversion factor you need.  The factor needed is: 1 mile/5280 ft

Why this factor and not 5280 ft/1 mi?  When determining which of the two factors to use, check the beginning units (in this case ft) and the ending units (in this case mi).  Use the factor that has the ending units in the numerator and the beginning units in the denominator.

Step 3: Calculate the conversion.

Conversion Example 3

 

METRIC SYSTEM

As mentioned above, chemistry uses the SI unit system and the Derived SI unit system.  The most common units used in this class are listed below:

Metric units w400h350

The  Liter unit is more commonly used in chemistry than meters cubed (m3)

The metric system uses prefixes to represent powers of ten to indicate larger and smaller quantites of the base units listed above.  See the metric system link for a complete list of prefixes.  We will focus on the following prefixes: micro, milli, centi, kilo.

Metric prefixes w811h314

YouTube has several videos showing conversion between metric units. Two listed below provide good examples.

The first video How to Convert Units of Measure uses the term “conversion ratio instead of “conversion factor” which has been used on this website.    The second video Metric conversion – unit fraction method uses the term “unit factor” instead of “conversion which has been used on this website.

A common conversion in chemistry is between liters (L) and milliliters (mL).  One L equals 1000 mL.  So the conversion factors are.

1 L/ 1000 mL and 1000mL/1 L

Example 4
How many mL of water are there in 1.75 L of water?  Following the process discussed above, you would use the conversion factor with the L unit in the denominator to get:

Conversion Example 4

Next cancel the L units and multiply the numbers to get 1750 ml of water.

 

Example 5

How many g of NaCl are there in 25 mg of NaCL? One gram (g) equals 1000 milligram (mg).  The conversion factors are 1 g/1000 mg or 1000 mg/1 g.  Because the ending unit is g, use the conversion factor with g in the numerator to get:

Conversion Example 5

Cancel the mg units and divide the numbers to get 0.025 g of NaCl.