# Chapter 3 Calculation with Chemical Formulas and Equations

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1 Chapter 3 Calculation with Chemical Formulas and Equations Practical Applications of Chemistry Determining chemical formula of a substance Predicting the amount of substances consumed during a reaction Predicting the amount of substances produced during a reaction Polymer chemist is preparing a new plastic and want to know how much material will a particular reaction yield? Chemical engineer and is working on a rocket engine thrust. He needs to calculate the amount of exhaust certain gas fuel will produce. An environmental chemist examining the quality of air pollutants. She is examining what a sample of coal will release into the air when burned. I) Molecular Weight, Moles and Molar Mass A) Molecular weight/formula weight The term molecular weight is used with covalent molecules, whereas formula weight is used with ionic compounds. Both terms have the same units and are calculated in the same way. Sum of the atomic weights of all atoms in the compound units of amu (atomic mass units) abbreviated MW - molecular weight FW - formula weight Example Calculate the MW or FW for the following substances H 2 H 2 x amu = amu 1 x amu = amu amu

2 C 12 H C 12 x amu = amu H 22 x amu = amu 11 x amu = amu amu NaCl Na 1 x amu = amu Cl 1 x amu = amu amu B) Moles Mole is a chemist counting unit used to count atoms, molecules, or compounds by weighting abbreviation: mol 1 mol objects = 6.02 x objects Avogadro's Number similar to 1 doz. eggs = 12 eggs 1 mole C atoms = 6.02 x C atoms 1 mole H 2 molecules = 6.02 x H 2 molecules 1 mol NaCl = 6.02 x NaCl formula units Calculation: If 1 mole CaCl 2 = 6.02 x CaCl 2 formula units, How many Cl ions are in 1 mole of CaCl 2? 1 mole of CaCl 2 consists of 1 mole Ca 2+ and 2 mole Cl. If 1 mole of Cl is 6.02 x Cl ions, then 1 mole of CaCl 2 contains (2 x 6.02 x ) Cl ions or 1.20 x Cl ions. C) Molar Mass What is the mass of 1 mole of a substance? Molar mass mass of 1 mole of a substance numerically equal to the MW or FW units of g/mol my abbreviation for molar mass is M m

3 example: substance MW or FW molar mass Fe amu g/mol H amu g/mol C 12 H amu g/mol NaCl amu g/mol Calculations: Molar mass is useful in converting between units of grams and moles example: How many grams of Ag are in mol Ag? Ag: M m = g/mol mol g 1 mol = 80.9 g Ag How many mole of NaCl are in g NaCl? NaCl: M m = g/mol g 1 mol g = mol NaCl How many molecules of H 2 are in 22.0 g H 2? H 2 : M m = g/mol 22.0 g H 2 1 mol H molecules 18.0 g H 2 1 mol H 2 = H 2 molecules

4 II) Stoichiometry A) Molar interpretation of chemical equation The coefficients within a chemical reaction indicate the number of molecules, formula units or moles of substance in needed or produced. for example, observe the coefficients in the following combustion reaction. C 3 H C H 2 What do the coefficients represent in a chemical reaction? Molecular interpretation: 1 molecule C 3 H molecules 2 3 molecules C molecules H 2 If each of the coefficients are multiplied by avogadro's number, the coefficients now represent the number of moles of each substance 1 (6.02 x ) C 3 H (6.02 x ) 2 3 (6.02 x ) C (6.02 x ) H 2 Molar interpretation: 1 mol C 3 H mol 2 3 mol C mol H 2 B) Amounts of substances in a chemical reaction Mole ratios of reactants and products can be written from a balance chemical reaction. These mole ratios are conversion factors, which converts from moles of one substance to moles of another substance. Using the following chemical reaction, several conversion factors (mole ratios) can be written. C 3 H C H 2 1 mole C 3 H 8 reacts with 5 moles 2 : 1 mol C 3 H 8 5 mol 2 or 5 mol 2 1 mol C 3 H 8 5 moles 2 produces 3 moles C 2 : 5 mol 2 3 mol C 2 or 3 mol C 2 5 mol 2 1 mol C 3 H 8 3 mol C 2 or 3 mol C 2 4 mol H 2 or 4 mol H 2 1 mol C 3 H 8 or etc

