Unit 4: Stoichiometry The last one!!! 1 Reaction Assumptions • Reaction (rxn) assumptions: – Rxns are spontaneous; when reactants are mixed they will react to form products – Rxns are fast – Rxns are quantitative; they go to completion – Rxns are stoichiometric; they will react in simple whole number ratios of chemical amounts expressed in the balanced chemical equation, regardless of conditions Stoichiometry Stoichiometry is the process of using a chemical equation to calculate the quantity of reactants and products involved in a reaction. The balanced equation for a chemical reaction describes the stoichiometry of the reaction. • Balanced equations have to be used in chemical reactions in order to have correct stoichiometric calculations • Ex: C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) 1mol of C3H8 reacts with 5mol of O2 to produce 3mol CO2 and 4mol H2O • Balanced equations allow us to set up the mole ratio between the substance we have and the one we want. 3 Mole Ratio The mole ratio is a conversion factor based on the balanced equation that allows us to find amounts of different substances by using the substance we have. • The mole ratio is always the same between two substances in a chemical equation no matter the amounts involved. • Ex: C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) the mole ratio between C3H8 and CO2 is always going to be 1:3; or the mole ratio between CO2 and O2 will always be 3:5 4 Mole-to-Mole Calculations Using Stoichiometry They give you moles, they ask for moles. Ex: What number of moles of O2 will be produced by the decomposition of 5.8 mol of water? Step 1: Write and balance the chemical equation Step 2: Set up the mole ratio between what you have (water) and what you need (oxygen) Step 3: Use the mole ratio as a conversion factor to answer the question 5 Mass-to-Mole Calculations Using Stoichiometry They give you mass, they ask for moles. Ex: Aluminum metal reacts vigorously with solid iodine to produce solid aluminum iodide. What mass of I2(s) should we weigh out to react exactly with 35.0g of aluminum? Step 1: Write and balance the chemical equation Step 2: Set up the mole ratio between what you have (aluminum) and what you need (iodine) Step 3: Use the Factor-Label Method (aka Chain Method or Unit-Factor Method) to convert the mass to moles and with the mole ratio to answer the question 7 Mass-to-Mole Calculations Using Stoichiometry • The procedure we just did: 2Al(s) + 35.0 g Al 3I2(s) 495 g I2 1 3 Use molar mass of Al (26.98 g/mol) Use molar mass of I2 (253.8 g/mol) 1 3 mol Al 2AlI3(s) Use mole ratio 2 3 𝑚𝑜𝑙 𝐼2 2 𝑚𝑜𝑙 𝐴𝑙 2 mol I2 9 Mass-to-Mass Calculations (Gravimetric Stoichiometry) • Stoichiometry of a chemical reaction is related to the amount of reactants used and products formed • Gravimetric stoichiometry relates specifically to masses of reactants or products. • We will be using the factor-label method in this course – Referred to as ‘chained method’ in textbook • It’s the standard in science, it’s efficient. Mass-to-Mass Calculations Using Stoichiometry They give you mass, they ask for mass (gravimetric stoichiometry) Step 1: Write and balance the chemical reaction Step 2: Convert masses to moles, find molar masses of the substances you have and need. Step 3: Use the mole ratio and factor-label method to answer the question 11 Mass-to-Mass Calculations Using Stoichiometry Ex: Solid lithium hydroxide has been used in space vehicles to remove exhaled carbon dioxide from the living environment. The products are solid lithium carbonate and liquid water. What mass of gaseous carbon dioxide can 875g of lithium hydroxide absorb? 