1. Problem Solving Chemistry: it makes sense!
Chemistry  college  life is all about solving problems
Chemistry: it makes sense!
Develop a logical plan (series of steps) from your known to your unknowns

2. Problem Solving and Dimensional Analysis
Many problems in chemistry involve using relationships to convert one unit of measurement to another
Conversion factors are relationships between two units
May be exact or measured
Conversion factors generated from equivalence statements
e.g., 1 inch = 2.54 cm can give or

3. Problem Solving and Dimensional Analysis
Arrange conversion factors so given unit cancels
Arrange conversion factor so given unit is on the bottom of the conversion factor
May “string” conversion factors
So we do not need to know direct relationships, as long as we can find steps that leads to the desired units (known  unknown)

4. “Must have a Plan”
a conceptual plan is a visual outline that shows the strategic route required to solve a problem
for unit conversion, the plan focuses on units and how to convert one to another
for problems that require equations, the conceptual plan focuses on solving the equation to find an unknown value

5. Concept Plans and Conversion Factors
Convert inches into centimeters
Find relationship equivalence: 1 in = 2.54 cm
Write concept plan in cm
Change equivalence into conversion factors with starting units on the bottom

6. A Systematic Approach Sort the information from the problem
identify the given quantity and unit, the quantity and unit you want to find, any relationships implied in the problem
Design a strategy to solve the problem (roadmap)
Concept plan
sometimes may want to work backwards
each step involves a conversion factor or equation
Apply the steps in the concept plan
check that units cancel properly
multiply terms across the top and divide by each bottom term
Check the answer
double check the set-up to ensure the unit at the end is the one you wished to find
check to see that the size of the number is reasonable
since centimeters are smaller than inches, converting inches to centimeters should result in a larger number

7. Example: Convert 1.76 yd. to centimeters
Sort information
Given:
Find:
1.76 yd
length, cm
Strategize
Concept Plan:
Relationship
1.094 yd = 1 m
1 m = 100 cm yd m cm
Follow the concept plan to solve the problem
Solution:
Sig. figs. and round
Round:
cm = 161 cm
Check
Check:
Units & magnitude are correct

8. Practice – Convert 30.0 mL to quarts (1 L = 1.057 qt)
(Hint: 1000 mL makes 1 L)

9. Units & magnitude are correct
Convert 30.0 mL to quarts
Sort information
Given:
Find:
30.0 mL
volume, qts
Strategize
Concept Plan:
Relationship:
1 L = qt
1 L = 1000 mL mL L qt
Follow the plan to solve the problem
Solution:
Sig. figs. and round
Round:
qt = qt
Check
Check:
Units & magnitude are correct

10. Problem Solving with Equations
When solving a problem using an equation, you are usually given all the variables except the one you want to find
Solve the equation for the variable you wish to find, then substitute and compute

11. Using Density in Calculations
Concept Plans:
m, V D
m, D V
V, D m

12. Density Calculations
We can use density as a conversion factor between mass and volume!!
density of H2O = 1.0 g/mL \ 1.0 g H2O = 1 mL H2O
density of Pb = 11.3 g/cm3 \ 11.3 g Pb = 1 cm3 Pb
How much does 4.0 cm3 of lead weigh? =
4.0 cm3 Pb
11.3 g Pb
1 cm3 Pb
45 g Pb x

13. Question: The mass of fuel in a jet must be calculated before each flight to ensure that the jet is not too heavy. A 747 jet is fueled with 173,231 L of jet fuel. If the density of the fuel is g/mL, what is the mass of the fuel in kilograms?

14. Units & magnitude are correct
Example: What is the mass in kg of 173,231 L of jet fuel whose density is g/mL?
Sort information
Given:
Find:
173,231 L
density = g/mL
mass, kg
Strategize
Concept Plan:
Relationship
1 mL = g, 1 mL = 10-3 L
1 kg = 1000 g L mL g kg
Follow the concept plan to solve the problem
Solution:
Sig. figs. and round
Round:
1.3 x 105 kg
Check
Check:
Units & magnitude are correct

15. Counting Atoms by Moles
If we can find the mass of a particular number of atoms, we can use this information to convert the mass of an element sample into the number of atoms in the sample.
The number of atoms we use is x 1023 and we call this a mole
1 mole = x 1023 entities
Like 1 dozen = 12 entities
Avogadro’s Number

16. Example: Calculate the number of atoms in 2.45 mol of copper
Given:
Find:
2.45 mol Cu
atoms Cu
Concept Plan:
1 mol = x 1023 atoms
mol Cu
atoms Cu
Solution:
Check:
since the number is slightly greater than twice Avogadro’s number, it make sense

17. Relationship Between Moles and Mass
The mass of one mole of atoms is called the molar mass
The molar mass of an element, in grams, is numerically equal to the element’s atomic mass, in amu
The lighter the atom, the less a mole weighs
The lighter the atom, the more atoms there are in 1 g

18. Mole and Mass Relationships
sulfur
32.06 g
1 mole
carbon
12.01 g

19. Example: Calculate the # moles of carbon in 0.0265 g of pencil “lead”
Given:
Find:
g C
mol C
Concept Plan:
1 mol C = g
g C
mol C
Solution:
Check:
since the given amount is much less than 1 mol C, the number makes sense

20. Example: How many copper atoms are in a copper penny weighing 3.10 g?
Given:
Find:
3.10 g Cu
atoms Cu
Concept Plan:
1 mol Cu = g,
1 mol = x 1023
g Cu
mol Cu
atoms Cu
Solution:
Check:
since the given amount is much less than 1 mol Cu, the number makes sense