The Mathematics of Chemistry Stoichiometry Dimensional Analysis

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

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

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)

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

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.

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?

Give it a try! 4.Record the appropriate answer with units. 5.5 days 24 hours 60 minutes 60 seconds= ? seconds 1 1 day 1 hour 1 minute 4.Record the appropriate answer with units. Note: Students may associate the X to mean “variable” as they learned in algebra I. A distinction may need to be made to point out that in these calculations, “X” means multiply. Another way of completing the calculations is to put each equivalent in parenthesis.

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) Encourage students to share equivalent measures to add to this list and confirm their understanding of the concept. Remind them that the mole and Avogadro’s number are units that allow us to quantify atoms since they are so small.

Stoichiometry Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. Greek root words: Stoicheion meaning " element“ Metron meaning "measure"

MOLE Mole equivalents G R A M S M O L E C U L E S Avogadro’s Number Molar Mass G R A M S MOLE Ask students to turn to their table partner and come up with a conclusion to describe the relationships depicted in this slide. Have some groups share their answers verbally with the entire class. Then, summarize to affirm main ideas.

The mass in grams of 1 mole of the compound Molar Mass The mass in grams of 1 mole of the compound C10 H6 O3 10 C = 10 X 12.01g = 120.11 6 H = 6 X 1.01g = 6.06 3 O = 3 X 16g = 48 TOTAL = *175.16 grams *Remember sig figs When calculating molar mass, it is recommended to have students carry the atomic mass as written on the STAAR Chemistry Reference materials to their calculations. Since the least number of decimal places with this addition problem is 2, then the answer would be written with two as the STAAR Reference Materials inform.

The mass in grams of 1 mole of the compound calcium carbonate Molar Mass The mass in grams of 1 mole of the compound calcium carbonate CaCO3 Ca 1 X 40.08 grams = 40.08 grams C 1 X 12.01 grams = 12.01 grams O 3 X 16 grams = 48 grams TOTAL = *100.09 grams *Remember the sig figs 40.078 g + 12.0111 g + 47.997 g = 100.086 g---This sum written is 100.086 g since the least number of decimal places is 3. (STAAR Chemistry Reference Materials)

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

Stoichiometric Calculations Give it a try! Stoichiometric Calculations If you have 4.92 moles of calcium carbonate how many grams do you have? 4.92 mol CaCO3 X 100.09g CaCO3 = 1 mol CaCO3 Following the suggested plan, students start with the measurement given. The units cancel using dimensional analysis. The product is 492.42312, so the answer written using the correct significant figures is 492 g.

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. For this type of problem, steps #1 and #2 do not apply since the calculation involves the same element or compound. The balanced equation steps (#1 and #2) are part of the plan if you are taking a measurement from one element or compound and determining the answer for another reactant or product. For this calculation, we are staying with calcium carbonate for our unknown, goal, so steps #1 and #2 are not applicable. Start with step #3 for this calculation.

Chemical Equations Recipe for a chemical reaction Relative number of reactants and products Coefficients represent the relative numbers. Bridge the connection from the models to the chemical formulas. Students did study equations in Grade 8 with this SE- recognize whether a chemical equation containing coefficients is balanced or not and how that relates to the law of conservation of mass. These slides serve as a review to make the relevant connections to using the balanced equation in stoichiometry. You could have students use the molecular model sets to build this reaction and reinforce the meaning of the coefficients and visualize the process and make connections to the model and this illustration. CH4 + 2O2  CO2 + 2H2O Coefficients

Balancing Chemical Equations Atoms are conserved in a chemical reaction. Coefficients are manipulated to balance chemical reactions and create equivalent measures. Identities cannot be changed. You many want to have students build this model before they manipulate the coefficients to help students visualize the concept of matter. Point out the way the number of each colored ball is the same on both sides of the arrow to demonstrate law of conservation of matter. _C2H5OH (l) + _O2 (g)  _CO2 (g) + _H2O (g)

Balancing Chemical Equations C2H5OH + O2  CO2 + H2O Count Atoms: Carbon 2 Carbon 1 Hydrogen 6 Hydrogen 2 Oxygen 3 Oxygen 3

Balancing Chemical Equations C2H5OH (l) + O2 (g)  CO2 (g) + H2O (g) C2H5OH + 3O2  2CO2 + 3H2O

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

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 grams of lithium hydroxide are used in a small scale experimental device, how much carbon dioxide will the device process?

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. For this type of problem, steps #1 and #2 do not apply since the calculation involves the same element or compound. The balanced equation steps (#1 and #2) are part of the plan if you are taking a measurement from one element or compound and determining the answer for another reactant or product. For this calculation, we are staying with calcium carbonate for our unknown, goal, so steps #1 and #2 are not applicable. Start with step #3 for this calculation.

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)

Stoichiometric Calculations – The Plan Follow steps to dimensional analysis: 48 g LiOH X 1 mole LiOH X 1 mole CO2 X 44.01g CO2 = 1 23.95 g LiOH 2 mole LiOH 1 mole CO2 2 LiOH + CO2 (g)  Li2CO3 (g) + H2O (g)

Stoichiometric Calculations – The Answer When 48 grams of lithium hydroxide are available for use in a reaction, 44.10 grams of carbon dioxide can be processed by the reaction. *Remember the significant figures.

Set it up! 2.35 g of Barium chloride react with sodium sulfate in a precipitation reaction to make how many grams of barium sulfate? OPTIONAL SLIDE: Walk around, and listen to the conversations of the table groups to guide misconceptions and check for understandings. Students may need a little help confirming the products are barium sulfate and sodium chloride. Remind them to use the STAAR Reference Materials as a resource. Have a few groups share their problem and solution with the entire class. Discuss similarities with the approach as well as significant figures in the answer.

Formula for all Stoich. problems