12 Calculations Using Stoichiometry Summary 2Al(s) + 3I2(s) g Al g I2 1 6 Use molar mass of Al (26.98 g/mol) Use molar mass of I2 (253.8 g/mol) 2 5 mol Al 2AlI3(s) Use mole ratio 3 3 𝑚𝑜𝑙 𝐼2 2 𝑚𝑜𝑙 𝐴𝑙 4 mol I2 14 Practice! • HW: • Gravimetric Stoichiometry Booklet – for marks • Read p.286-292, p. 278-283 • Use the factor-label method • Is it: – Mole-to-mole? (easy-peasy, one-step calculation) – Mass-to-mole? (need molar mass for given substance) – Mass-to-mass? (need molar mass of both given substance and wanted substance) – (need mole ratios for all) 15 Limiting Reactants/Reagents A chemical rxn is limited by the substance that is in the least amount (according to the mole ratio) limiting reagent Analogy: For every car, you need 4 tires. So the car to tire ratio is 1:4. What if the auto manufacturer had 8 car bodies and ordered 48 tires? 16 Limiting Reactants/Reagents • With 8 cars, how many tires do we need? Use factor-label method: • Is the # of tires we need more or less than what we have (48 tires)? If we have more tires than we need = excess tires If we have less tires than we need = limited There was excess of tires but a limited amount of car bodies. The same idea applies to chemical reactions; one reagent is given in excess quantity (excess reagent) and another is in limited quantity (limiting reagent). 17 Limiting and Excess Reagents • Consider the following reaction outlined and illustrated Cu(s) + 2 AgNO3(aq) 2 Ag(s) + Cu(NO3)2(aq) Net ionic eq’n: • The copper atoms have become copper(II) ions (∴ the sol’n is blue) and the silver ions (in silver nitrate) have formed pure silver solid around the copper coil (white precipitate). • Since there was still copper left at the end of an extended period of time, more copper was present than was needed. • Copper was in excess and ∴ is called the excess reagent. – This means that the reaction proceeded until all the silver ions were used up in the reaction. – Silver ions were the limiting reagent (the amount of copper(II) ions you can make is limited by the amount of silver ions you have.) Limiting & Excess Reagents Group Work! You are making cookies and are missing a key ingredient – eggs. You have plenty of the other ingredients, except that you only have 1.33 cups of butter and no eggs. The recipe calls for 2 cups of butter and 3 eggs (plus the other ingredients) to make 6 dozen cookies. You telephone a friend and have him bring you some eggs. a) How many eggs do you need if you are going to use only your 1.33 cups of butter? b) If you use all the butter (and get enough eggs), how many cookies can you make? When your friend arrives, he has a surprise for you—to save time he has broken the eggs in a bowl for you. You ask him how many he brought, and he replies, “All of them, but I spilled some on the way over.” You weigh the eggs and find that they weigh 62.1 g. Assuming that an average egg weighs 34.21 g: a) How much butter is needed to react with all the eggs? b) How many cookies can you make? c) Which will you have left over, eggs or butter? d) How much is left over? Limiting Reagents • Limiting reagent – The reactant that limits the amount of product that can be formed – The reaction will stop when all of the limiting reactant is consumed • Excess reagent – The reactant that remains when the reaction stops. – The excess reactant remains because there is nothing left for it to react with (the limiting reactant is already completely consumed) 22 Limiting Reagents Ex: Nitrogen can be prepared by passing gaseous ammonia over solid copper (II) oxide at high temperatures. The other products of the rxn are solid copper and water vapor. How many grams of N2 are formed when 18.1 g of NH3 is reacted with 90.4 g of CuO? Step 1: Write and balance the chemical equation Step 2: Convert masses of reactants to moles 23 Limiting Reactants Ex: Nitrogen can be prepared by passing gaseous ammonia over solid copper (II) oxide at high temperatures. The other products of the rxn are solid copper and water vapor. How many grams of N2 are formed when 18.1 g of NH3 is reacted with 90.4 g of CuO? Step 3: Determine the limiting reagent and use that to find the product they’re asking for (use Factor Label Method) - Pick one of the reactants and calculate how many moles of the other reactant is needed to react with it: - Compare the # moles needed to # moles