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Chapter 3

- Problem Solving and Conversion Factors

Word Problems

- The laboratory does not give you numbers already

plugged into a formula - You have to decide how to get the answer.
- Like word problems in math.
- The chemistry book gives you word problems.

Problem solving

- Identify the unknown.
- Both in words and what units it will be

measured in. - May need to read the question several times.
- Identify what is given
- Write it down if necessary.
- Unnecessary information may also be given

Problem solving

- Plan a solution
- The heart of problem solving
- Break it down into steps.
- Look up needed information.
- Tables
- Formulas
- Constants
- Equations

Problem solving

- Do the calculations math (algebra)
- Finish up
- Sig Figs
- Units
- Check your work
- Reread the question, did you answer it
- Is it reasonable?
- Estimate

Dimensional Analysis

- Dimension unit
- Analyze solve
- Using the units to solve the problems.
- If the units of your answer are right, chances

are you did the math right.

Initial and Final Units

1. A person has a height of 2.0 meters. What is

that height in inches? Initial unit

m Final unit _______ 2) Blood has a density

of 0.05 g/mL. If a person lost 0.30 litres of

blood at 18C, how many grams of blood would that

be? Initial litres Final unit _______

Conversion factors

- A ratio of equivalent measurements
- Start with two things that are the same
- one meter is one hundred centimeters
- write it as an equation
- 1 m 100 cm
- can divide by each side to come up with two ways

of writing the number 1

Conversion factors

- Called conversion factors because they allow us

to convert units. - really just multiplying by one, in a creative way.

Conversion factors

1

Conversion factors

1

1 m

100 cm

Conversion factors

1

1 m

100 cm

Conversion factors

1

1 m

100 cm

100 cm

1

1 m

Conversion Factors

- The units of measurement are not always

convenient dimensions and it may become necessary

to change units. In a lab the distance could only

be measured in cm. To calculate the speed the cm

must be converted to m without changing the value

of the measurement. - Distance in cm x conversion factor distance

in m

Conversion Factors

- The only number that can multiply any other

number without changing the numbers value is 1.

The conversion factor is a ratio. The value of

the ratio is 1. For the ratio to have a value of

one the top term has to equal the bottom term. - Start with 1255cm, want to find the number of m,

then - By definition 1m 100 cm
- 1 m 1
- 100cm
- 1255 cm x 1 m 12.55m
- 100cm
- The conversion factor must cancel the present

unit and introduce the desired unit

Conversion factors

- A unique way of writing the number 1
- In the same system they are defined quantities so

they have unlimited significant figures - Equivalence statements always have this

relationship - big small unit small big unit
- 1000 mm 1 m

Write the conversion factors for the following

- kilograms to grams
- feet to inches (1 foot 12 inches)
- 1.096 qt. 1.00 L

How many minutes are in 2.5 hours?

- Initial unit
- 2.5 hr
- Conversion Final
- factor unit
- 2.5 hr x 60 min 150 min
- 1 hr
- cancel Answer (2 SF)

Learning Check

- A rattlesnake is 2.44 m long. How long is the

snake in cm? - 1) 2440 cm
- 2) 244 cm
- 3) 24.4 cm

Solution

- A rattlesnake is 2.44 m long. How long is the

snake in cm? - 2) 244 cm
- 2.44 m x 100 cm 244 cm
- 1 m

Learning Check

- How many seconds are in 1.4 days?
- Unit plan days hr min

seconds - 2 SF Exact
- 1.4 day x 24 hr x 60 min x 60 sec
- 1 day 1 hr 1 min
- 1.2 x 105 sec

Unit Check

- What is wrong with the following setup?
- 1.4 day x 1 day x 60 min x 60

sec - 24 hr 1 hr

1 min

Steps to Problem Solving

- Read problem
- Identify data
- Write down a unit plan from the initial

unit to the desired unit - Select conversion factors
- Change initial unit to desired unit
- Cancel units and check
- Do math on calculator
- Give an answer using significant figures

Learning Check

- If the ski pole is 3.0 feet in length, how long

is the ski pole in m? - 2.54 cm 1.00 inch 12 inches 1 foot

Solution unit plan ft in cm m

- 3.0 ft x 12 in x 2.54 cm x 1m

0.91m - 1 ft 1 in.

100 cm

- The solutions for some problems contain

multi-steps (require more than one calculation to

solve). - Using Dimensional Analysis can solve this type of

problem. - Dimensional Analysis
- Identify the given or known data (information).
- Identify the unknown.
- Plan the solution or calculations by either
- setting up a series of conversion factors OR
- using a formula.
- Check your work by canceling out units.
- 1. Calculate the number of seconds of

Chemistry class there is in a week. - The density of gold is 19.3 g.
- cm3
- What is the density of gold expressed in kg?
- m3

Practice

- Use conversation factors to solve the following
- A pain relief tablet contains 325 mg of ASA.

There are 80 tablets in the package of tablets. - (a) What is the mass of ASA in grams for each

tablet? - (b) What is the total mass, in grams, of ASA in

the package? - (c) A person is permitted to take 1950 mg of ASA

per day. How many days will this package last?

- T
- H
- E
- E
- N
- D

What are they good for?

- We can multiply by one creatively to change the

units . - 13 inches is how many yards?
- 36 inches 1 yard.
- 1 yard 1 36 inches
- 13 inches x 1 yard 36 inches

What are they good for?

- We can multiply by one creatively to change the

units . - 13 inches is how many yards?
- 36 inches 1 yard.
- 1 yard 1 36 inches
- 13 inches x 1 yard 0.36 inches 36

inches

Dimensional Analysis

- A ruler is 12.0 inches long. How long is it in

cm? ( 1 inch is 2.54 cm) - in meters?
- A race is 10.0 km long. How far is this in miles?

- 1 mile 1760 yds
- 1 meter 1.094 yds)
- Pikes peak is 14,110 ft above sea level. What is

this in meters?

Example of Problem Solving

- How much heat is needed to raise the temperature

of 56.8 g of iron by 65ºC? - Identify the unknown
- Heat - calories.
- Knowns
- Mass, Change in temperature

Example of Problem Solving

- Plan a solution
- Formula Heat SH x mass x DT
- look up SH of Iron 0.106 cal/gºC
- Do the calculations
- heat 0.106 cal/gºC x 56.8 g x 65ºC
- heat 391.352 cal/gºC x g x ºC
- heat 390 cal
- Check your work.

Dimensional Analysis

- Another measuring system has different units of

measure. 6 ft 1 fathom 100 fathoms

1 cable length 10 cable lengths 1 nautical

mile 3 nautical miles 1 league - Jules Verne wrote a book 20,000 leagues under the

sea. How far is this in feet?