5 Calculations: Converting moles of one substance to moles of another substance can be performed using a balanced chemical reaction. mole A mole B, where A and B represent different substances. 2 H H 2 How many moles of H 2 are produced when 3.5 mol H 2 react with 2? 2 mol H 3.5 mol H mol H 2 = 3.5 mol H 2 Determine the moles of H 2 are needed to react with 4.00 mol 2? 2 mol H 4.00 mol mol 2 = 8.00 mol H 2 In lab, the common way to measure substance for a reaction is to measure its mass. The mass of a substance can easily be converted to moles using the molar mass of the substance. a b c g A mol A mol B g B use molar mass of substance A use mole ratios obtained from chem. rxn. use molar mass of substance B 2 H H 2 How many grams or 2 are needed to yield 46 g H 2? 46 g H 2 1 mol H 2 18 g H 2 1 mol 2 2 mol H 2 a b c g 2 1 mol 2 = 41 g 2

6 example: Thermite is a mixture of iron(iii) oxide and aluminum powders that were once used to weld railroad tracks. It undergoes a spectacular reaction to yield solid aluminum oxide and molten iron. Fe Al Al Fe How many mole Al 2 3 are produced from 12.0 mol Al? 12.0 mol Al 1 mol Al mol Al = 6.00 mol Al 2 3 How many grams of iron form when 135 g Al react? 135 g Al 1 mol Al 2 mol Fe 27.0 g Al 2 mol Al 55.8 g Fe 1 mol Fe = 279 g Fe How many atoms of Al react for every 1.00 g Al 2 3 that forms? 1.00 g Al mol Al mol Al 102 g Al mol Al Al atoms 1 mol Al = Al atoms C) Limiting reactants (limiting reagents) 1) The reactant which is used up entirely during the reaction is the limiting reagent 2) The reactant which is left over after the limiting reagent is used up is the excess reagent To determine which reagent or reactant is limiting, calculate the amount of product that can be formed with each reactant. The reactant that produces the least amount of product is the limiting reagent. The other reactants are considered the excess reagents. 2 scoops of ice cream + 1 cherry + 50 ml syrup 1 sundae How many sundaes can be if 50 scoops of ice cream, 30 cherries and 1 L of syrup are available? 50 scoops 1 sundae 2 scoops = 25 sundaes

7 30 cherries 1 sundae = 30 sundaes 1 cherry 1000 ml syrup 1 sundae 50 ml syrup = 20 sundaes The syrup will run out first before the ice cream or cherries, so it is the limiting reagent, while the ice cream and cherries are the reagents in excess. A limiting reagent problem in chemistry usually involves determining the amount of a product that can be formed given the various amounts of reactants mixed together in the reaction. For example: a) Calculate the mass of iodic acid (HI 3 ) that forms when 735 g iodine trichloride reacts with 97.7 g water. 2 ICl H 2 ICl + HI HCl 1) Calculate the number of moles of HI 3 produced with each one of the reactants. 735 g ICl 3 1 mol ICl 3 1 mol HI g ICl 3 2 mol ICl 3 = 1.57 mol HI g H 2 1 mol H g H 2 1 mol HI 3 3 mol H 2 = 1.81 mol HI 3 2) Because ICl 3 produces the lesser amount of product, it is the limiting reagent. Use 1.57 mol HI 3 to calculate the mass g HI mol HI 3 1 mol HI 3 = 276 g HI 3 b) Now calculate the mass of the excess reagent remaining after the reaction in question 1 is completed. 1) Using the amount of product produced by the limiting reagent, back calculate the mass of the excess reagent used in the reaction. 3 mol H 1.57 g HI mol HI g H 2 1 mol H 2 = 84.8 g H 2 used 2) To find the amount of excess reagent remaining, subtract the amount used in the reaction from the given amount at the beginning of the reaction. starting mass mass used = mass remaining 97.7 g 84.8 g = 12.9 g H 2 remaining

