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
in^{2}
3600 s = 60 min = 1 hour
1 km = 10^{3 }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.
Write
one equivalent measurement and two conversion factors for three English
unit to metric unit conversions.
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 (C_{12}H_{22}O_{11)}.
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: 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 10^{2}
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 m^{2}
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 10^{2} km to mm
7. Convert 42 grams of
sucrose to ounces Problem Solving: Use
formulas (density or area) for 14 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 ^{o}C.
Calculate this temperature on the Fahrenheit scale. 3.
“Dry ice” is prepared by freezing carbon dioxide at – 56.5 ^{o}C.
Express the freezing point of carbon dioxide in Kelvin. 4.
A weather balloon is inflated to a volume of 2.2 x 10^{3} 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 m^{2} to ft^{2 } ^{ } ^{ } ^{ } 10.
Convert 100.0 m^{3} to
in^{3 }? 11.
Which is bigger 3 L or 3000. mm^{3}?
(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 in^{2 } ^{ } ^{ } ^{ } 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 –
^{ }


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