Chapter 1. Matter, Measurement, and Problem Solving

1. Chapter 1. Matter, Measurement, and Problem Solving CHE 123: General Chemistry I Dr. Jerome K. Williams, Ph.D. Saint Leo University

2. SolvingChemicalProblems Equations & Dimensional Analysis Tro: Chemistry: A Molecular Approach, 2/e

3. Units Always write every number with its associated unit Always include units in your calculations you can do the same kind of operations on units as you can on numbers cm × cm = cm2 cm + cm = cm cm ÷ cm = 1 using units as a guide to problem solving is called dimensional analysis Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 3

4. 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 can be generated from equivalence statements e.g., 1 inch = 2.54 cm can give or Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 4

5. Problem Solving and Dimensional Analysis Arrange conversion factors so the starting unit cancels arrange conversion factors so the starting unit is on the bottom of the first conversion factor May string conversion factors so you do not need to know every relationship, as long as you can find something else the starting and desired units are related to Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 5

6. Conceptual Plan A conceptual plan is a visual outline that shows the strategic route required to solve a problem For unit conversion, the conceptual 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 Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 6

7. Conceptual Plans and Conversion Factors Convert inches into centimeters 1. Find relationship equivalence: 1 in. = 2.54 cm 2. Write a conceptual plan in. cm 3. Change equivalence into conversion factors with starting units on the bottom Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 7

8. Systematic Approach to Problem Solving 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 devise a conceptual plan sometimes may want to work backward each step involves a conversion factor or equation Apply the steps in the conceptual plan to solve the problem 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 because centimeters are smaller than inches, converting inches to centimeters should result in a larger number Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 8

9. Example 1.7: Convert 1.76 yd to centimeters yd m cm • Sort the information Given: Find: 1.76 yd length, cm • Strategize Conceptual Plan: Relationships: 1 m = 1.094 yd 1 m = 100 cm • Follow the conceptual plan to solve the problem Solution: • Sig. figs. and round Round: 160.8775 cm = 161 cm • Check Check: units are correct; number makes sense: cm << yd Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 9

10. Practice – Convert 30.0 mL to quarts(1 mL = 0.001 L; 1 L = 1.057 qt) Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 10

11. Practice – Convert 30.0 mL to quarts mL L qt • Sort information Given: Find: 30.0 mL volume, qts • Strategize Conceptual Plan: Relationships: 1 L = 1.057 qt 0.001 L = 1 mL • Follow the conceptual plan to solve the problem Solution: • Sig. figs. and round Round: 0.03171 qt = 0.0317 qt • Check Check: units are correct; and number makes sense: mL << qt Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 11

12. Conceptual Plans for Units Raised to Powers Convert cubic inches into cubic centimeters 1. Find relationship equivalence: 1 in. = 2.54 cm 2. Write concept plan in.3 cm3 3. Change equivalence into conversion factors with given unit on the bottom Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 12

13. Example 1.9: Convert 5.70 L to cubic inches L mL cm3 in3 • Sort information Given: Find: 5.70 L volume, in.3 • Strategize Conceptual Plan: Relationships: 1 mL = 1 cm3, 1 mL = 10−3 L 1 cm = 2.54 in. • Follow the conceptual plan to solve the problem Solution: • Sig. figs. and round Round: 347.835 in.3 = 348 in.3 • Check Check: units are correct; number makes sense: in.3 << L Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 13

14. Practice 1.9 – How many cubic centimeters are there in 2.11 yd3? Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 14

15. Practice 1.9 – Convert 2.11 yd3 to cubic centimeters yd3 in3 cm3 Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 15

16. Density as a Conversion Factor 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? Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 16

17. Example 1.10: What is the mass in kg of 173,231 L of jet fuel whose density is 0.768 g/mL? L mL g kg Given: Find: • Sort information 173,231 L density = 0.768 g/mL mass, kg Conceptual Plan: Relationships: • Strategize 1 mL = 0.768 g, 1 mL = 10−3 L 1 kg = 1000 g Solution: • Follow the conceptual plan to solve the problem • Sig. figs. and round 1.33041 x 105 = 1.33 x 105 kg Round: Check: • Check units and number make sense Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 17

18. Practice Problems How much does 3.0 x 102 mL of ether weigh? (d = 0.71 g/mL) Answer: 2.1 x 102 g = 210 g What volume does 100.0 g of marble occupy? (d = 4.0 g/cm3) Answer: 25 cm3 Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 18

19. Problem Solving with Equations When solving a problem involves using an equation, the concept plan involves being 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 Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 19

20. Example 1.12: Find the density of a metal cylinder with mass 8.3 g, length 1.94 cm, and radius 0.55 cm l, r V m, V d Sort information Given: Find: m = 8.3 g l = 1.94 cm, r = 0.55 cm density, g/cm3 Strategize Conceptual Plan: Relationships: V = πr2 l d = m/V Follow the conceptual plan to solve the problem Sig. figs. and round Solution: V = π (0.55 cm)2 (1.94 cm) V = 1.8436 cm3 Check Check: units and number make sense Tro: Chemistry: A Molecular Approach, 2/e

21. Practice – What is the mass in kilograms of a cube of lead that measures 0.12 m on each side?(dPb = 11.3 g/cm3) Tro: Chemistry: A Molecular Approach Tro: Chemistry: A Molecular Approach, 2/e 21

22. Practice – What is the mass in kilograms of a cube of lead that measures 0.12 m on each side? l V m3 cm3 g kg Sort information Given: Find: l = 0.12 m, d = 11.3 g/cm3 mass, kg Strategize Conceptual Plan: Relationships: V = l3, 11.3 g = 1 cm3, 1 cm = 10-2 m, 1 kg = 103 g Follow the conceptual plan to solve the problem Sig. figs. and round Solution: V = (0.12 m)3 V = 1.728 x 10−3 m3 Check units and number make sense Check: Tro: Chemistry: A Molecular Approach, 2/e