8 3. How many grams of solid aluminum sulfide can be prepared by the reaction of 10.0 g aluminum and 15.0 g sulfur? 2 Al + 3 S Al 2 S g Al 1 mol Al 1 mol Al 2 S g Al 2 mol Al 15.0 g S 1 mol S 32.1 g S 1 mol Al 2 S 3 3 mol S = mol Al 2S 3 = mol Al 2S 3 Sulfur is the limiting reagent g Al 2 S g Al 2 S 3 1 mol Al 2 S 3 = 23.4 g Al 2S 3 Limiting 4. How much of the nonlimiting reactant is in excess in question 3? mol Al 2 S 2 mol Al 27.0 g Al 3 = 8.42 g Al used 1 mol Al 2 S 3 1 mol Al starting mass mass used = mass remaining 10.0 g 8.42 g = 1.6 g Al remaining D) Yields of a reaction Two types of yields 1) actual yield: quantity of product obtained from the reaction 2) theoretical yield: amount of product predicted when all the limiting reagent is used up. % yield = actual yield theoretical yield Ca + V Ca + 2 V In one process 1.54 x 10 3 g of V 2 5 reacted with 1.96 x 10 3 g Ca a) Calculate the theoretical yield of vanadium. In order to calculate the theoretical yield, the limiting reagent must be determined first mol V g V g V mol V = 16.9 mol V lim iting 1 mol V g Ca 1 mol Ca g Ca 2 mol V 5 mol Ca = 19.6 mol V

9 The limiting reagent is V mol V g 1 mol V = 863 g V The theoretical yield of vanadium is 863 g. b) Calculate the percent yield of the above reaction if 803 g of V are obtained. actual yield 803 g 100 = 100 = 93.0% theoretical yield 863 g III) Molarity and Dilutions A) Molarity Molarity is a concentration unit which gives the moles of solute in a liter of solution. Molarity = mol solute L solution What is the molarity of the resulting solution when g NaCl is placed into a 100 ml volumetric flask? First convert the mass of the solute into moles g NaCl 1 mol NaCl = mol NaCl g NaCl Next calculate the molarity. mol solute = mol NaCl = 0.915mol NaCl = M NaCl L solution L solution L Molarity can be used as a conversion factor in solving problems. example: How many grams of NaCl are in L of a M NaCl solution? The given molarity is M NaCl = mol NaCl 1 L solution L mol NaCl 1 L = mol NaCl g NaCl = 18.3 g NaCl 1 mol NaCl

10 B) Dilutions What happens during a dilution? solvent is added volume of the solution increases concentration of the solution decreases moles of the solute remains the same Because the moles of solute remains constant during a dilution, a relationship between the old and new concentrations can be derived. M = mol solute L solution rearrange this definition to solve for moles of solute mol solute = M x (L solution) mol solute = M x V let V = L solution The product the molarity and the volume gives the moles of solute in the solution. mol solute = M 1 x V 1 mol solute = M 2 x V 2 moles of solute at the initial molarity and volume moles of solute at the final molarity and volume since the moles of solute remains constant during the dilution M 1 x V 1 = M 2 x V 2 This relationship determines either the new volume or molarity of the diluted solution or the volume or molarity of the original solution. A stock solution of NaCl is 6.00 M. How much of this stock solution is needed to prepare 1.00 L of physiological saline solution, which is M NaCl? M 1 V 1 = M 2 V 2 V 1 = M 2V 2 (0.154 M)(1.00 L) = = L = 25.7 ml M 1 (6.00 M)

11 IV) Empirical Formulas A) Mass percent from a chemical formula The mass percentage of each element in a compound is the percent composition mass % element = mass of element in compound mass of compound 100 Find the mass percentage of each element in ascorbic acid HC 6 H 7 6. The molar mass of ascorbic acid is g/mol % H = % C = % = (8)(1.01 g/mol) g/mol (6)(12.0 g/mol) g/mol (6)(16.0 g/mol) g/mol 100 = 4.59 % 100 = 40.9 % 100 = 54.5 % Perform a check: The mass percentages of each element should sum to 100 % 4.59 % % % = % B) Determining the empirical formula from the composition Empirical formula is the smallest whole-number ratio of moles of each element in a compound. Molecular formula shows all atoms in the compound. name empirical formula molecular formula hydrogen peroxide H H 2 2 Note: compounds can have the same empirical formulas but different molecular formulas.

