Unit Analysis Problem Solving

Chemistry word problems sometimes may be difficult. There are several methods for solving chemical word problems. A powerful technique for solving problems is called unit analysis method, sometimes referred to as dimensional analysis method, or factor label method of problem solving. Unit analysis cannot solve every chemistry word problem, but it is very effective for the problems we encounter in begining and college chemistry.

I. Read the problem. Write down the unit asked for in the answer.

Sample:

Insurance statistics state that a person loses 8 minutes of average life for each cigarette smoked. If there are 20 cigarettes in a pack and the average cost of cigarette is $4.50 per pack over the next 25 years, how many years of average life would a person lose for smoking 0.5 packs a day for 25 years? How much would the person spend?

translates:

II. Write down the given value related to the answer. Or Connect the unknown unit to the GIVEN unit

1. Analyize the dimension of the unknown: years_lost


2. years_lost is a single dimension of time.


1. Single Dimensions include: length, mass, time, count, Also Simple includes temperature
2. Although volume is (length)³ and not a single dimension, treat volume in chemistry as a Simple dimension
3. Compound Dimensions include:
   
   Density:   Mass/unit Volume    g/mL
        Density _tin = 7.43 g_Sn / 1 cm³_Sn
   
   Velocity:   Length/unit Time    mi/hr
        Velocity = 55 mi / 1 hr;
   
   Molecular Mass:   Mass/unit Count    g/mol
        Molar Mass_CO2 = 44.0 g_CO2 / 1 mol_CO2
   
   Mole Ratio from balanced Equation:  x Count_A / y Count_B
        Balanced Equation: 2A + 3B ---> 4C + 1D
        Sample Mole Ratio of A to B:     2 mole_A / 3 mole_B
   
   
   Molarity:   Count_solute / unit Volume_solution   mol/L
   mole_solute / Liter_solution
   
   
   %_{by weight}:    parts_pure / 100 parts_mixture
   
       Bleach = 5%_NaClO = 5 g _{NaClO solute} / 100 g _{NaClO solution}
   
   
4. d. Note the labels placed on each unit. Labels must match before cancelling.


3. The Given Unit must have the same number of dimensions as the Unit of the Unknown. In the above problem years_lost is time and only has one dimension. After the verb: "would a person lose" is a unit factor: 0.5 packs a day which can not be the GIVEN since it is a compund dimension. The Given is: = 25 years_smoking another single/simple dimension

The Question:

III. From the word problem, write down all unit factors given:

1. '8 minutes of average life for each cigarette smoked' translates to:
   8 min_lost=1 cig
2. '20 cigarettes in a pack' translates to:
   20 cig = 1 pack
3. the average cost of cigarette is $4.50 per pack over the next 25 years translates to:
   4.50 dollars_average = 1 pack
4. a person lose for smoking 0.5 packs a day translates to:
   0.5 packs = 1 day_smoking

• 365 days = 1 year
• 1 day = 24 hours
• 1 Hour = 60 minutes

Simple/Single Unit Conversion Problem

• 1 unit Factor Needed
• 2 unit Factors Needed
• 3 unit Factors Needed
• 4 unit Factors Needed
• 5 unit Factors Needed
• 6 unit Factors Needed

Compount Unit Conversion Problem

• 5 unit Factors Needed

1. Write the Question into the dimensional Analysis Calculator:

2. Insert the units and numbers into 1st Unit Factor

3. Cancel the matching Units:

4. Insert the units and numbers into 2^nd Unit Factor and Cancel:

5. Insert the units and numbers into 3^rd Unit Factor and Cancel:

6. Insert the units and numbers into 4^th Unit Factor and Cancel:

7. Insert the units and numbers into 5^th Unit Factor and Cancel:

8. Insert the units and numbers into 6^th Unit Factor and Cancel:

9. Check Uncancelled Unit with Unit of Unknown then push Calculate:

10. The Answer is inserted into the The Answer Box:

11. Your answer is 1.4 years_Lost to two significant digits