we have: If we have more moles than what we need excess reagent If we have less moles than what we need limiting reagent 24 Limiting Reactants Ex: Nitrogen can be prepared by passing gaseous ammonia over solid copper (II) oxide at high temperatures. The other products of the rxn are solid copper and water vapor. How many grams of N2 are formed when 18.1 g of NH3 is reacted with 90.4 g of CuO? Step 3: Determine which reacting is limiting and use that to find the product they’re asking for (use Factor Label Method) - ∴ ____ is the limiting reagent. Use this to find the product they’re asking for: 25 Summary for Solving Stoichiometry Problems with Limiting Reagents • When they ask you for how much product is produced and they give you amounts of reactants: – Write and balance the chemical equation – Convert known masses of reactants to moles – Determine the limiting reagent (using the moles of one reactant and the mole ratio between the reactants) – Use the factor label method to determine the mass of the product they’re asking for (using the limiting reagent, the mole ratio between the product and the limiting reagent and the molar mass of the product) 28 Practice! • Practice HW: Limiting Reagents Worksheet, p. 327 # 1, 4, 5 • Read: p. 284, 320-327 29 Percent Yield • Theoretical yield (the amount of product you could have gotten in the lab) – The maximum amount of product produced using stoichiometry of the chemical reaction and the given amount(s) of reactant(s) – Theoretical yields are rarely produced due to the presence of side rxns (other rxns that consume one or more of the reactants/products) • Actual yield (the amount of product you actually got in the lab) – Amount of the product actually obtained during the chemical reaction • Percent yield (what you got over what you could have gotten – like a test score) – Comparison of actual yield to theoretical yield expressed as a percentage % 𝑦𝑖𝑒𝑙𝑑 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 × 100% 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 30 Determining Percent Yield Ex: Methanol can be produced by the reaction between carbon monoxide and hydrogen. Suppose 6.85g of CO(g) is reacted with 0.860g of H2(g). What is the percent yield of methanol if 3.57g of CH3OH(l) is actually produced? What is the remaining amount of excess reagent? (We need to find the theoretical yield of methanol and then compare it to the actual yield.) Step 1: Write and balance the chemical equation Step 2: Convert the mass of both reactants to moles 31 Determining Percent Yield Ex: Methanol can be produced by the reaction between carbon monoxide and hydrogen. Suppose 6.85g of CO(g) is reacted with 0.860g of H2(g). What is the percent yield of methanol if 3.57g of CH3OH(l) is actually produced? What is the remaining amount of excess reagent? (We need to find the theoretical yield of methanol and then compare it to the actual yield.) Step 3: Find the limiting reagent by using the mole ratio between H2 and CO 32 Determining Percent Yield Ex: Methanol can be produced by the reaction between carbon monoxide and hydrogen. Suppose 6.85g of CO(g) is reacted with 0.860g of H2(g). What is the percent yield of methanol if 3.57g of CH3OH(l) is actually produced? What is the remaining amount of excess reagent? (We need to find the theoretical yield of methanol and then compare it to the actual yield.) Step 4: Use the limiting reagent to find the theoretical yield of methanol (using mole ratios and molar mass of methanol) 33 Determining Percent Yield Ex: Methanol can be produced by the reaction between carbon monoxide and hydrogen. Suppose 6.85g of CO(g) is reacted with 0.860g of H2(g). What is the percent yield of methanol if 3.57g of CH3OH(l) is actually produced? What is the remaining amount of excess reagent? (We need to find the theoretical yield of methanol and then compare it to the actual yield.) Step 5: Calculate the percent yield % 𝑦𝑖𝑒𝑙𝑑 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 × 100% 