12 Method for determining the empirical formula from the % composition (finding the subscripts) 1) Assume g of sample (unless given) 2) convert grams of each element into moles 3) the number of moles become the subscript in the chemical formula 4) divide subscripts by smallest (goal: whole number subscripts) 5) If any subscript is not an integer, then multiply all subscript by the smallest whole number to convert all subscripts into integers. sodium pyrophosphate is used in detergent preps. The mass percentages of the elements in this compound are Na 34.6 %, P 23.3 %, 42.1 %. What is the empirical formula of sodium pyrophosphate? 1) convert % composition into grams by assuming g of sample Na: 100 g (0.346) = 34.6 g Na P: 100 g (0.233) = 23.3 g P : 100 g (0.421) = 42.1 g 2) convert grams to moles Na: 34.6 g Na 1 mol Na 23.0 g Na = 1.5 mol Na P: 23.3 g P 1 mol P 31.0 g P = 0.75 mol P : 42.1 g 1 mol 16.0 g = 2.6 mol 3) moles become subscripts Na 1.5 P ) divide by smallest subscript Na 1.5/0.75 P 0.75/ /0.75 = Na 2 P ) multiple by smallest whole number to convert all subscripts into integers ( Na 2 P ) = Na 4 P 2 7 Na 4 P 2 7 is the empirical formula of sodium pyrophosphate

13 C) Determining the molecular formula from the empirical formula To find the molecular formula to pieces of information is needed. 1) the molecular weight or molar mass of the compound 2) the empirical weight of the compound which is the sum of the atomic weights in the empirical formula n = molecular weight empirical weight n is a whole number multiplier which converts the empirical formula into the molecular formula. n multiplies the subscripts in the empirical formula Lactic acid forms in the muscles and is responsible for muscle soreness. Elemental analysis shows that lactic acid contains 40.0 % C, 6.71 % H, and 53.3 %. The molar mass of this compound was found to be amu. a) Determine the empirical formula of lactic acid. b) Determine the molecular formula of lactic acid. a) assume 100 g of sample C: 40.0 g C 1 mol C 12.0 g C = 3.33 mol C H: 6.71 g H C 3.33/3.33 H 6.71/ mol H 1.0 g H = 6.71 mol H 3.33/3.33 : 53.3 g C 1 H 2 1 empirical formula 1 mol 16.0 g = 3.33 mol empirical wt. = 12.0 amu amu amu = 30.0 amu b) n = amu (C 1 H 2 1 ) 3 = C 3 H 6 3 molecular formula 30.0 amu = 3

14 V) Quantitative analysis A) Gravimetric analysis Gravimetric analysis is a type of quantitative analysis in which the amount of a species in a material is determined by converting the species to a product that can be isolated completely and weighed. Precipitation reactions are used often in gravimetric analyses. A soluble silver compound was analyzed for the percentage of silver by adding sodium chloride solution to precipitate the silver ion as silver chloride. If g of silver compound gave g of AgCl, what is the mass % of Ag in the compound? From the chemical formula, 1 mole of AgCl consists of 1 mol of Ag + and 1 mol Cl g AgCl 1 mol AgCl 1 mol Ag g Ag g AgCl 1 mol AgCl 1 mol Ag + = g Ag + mass % = mass of element g 100 = 100 = % Ag mass of compound g B) Volumetric analysis Volumetric analysis is a method of analysis based on titration. Titration is a procedure for determining the amount of substance A by adding a carefully measured volume of a solution with known concentration of B until the reaction of A and B is just complete. Zinc sulfide reacts with hydrochloric acid to produce dihydrogen sulfide gas ZnS (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 S (g) How many ml of M HCl are required to react with g ZnS? g ZnS 1 mol ZnS 97.5 g ZnS 2 mol HCl 1 mol ZnS 1 L HCl mol HCl 103 ml 1 L = 157 ml HCl sol n recall that molarity can be used as a conversion factor to convert mole of a substance into volume.

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