# 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.

The following are the steps should be followed for consistant and systematic unit analysis problem solving:

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

The method to do this is to Find the ADVERB:
How many, how much, determine the, solve for, calculate the, etc.

### 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:

____?_____yearslost = GIVEN

### 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: yearslost

2. yearslost 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 gSn / 1 cm3Sn

Velocity:   Length/unit Time    mi/hr
Velocity = 55 mi / 1 hr;

Molecular Mass:   Mass/unit Count    g/mol
Molar MassCO2 = 44.0 gCO2 / 1 molCO2

Mole Ratio from balanced Equation:  x CountA / y CountB
Balanced Equation: 2A + 3B ---> 4C + 1D
Sample Mole Ratio of A to B:     2 moleA / 3 moleB

Molarity:   Countsolute / unit Volumesolution   mol/L
molesolute / Litersolution

%by weight:    partspure / 100 partsmixture

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 yearslost 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 yearssmoking another single/simple dimension

## The Question:

____?_____yearslost = 25 yearssmoking

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

1. '8 minutes of average life for each cigarette smoked' translates to:
8 minlost=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 dollarsaverage = 1 pack
4. a person lose for smoking 0.5 packs a day translates to:
0.5 packs = 1 daysmoking
IV. Chemistry teachers are famous for leaving necessary unit factors out of the wording of the problem. In stoichiometry molecular mass is almost always left out as well as the balanced equations which provide the mole ratios. Also while studying the metric system simple inter metric and english conversions are always left out, as well as the metric to English conversion factors. In Gas law problems temperatures are always given in Celcius while Kelvin temperature are needed for formula problem solving. The following are needed for out sample problem, but left out:
• 365 days = 1 year
• 1 day = 24 hours
• 1 Hour = 60 minutes
V. Of Course, chemistry teachers often insert un-needed unit factors into problems just to fool the number juggler. Dimension analysis problem solvers are word juggles by cancelling like words so that the uncancelled words are the units of the answer.

VI. Apply a unit factor to convert the unit in the given value to the unit in the answer. If it can not be done with one unit factor, apply as many as needed to juggles the word (unit) of the given into the word (unit) of the unknown. Decide how many unit factors must be applied to maske the conversion then connect to one of the following web pages to actually step up and calculate the answer: ## Compount Unit Conversion Problem

For the above problem, the following steps are performed into Single Unit Calculator with 6 unit factors.:

## 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 2nd Unit Factor and Cancel: ## 5. Insert the units and numbers into 3rd Unit Factor and Cancel: ## 6. Insert the units and numbers into 4th Unit Factor and Cancel: ## 7. Insert the units and numbers into 5th Unit Factor and Cancel: ## 8. Insert the units and numbers into 6th 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: 