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 34 Determining Percent Yield Ex: Methanol can be produced by the reaction between carbon monoxide and hydrogen. Suppose 6.85g of CO(g) is reacted with 0.860g of H2(g). What is the percent yield of methanol if 3.57g of CH3OH(l) is actually produced? What is the remaining amount of excess reagent? MAKE SURE YOU’VE ANSWERED WHAT THEY ASKED! Step 6: Calculate the mass of excess reagent used (a moles-to-mass stoichiometry question) using factor-label method Step 7: Calculate the mass of excess reagent (subtraction) 35 Percent Yield Ex: 2S(s) + 3O2(g) 2SO3(g), if 3.2g S reacts with 9.0g O2 Determine the: a) b) c) d) Limiting reagent Theoretical yield of SO3 in grams % yield if 5.0g SO3 was formed Remaining amount of excess reagent S 8.0 g SO3 63% 4.2 g O2 40 Percent Error • Usually there is difference between the two yields. This is due to experimental errors, which can include: – limitations of the equipment, there is always uncertainty in measurement. This has nothing to do with the operator doing anything wrong/incorrect. – the purity of the grade of chemical used – washing of any precipitate involved (some dissolving or lost through the filter paper) – any qualitative judgments. These include such things as color or color changes. Percent Error • The predicted value is the accepted value, frequently calculated from stoichiometry or as otherwise provided. • The experimental value is the value as calculated from the evidence in an investigation (experiment) % 𝑒𝑟𝑟𝑜𝑟 = 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 × 100% • For most school labs, investigations usually involve a total of all experimental errors in the range of 5 – 10 %. • Percent yields below 90% are unacceptable and generally suggest there has been some “human error” which is NOT an acceptable category of experimental error Percent Yield vs Percent Error Ex 1: A solution is made by dissolving 9.8g of barium chloride and is completely reacted with a second solution containing dissolved sodium sulfate. a) b) c) Predict the mass of precipitate expected. If 10.0g of precipitate is actually formed, calculate the percent yield. Calculate the percent error. 11 g 91% 9.1% Percent Yield vs Percent Error Ex 2: When 30.0g carbon are heated with silicon dioxide, 28.2g carbon monoxide are produced. What is the percent yield of this reaction? What is the percent error? SiO2(s) + 3C(s) SiC(s) + 2CO(g) 60.5% yield, 39.5% error Percent Yield vs Percent Error Ex 3: Aluminium reacts with oxygen to produce aluminum oxide. The reaction of 50.0g aluminum and sufficient oxygen has a 75.0% yield. How many grams of aluminum oxide are produced? 70.9 g Percent Yield vs Percent Error Ex 4: Acetylene, C2H2, used in welders’ torches, burns according to the following equation: 2C2H2(g) + 5O2(g) 4CO2(g) + 2H2O(g) a) b) c) How many molecules of oxygen are needed to react with 22.0g acetylene? 1.27×1024 molecules O2 How many grams of carbon dioxide could be produced from the complete reaction of the acetylene in part (a)? 74.4 g If the reaction in part (a) produces 64.0g CO2, what is the percent yield for the reaction? Percent error? 86.0% yield, 14.0% error Practice! • Practice HW: Percent Yield/Error Worksheet; p. 327 #3, 8; p. 393 #8, 10 50 Gas Stoichiometry • Chemical rxns with gases, same rules and methods of gravimetric stoichiometry apply! (Yay!) • The only difference is that we also use volumes of gases. • So we use the molar volume of gases at SATP (24.8L/mol) and STP (22.4L/mol) to find moles and/or volume. If they give you mass, then you convert mass to moles and then use molar volume to find volume. • If the question does NOT indicate conditions that are STP or SATP, then we have to use the ideal gas law to find moles and/or volume. Gas Stoichiometry • If it is a volume-to-volume calculation and the conditions are NOT changing, then the volume ratio is the same as the mole ratio (Law of Combining Volumes) and you just do a very simple calculation