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Problem Solving
 
1.  Identify and even list what is given.

Write down what is given in a problem.  Sometimes you may not use everything that is given, but write it down anyway.  A problem will not remind you, for example, that there are 60 minutes in an hour.

2.  Identify what is wanted.

Problems are usually quite clear in telling you what to calculate, but it still helps to know exactly where you are going.

3.  Identify and write the mathematical connection between the given quantity (or quantities) and the wanted quantity.

This step is the key to chemical problem solving.  We analyze the given quantity and wanted quantities with respect to the theories, principles, and relationships that we have learned and translate them into an equation or calculation step.  Most chemical problems fit into one or two classes - and sometimes a combination of both of them.

Algebraic Equation When the given quantity and the wanted quantity make up an algebraic equation - solve the equation algebraically for the wanted quantity first.  Then substitute the known values, with units, and calculate the answer.

Dimensional Analysis  If there is a proportional relationship between the given and wanted quantities, the problem is most easily solved by dimensional analysis.  The setup begins with a starting quantity, which is multiplied by one or more conversion factors that give the desired result.

4.  Calculate and write down the answer.

The real work was done in step 3.  Now it is up to you and your calculator to find the numerical result.  Remember the units.

5.  Confirm that the answer is reasonable in both size and units.

Problem Solving in Chemistry

           Chapter 4 (pp. 82 – 104)

 

Equivalent measurements (measurements of the same amount

expressed with different units in the form of an equality:      ?      =      ?   )

        365 days = 1 year

        24 hours = 1 day

        1 foot = 12 inches

        1 atm = 14.7 lbs = 101.3 kPa = 760 mm Hg = 29.92 in Hg

                           in2

        3600 s = 60 min = 1 hour

        1 km = 103 m

        1cm = 10-2 m

 

Conversion factors     

 

Conversion factors - _________________________________

Every equivalent measurement gives you ____ conversion factors!

 

Example:

 

Equivalent measurement: 365 days = 1 year

 

Conversion factors:            365 days          or               1 year      

                                         1 year                              365 days

 

The ratio of the two equivalent measurements will equal ____, or unity.

 

Example:

 

Equivalent measurement:    1 cm  =  10-2 m

 

Conversion factors:

 

Practice: Equivalent measurements and Conversion factors

Write one equivalent measurement and two conversion factors for each of the metric prefixes that you are required to know.  See notes from Scientific Measurement unit to find these.

 

1.

 

 

 

6.

2.

 

 

 

7.

3.                                

 

 

 

8.

4.

 

 

 

9.

5.

 

 

 

10.

 

Write one equivalent measurement and two conversion factors for three English unit to metric unit conversions.

 

1.

 

2.

 

3.

 

 

How to handle UNITS in calculations:

1) Only quantities with the same _______ can be added or subtracted.

2) When quantities are multiplied or divided, their ________ are

     also multiplied or divided.

 

Dimensional Analysis: numbers & units

A way to analyze and solve problems that uses the units (dimensions) of the measurements.

General form of a Dimensional Analysis setup:

 

                  Given quantity x  Conversion =  ANSWER

                                        factor(s)

 

How to express your ANSWER:

1) ___________________________________________________

2) ___________________________________________________

3) ___________________________________________________

4) ___________________________________________________

 

Try it…

Sample problem #1: If you studied 4.25 hours for your Chemistry test, how many seconds did you study?

 

Given:     4.25 hours

Find:      ? seconds

Unit path:      hours ŕ seconds

Equivalent measurement: 1 hour = 3600 seconds

Conversion factors:        1 hr             or       3600 s

                                        3600 s                    1 hr

Solution (Dimensional           

            Analysis

            Setup)

 

√Check that your answer is reasonable.

Sample problem #2:  You have 5.0 kg of sucrose (C12H22O11). 

 

a) How many grams of sucrose is this? 

Given:

Find:

Unit path:

Equivalent measurement:

Conversion factors:

 

 

Solution:

 

 

Check

 

b) How many pounds of sucrose is this?

Given:

Find:

Unit path:

Equivalent measurement:

Conversion factors:

 

 

Solution:

 

 

Check

 

 

Now combine a) and b) to find the number of lbs equal to 5.0 kg Of sucrose.

 

 

 

 

Sample problem #3: A can of regular Pepsi contains 42 grams (g) of sugar. What is this measurement equivalent to in milligrams (mg)?

