The Mathematics of Chemistry

1. The Mathematics of Chemistry Stoichiometry Dimensional Analysis

2. Stoichiometry • Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. • Greek root words: • Stoicheionmeaning " element“ • Metronmeaning "measure"

3. What is Dimensional Analysis? • Using the units, or dimensions, of measurements to express and calculate chemical quantities

4. What is the relationship? • Dimensional analysis is a strategy used for doing stoichiometric calculations.

5. What are some common equivalent measurements? • 1 inch =______centimeter(s) • 1 week = ______ day(s) • 60 seconds = ______minute(s) • 1 lb =______ ounce(s) • 1 cup = _____ fluid ounces • 1 tablespoon = _____ teaspoon(s) • 4 quarts = _____ gallon(s)

6. Common Equivalent Measurements • 1 mile = _____ feet • 1 kg = _____ 2.2 lb • 1 ft = ____ inches • 365 days = _____ year(s) • 1 ton = _____ pounds

7. Dimensional Analysis –The Plan • What is given? Start your calculation with this quantity with units. • What is your goal? What you are solving for is your goal and should be on top of the last step of the problem. • Set up a series of equivalent measures that cancels out all units except the goal units. 4. Solve the problem, and remember to mark through the cancelled units. 5. Record the appropriate answer with units.

8. Give it a try!How many seconds are there in 5.5 days? Follow the steps: • What is given? 5.5 days • What is your goal, and what are the units? Determine # of seconds in 5.5 days • Set up a series of equivalent measure that cancels out all units except the goal units. Get started: **What fractions “equal to 1” help transition from days to seconds?

9. Give it a try! 5.5 days X 24 hours X 60 minutes X 60 seconds= ? seconds 1 1 day 1 hour 1 minute 1 4.Record the appropriate answer with units.

10. What are some common equivalent measurements in chemistry? • 1,000 g = _____kg • 100 cm = ______ m • 1 m = _____dm • 1 L = _____ml • 1 mole = _______ particles/atoms • molar mass = _____ mole(s) • Avogadro’s number = _____ mole(s)

11. Mole equivalents P A R T I C L E S G R A M S Avogadro’s Number Molar Mass MOLE

12. Molar Mass The mass in grams of 1 mole of the compound C10 H6 O3 10 C = 10 X 12.011g = 120.11 6 H = 6 X 1.008g = 6.048 3 O = 3 X 15.999g = 48.997 TOTAL = *175.16 grams *Remember the significant figures rules.

13. Molar Mass The mass in grams of 1 mole of the compound calcium carbonate CaCO3 Ca 1 X 40.078 grams = 40.078 grams C 1 X 12.011 grams = 12.011 grams O 3 X 15.999 grams = 47.997 grams TOTAL = *100.086 grams *Remember the significant figures rules.

14. Give it a try! • How many grams are in 4.92 moles of calcium carbonate?

15. Stoichiometric Calculations –The Plan • Write the chemical equation. • Balance the chemical equation. • *Follow steps to dimensional analysis: • Start with what is given. • Set up a series of equivalent measures. • End with your goal. • Solve the problem by cancelling units. • Record the appropriate answer with units.

16. Give it a try! Stoichiometric Calculations 4.92 mol CaCO3X 100.086g CaCO3 = 1 mol CaCO3 492.42312 g = 492 g CaCO3

17. Chemical Equations • Recipe for a chemical reaction • Relative number of reactants and products • Coefficients represent the relative numbers. CH4 + 2O2 CO2 + 2H2O

18. Law of Conservation of Matter: BalancingChemical Equations • Atoms are conserved in a chemical reaction. • Coefficients are manipulated to balance chemical reactions and create equivalent measures. • Identities cannot be changed. _C2H5OH (l) + _O2 (g)  _CO2 (g) + _H2O (g)

19. BalancingChemical Equations C2H5OH (l) + O2 (g)  CO2 (g) + H2O (g) Count Atoms: Carbon 2 Carbon 1 Hydrogen 6 Hydrogen 2 Oxygen 3 Oxygen 3

20. BalancingChemical Equations C2H5OH (l) + O2 (g)  CO2 (g) + H2O (g) C2H5OH (l) + 3O2 (g)  2CO2 (g) + 3H2O (g)

21. Chemical Equations as Equivalents • Coefficients from a balanced equation represent the number of theoretical mole equivalents and can be used in stoichiometric calculations.

22. Stoichiometric Calculations – The Plan • Write the Chemical Equation. • Balance the Chemical Equation. • Follow steps to Dimensional Analysis: • Start with what is given. • Set up a series of equivalent measures. • End with your goal. • Solve the problem by cancelling units. • Record the appropriate answer with units.

23. Stoichiometric Calculations – The Problem Lithium hydroxide is used in an outer space environment to remove excess exhaled carbon dioxide from the living environment. The products of the reaction are lithium carbonate and water. If 48.0 grams of lithium hydroxide are used in a small scale experimental device, how much carbon dioxide will the device process? • The Plan: • Write the chemical equation. • Balance the chemical equation. • Follow steps to dimensional analysis: • Start with what is given. • Set up a series of equivalent measures. • End with your goal. • Solve the problem by cancelling units. • Record the appropriate answer with units. • * Remember Significant Figures.

24. Stoichiometric Calculations – The Plan 1. Write the chemical equation. LiOH + CO2 (g)  Li2CO3 + H2O (g) 2. Balance the chemical equation. 2 LiOH + CO2 (g)  Li2CO3 + H2O (g)

25. Stoichiometric Calculations –The Plan • Follow steps to dimensional analysis: 48.0 g LiOH X 1 mole LiOH X1 mole CO2 X 44.009g CO2 = 1 23.948 g LiOH 2 mole LiOH 1 mole CO2 2 LiOH + CO2 (g)  Li2CO3 (g) + H2O (g)

26. Stoichiometric Calculations – The Answer When 48.0 grams of lithium hydroxide are available for use in a reaction, 44.1 grams of carbon dioxide can be processed by the reaction. *Remember the significant figures.

27. Partner Share Write your own stoichiometry question for this reaction, and switch with your table partner: Barium chloride reacts with sodium sulfate in a precipitation reaction to make barium sulfate.