using the volume ratio like you would a mole ratio. • If it is a volume-to-volume calculation and conditions ARE changing, then you have to convert volume to moles, use mole ratio and then convert moles to volume (using factorlabel method). It’s like replacing “mass” with “volume.” Gas Stoichiometry Ex 1: The first step in the industrial manufacture of sulfuric acid is the complete combustion of sulfur, S8(s). What mass of sulfur is required to produce 112L of sulfur dioxide at STP? 160g Ex 2: Coal can undergo an incomplete combustion in the absence of a plentiful supply of air to produce deadly carbon monoxide gas. What volume of carbon monoxide is produced at SATP by the incomplete combustion of 150kg of coal (C(s))? 3.10×105 L Gas Stoichiometry Ex 3: The first recorded observation of hydrogen gas was made by the famous alchemist Paracelsus when he added iron to sulfuric acid. Calculate the volume of hydrogen gas at STP produced by adding 10.0 g of iron to an excess of sulfuric acid to also produce iron (III) sulfate. 6.02 L Ex 4: Ammonia reacts with sulfuric acid to form the important fertilizer, ammonium sulfate. What mass of ammonium sulfate can be produced from 75.0 L of ammonia at 10°C and 110 kPa? 200 g Practice • Practice HW: Gas Stoichiometry Worksheet; p. 296 #2, 3 • Read: p. 294-298 55 Solution Stoichiometry • The majority of stoichiometric work in research and industry involves aqueous solutions. Solutions are easy to transport and handle, and solution reactions are relatively easy to control. • The general method of gravimetric stoichiometry remains the same in solution stoichiometry. (Yay!) • The major difference is the concentration and volume of solutions are used as conversion factors to convert to and from the chemical amount of substance. Solution Stoichiometry Ex 1: What is the amount/molar concentration of a KOH(aq) solution if 12.8mL of this solution is required to react with 25.0mL of 0.110 mol/L H2SO4(aq)? 0.430 mol/L Ex 2: What volume of 0.125mol/L NaOH(aq) is required to react completely with 15.0mL of 0.100 mol/L Al2(SO4)3(aq)? 72.0 mL Solution Stoichiometry Ex 3: In a chemical analysis, a 10.0mL sample of H3PO4(aq) was reacted with 18.2mL of 0.259mol/L NaOH(aq). Calculate the amount concentration of the phosphoric acid. 0.157 mol/L Ex 4: The concentration of magnesium ions (assume magnesium chloride) in seawater was analyzed and found to be 5.00×10–3mol/L. What volume of 0.200mol/L sodium hydroxide solution would be needed in an industrial process to precipitate all of the magnesium ions from 1.00L of seawater? 50.0 mL Solution Stoichiometry Ex 5: A student has accidentally spilled 100.0mL of 3.0mol/L sulfuric acid onto the lab bench. The lab instructor sprinkles some baking soda (sodium hydrogen carbonate) on the spill to neutralize the acid according to the following chemical equation: H2SO4(aq) + NaHCO3(s) CO2(g) + H2O(l) + Na2SO4(aq) a) What mass of baking soda would the instructor need to sprinkle on this spill to neutralize and clean it up? 50.g b) Calculate the volume of carbon dioxide that would be produced at a temperature of 25°C and a pressure of 100kPa. 15.L Practice! • HW Practice: Solution Stoichiometry Worksheet; p. 303 #1, 2, 5 • Read: p. 300-302 60 Erlenmeyer Titration Steps 64 Titration Steps 65 Acid-Base Titration: Terminology • Titration – is the process of carefully measuring and controlling the addition of a solution (the titrant) from a burette into a measured fixed volume of another solution (sample) until the reaction is judged to be complete. • Titrant – the solution in the burette during a titration • Sample/Analyte/Titrand – the solution of unknown concentration that is being titrated in the Erlenmeyer Flask Titration Calculations • The equivalence point will occur when the chemical amount of acidic solution is equal to the chemical amount of the basic solution. • This is detected by the endpoint – a sudden colour change or pH change what you see in the lab Ex 1: Titration of 