 

Given:          g

Find:      ? mg

Unit path:      g ŕ mg

Equivalent measurement: 1 mg = 10-3 g

Conversion factors:        1 mg           or        10-3 g

                                        10-3 g                            1 mg

 

Solution (Dimensional                 

            Analysis                  

            Setup)

√Check that your answer is reasonable.

 

 

Sample problem #4: Normal atmospheric pressure is 14.7 lbs./in2. This force is equivalent to about three 5 lb. bags of sugar per square inch. How many mg of sugar is 14.7 lbs?

 

Given:     14.7 lbs 

Find:      ? mg

Unit path:      lbs ŕ g  ŕ mg

Equivalent measurement(s):  1 lb = 454 g       1 mg = 10-3 g

Conversion factors:        1  lb     or     454 g

                              454 g             1 lb

 

1 mg           or        10-3 g

                                        10-3 g                            1 mg

 

Solution (Dimensional                  

            Analysis                  

            Setup)

√Check that your answer is reasonable.

 

Problem Solving: Using Dimensional Analysis to solve

 

1. Every time you clean your bedroom, your grandmother makes you an apple pie.  You cleaned your room 9 times.  How many apple pies do you get?  ( Equivalent measurement: 1 clean room  = 1 apple pie )

 

 

 

 

2.  A Moravian Academy senior is applying to college and is wondering how many applications she needs to send.  She is told that with the excellent grade she received in Chemistry, she will probably be accepted to one school out of every three to which she applies.

(3 applications = 1 acceptance)  She immediately realizes that for each application she needs to write three essays ( 1 application = 3 essays) and each essay requires 2 hours of work ( 1 essay = 2 hours). Of course, writing essays is hard work.  For each hour of essay writing, she will need to expend 500 calories ( 1 hour = 500 calories) which she could derive from grandma’s apple pies  ( 1 pie = 1000 calories).  How many times does she have to clean her room in order to gain acceptance to ten colleges?  (Hint: 10 college acceptances is the Given information in this problem.)

 

 

 

 

 

 

 

 

 

 

 

Give the setups only (proper dimensional analysis form) for the following problems:  (Exceptions #3a: use algebra to find length and width; #3b: use formula for area!)

 

1.      How many seconds old are you?

 

 

    2. The perimeter of a football field is 4.80 x 102  feet.  Express this in       

        cm.  (1 in = 2.54 cm)

 

 

    3. The length of the field above is 67 ft longer than the width.

a) find the length and width in cm  

       

 

     b) find the area 

 

 

     c) convert the area to m2

 

 

 

    4. A bottle of diet coke holds 591 mL.  How many L is this?

 

 

 

    5. Convert 246 ns to s

 

 

 

6.    Convert 2.9 x 102 km to mm

 

  

 

    7.  Convert 42 grams of sucrose to ounces

Problem Solving: Use formulas (density or area) for 1-4 and

                    use dimensional analysis for 5 - 14.

 

1.  The density of a liquid is 0.821 g/mL.  What is the volume of 71.3 g of this liquid.

 

 

2.  Sodium chloride, NaCl, melts at 801 oC.  Calculate this temperature on the Fahrenheit scale.

 

 

 

3.  “Dry ice” is prepared by freezing carbon dioxide at – 56.5 oC.  Express the freezing point of carbon dioxide in Kelvin.

 

 

 

4.  A weather balloon is inflated to a volume of 2.2 x 103 L with 37.4 g of helium.  What is the density of helium in g/L.

 

 

 

5.  Convert 125.7 g to mg

 

 

 

 

6.  Convert 0.67 s to ms

 

 

 

 

7.  Convert 3.72 x 10-3  Mg to g

 

 

8.  Convert 145 cm to km

 

 

 

 

9.  Convert  100.0 m2  to  ft2

 

 

 

 

10.  Convert 100.0 m3  to  in3 ?

 

 

 

 

11.  Which is bigger 3 L or 3000.  mm3? (Hint: use DA to convert the units of one of the measurements to the units of the other.)

 

 

 

 

12.  Convert 20.6 km  to  m

                          hr        s

 

 

 

 

13.  Convert 32 lbs  to  

                        in2

 

 

 

14.  Convert 1.00  g   to  kg

                           mL       L

 

Text assignment

Chapter 4: Problem Solving in Chemistry

 

p. 95:     16  a, b, f,  18

p. 100:    28 a, b,  29

p. 103 – 4: 43 a, c, e, f,  44 a,  48,  50,  53,  61,  65,  66

 

 

 

     

 

 

 

 
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