Problem Solving

1. Problem Solving • 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 http://www.geneseo.edu/~mcknight/

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. yd m cm 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 • Follow the concept plan to solve the problem Solution: 160.8775 cm = 161 cm • Sig. figs. and round Round: • 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. mL L qt Convert 30.0 mL to quarts • Sort information Given: Find: 30.0 mL volume, qts • Strategize Concept Plan: Relationship: 1 L = 1.057 qt 1 L = 1000 mL • Follow the plan to solve the problem Solution: • Sig. figs. and round Round: 0.03171 qt = 0.0317 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. 11.3 g Pb 1 cm3 Pb x = 4.0 cm3 Pb 45 g Pb 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?

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 0.738 g/mL, what is the mass of the fuel in kilograms?

14. L mL g kg Example: What is the mass in kg of 173,231 L of jet fuel whose density is 0.738 g/mL? • Sort information Given: Find: 173,231 L density = 0.738 g/mL mass, kg • Strategize Concept Plan: Relationship 1 mL = 0.738 g, 1 mL = 10-3 L 1 kg = 1000 g • 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 is6.022 x 1023 and we call this a mole • 1 mole = 6.022 x 1023 entities • Like 1 dozen = 12 entities Avogadro’s Number

16. mol Cu atoms Cu Example: Calculate the number of atoms in 2.45 mol of copper Given: Find: 2.45 mol Cu atoms Cu Concept Plan: 1 mol = 6.022 x 1023 atoms 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. 1 mole sulfur 32.06 g 1 mole carbon 12.01 g Mole and Mass Relationships

19. g C mol C Example: Calculate the # moles of carbon in 0.0265 g of pencil “lead” Given: Find: 0.0265 g C mol C Concept Plan: 1 mol C = 12.01 g Solution: Check: since the given amount is much less than 1 mol C, the number makes sense

20. g Cu mol Cu atoms Cu 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 = 63.55 g, 1 mol = 6.022 x 1023 Solution: Check: since the given amount is much less than 1 mol Cu, the number makes sense