10.00mL of CH3COOH(aq) with 0.202mol/L of NaOH(aq) Titrant: ________________ Sample: _______________ Equation: Trial Final burette reading (mL) 1 14.8 2 26.9 3 39.8 4 13.6 Initial burette reading (mL) 0.7 13.9 26.9 0.5 blue green green green Volume of NaOH used (mL) Colour of the endpoint 1. What is the molar concentration of the acetic acid used? (Answer: 0.263mol/L) 69 Ex 2: Titration of 25.0mL of Na2CO3(aq) with 0.352mol/L HI(aq) Titrant: __________________ Sample: __________________ Equation: Trial Final burette reading (mL) Initial burette reading (mL) Volume of HI used (mL) 1 16.5 0.6 2 31.8 16.5 3 47.0 31.8 4 16.4 1.2 2. What is the molar concentration of the sodium carbonate solution? 70 Ex 3: Titration of 10.0mL of Mg(OH)2(aq) with 0.150mol/L H2CO3(aq) Titrant: __________________ Sample: __________________ Equation: Trial Final burette reading (mL) Initial burette reading (mL) Volume of H2CO3 used (mL) 1 12.8 0.2 2 25.3 12.8 3 37.9 25.3 3. What is the molar concentration of the magnesium hydroxide solution? 71 Ex 4: Titration of 10.00mL of NH3(aq) with 1.48mol/L HCl(aq) Titrant: __________________ Sample: __________________ Equation: Trial Final burette reading (mL) Initial burette reading (mL) Volume of HCl used (mL) 1 29.1 15.0 2 43.0 29.1 3 14.4 0.4 4. What is the molar concentration of the ammonia solution? 72 pH Curves Tell us 5 things: • Type of rxn • # of rxns • Buffer regions • Endpoint • Equivalence point 80 Endpoint – (steep slopes) sudden observable Δ (like colour or pH) has occurred • The region of rapid change in pH (the steep slope in the graphinflection) indicates that the buffer is used up. The midpoint are of the inflection/change is called Endpoints VISIBLE colour Δ’s or pHthe Δ’s that you can ______ of the titration. only see in the LAB. Endpoints tell you that you’ve • The endpoint indicates that neutralization has occurred in an acidreached the equivalence point. base titration. • Neutralization is the pH where the chemical amount of acidic Wesolution use endpoint equivalence point and basic&solution are equal. (Thisinterchangeably, does not mean equal though endpoint does not always match exactly volumes!) Neutralization is NOT always at pHup 7, only if it isto a strong acid mixed with a strong base (or a weak acid with a weak base). equivalence point. – All endpoints are ! 84 Equivalence Point – volume of titrant added to reach neutralization or endpoint • The pH of the solution at the equivalence point for a strong monoprotic acid-strong monoprotic base rxn will be 7. • The pH of the solution at the equivalence point for any other acid-base reaction must be determined experimentally, by plotting a titration pH curve. pH Curves Tell us 5 things: • Type of rxn • # of rxns • Buffer regions • Endpoint • Equivalence point 87 Strong Base Titrated with a Strong Acid 0.48mol/L NaOH(aq) is titrated with 0.50mol/L HCl(aq) Since the initial pH is above 7, this indicates that the: Sample is a _____________ (_________), and the titrant is an _____________ (_______). Equivalence point is _________________, and the endpoint is _________________. 89 Strong Acid Titrated with a Strong Base 0.50mol/L HCl(aq) is titrated with 0.48mol/L NaOH(aq) Since the initial pH is below 7, this indicates that the: Sample is an _____________ (_________), and the titrant is a _____________ (________). Equivalence point is _________________, and the endpoint is _________________. 90 Important Point! • Only for the rxn between a strong monoprotic acid and a strong monoprotic base, is the pH 7 at the equivalence point. 91 Choosing Acid-Base Indicators for Titration Practice • For each titration curve on the following slide, a) Determine the volume of titrant used to reach the equivalence point b) Determine the pH at the equivalence point (to the nearest whole number) c) Suggest a suitable indicator for a titration analysis to be done using these reagents. Practice! • Practice HW: Titration Worksheet; p. 339 #1, 3, 6, 9 • Read: p. 328-339 97