# stoichiometry = the numerical relationships between chemical amounts in a reaction.

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1 1 REACTIONS AND YIELD ANSWERS stoichiometry = the numerical relationships between chemical amounts in a reaction. 2C 8 H 18 (l) + 25O 2 16CO 2 (g) + 18H 2 O(g) From the equation, 16 moles of CO 2 (a greenhouse gas resulting in global warming) are produced for every 2 moles of octane burned (by combustion). Estimate the mass of CO 2 produced in 2004 by the combustion of 3.4 x g gasoline. Solution: number of moles = mass/molar mass; molar mass = molecular mass molecular masses: C 8 H 18 = ; CO 2 = gmol x / = x moles C8H18. stoichiometric ratio CO 2 : C 8 H 18 = 16: x x (16/2) = x moles CO 2 = 1.05 x g CO 2. limiting reactant (or reagent) = the reactant that limits the amount of product excess reactants = reactants not completely consumed theoretical yield = the amount of product that can be made from the limiting reactant actual yield = the amount of product that is made in a reaction; actual yield generally less than the theoretical yield, never more! percent yield = the efficiency of product recovery actual yield Percent yield = x 100% theoretical yield When 28.6 kg of C reacts with 88.2 kg of TiO 2, 42.8 kg of Ti are obtained. Find the Limiting Reactant, Theoretical Yield, and Percent Yield. TiO 2 (s) + 2 C(s) Ti(s) + 2CO(g) Solution: 1 mole TiO 2 gives 1 mole Ti; 2 moles C gives 1 mole Ti. molar masses C = 12.01; TiO 2 = 79.87; Ti = gmol -1. Number of moles of C = 2.38 x 10 3 moles Number of moles of TiO 2 = 2.38 x 10 3 moles x 10 3 moles Ti x 10 3 moles Ti TiO 2 = limiting reactant x 10 3 x = 52.9 kg Ti = theoretical yield Percent yield = 100% x 42.8 / 52.9 = 80.9 %. PRACTICE EXAMPLE ONE Mining companies use the following reaction to obtain iron from iron ore: Fe 2 O 3 (s) + 3CO(g) 2Fe(s) + 3CO 2 (g) The reaction of 167g of Fe 2 O 3 with 85.8g of CO produces 72.3g Fe. Find the limiting reagent, theoretical yield and percent yield.

2 2 CO is the limiting reagent since it only produces 114 g Fe (work out number of moles CO = 85.8/28.01= so max Fe = 2 / 3 x = 2 = 2 x = 114 g Fe) Therefore 114 g Fe is the theoretical yield; percentage yield = 100% x 72.3 / 114 = 63.4 % Making aqueous solutions When an ionic compound dissolves in water, the water molecules surround the cations and anions; e.g. KCl(s) K + (aq) + Cl - (aq). Heating the solution increases solubility. Substances such as potassium chloride or hydrogen chloride (strong acid) that completely dissociate into ions are strong electrolytes (solution conducts electrical current). Weak electrolytes dissolve mostly as molecules but partly dissociate into ions: CH 3 COOH(aq) CH 3 COO - (aq) + H + (aq) dilute solutions = small amount of solute compared to solvent concentrated solutions = large amount of solute compared to solvent amount of solute (in moles) Molarity = amount of solution (in L or dm 3 ) Find the molarity, M (or concentration, C) of a solution that has 25.5 g KBr dissolved in 1.75 L of solution Solution: molar mass KBr = gmol -1 number of moles = 25.5 / 119 = mol KBr molarity = / 1.75 = M (or mol dm -3 ). Dilution = make a solution less concentrated moles solute in solution 1 = moles solute in solution 2 M 1 V 1 = M 2 V 2 To what volume should you dilute L of 15.0 M NaOH to make 3.00 M NaOH? Solution: V 2 = M 1 V 1 / M 2 = 15 x 0.2 / 3 = 1 L PRACTICE EXAMPLE TWO What volume of a 6.00 M NaNO 3 solution should you use to make L of a 1.20 M NaNO 3 solution? V 2 = M 1 V 1 /M 2 = 1.20 x / 6 = L

3 3 What volume of M KCl is required to completely react with L of M Pb(NO 3 ) 2 in the reaction 2KCl(aq) + Pb(NO 3 ) 2 (aq) PbCl 2 (s) + 2 KNO 3 (aq)? 1 L Pb(NO 3 ) 2 = mol, 1 L KCl = mol, stoichiometry: 1 mol Pb(NO 3 ) 2 reacts with 2 mol KCl Number of moles of Pb(NO 3 ) 2 used = molarity x volume = moles Number of moles of KCl used = moles x 2 = moles volume KCl = moles / molarity = /0.150 = 0.35 L PRACTICE EXAMPLE THREE Consider the following reaction: Li 2 S(aq) + Co(NO 3 ) 2 (aq) 2LiNO 3 (aq) + CoS(S) What volume of M Li 2 S solution is required to completely react with 125 ml of M Co(NO 3 ) 2? Stoichiometry: 1:1 so number of moles Co(NO 3 ) 2 = x = moles = volume Li 2 S = 0.031/0.150 = L= 208 ml soluble = compounds that dissolve in a solvent (e.g. NaCl dissolves in water) insoluble = compounds that do not dissolve (e.g. AgCl does not) Most Group I compounds are soluble in water (e.g. NaOH, Na 2 SO 4 ). Some Group II compounds are soluble (e.g. CaCl 2 ), slightly soluble e.g. Ca(OH) 2, others are not (e.g. CaSO 4 ). Many ammonium NH 4 + compounds are soluble (e.g. NH 4 Cl) and ALL NITRATES (e.g. Ca(NO 3 ) 2 ) are soluble. Precipitation reactions = reactions between aqueous solutions of ionic compounds that produce an ionic compound that is insoluble (precipitate) in water: 2KI(aq) + Pb(NO 3 ) 2 (aq) PbI 2 (s) + 2 KNO 3 (aq); PbI 2 (s) is the precipitate Discussed in more detail (book p. 153). Writing and simplifying equations molecular equations = equations which describe the chemicals put into the water and the product molecules molecular equations, e.g. 2KI(aq) + Pb(NO 3 ) 2 (aq) PbI 2 (s) + 2 KNO 3 (aq) complete ionic equations = equations which describe the actual dissolved species: 2K + (aq) + 2I - (aq) + Pb 2+ (aq) + 2NO 3 2- (aq) 2K + (aq) + 2NO 3 2- (aq) + PbI 2 (s) ions that are both reactants and products are called spectator ions (they do not react and remain in the solution)

4 4 net ionic equation = an ionic equation in which the spectator ions are removed: Pb 2+ (aq) + 2I - (aq) PbI 2 (s) neutralization reactions = the acid and base neutralize each other s properties 2HNO 3 (aq) + Ca(OH) 2 (aq) Ca(NO 3 ) 2 (aq) + 2 H 2 O(l) the net ionic equation for an acid-base reaction is: H + (aq) + OH (aq) H 2 O(l) PRACTICE EXAMPLE FOUR Write complete ionic and net ionic equations for each reaction: K 2 SO 4 (aq) + CaI 2 (aq) CaSO 4 (s) + KI(aq) NH 4 Cl(aq) + NaOH(aq) NH 3 (g) + NaCl(aq) + H 2 O(l) 2K + (aq) + SO 4 (aq) + Ca 2+ (aq)+ 2 I - (aq) CaSO 4 (s) + 2K+(aq) + 2I - (aq) = Ca 2+ (aq)+ SO 4 2- (aq) CaSO 4 (s) NH 4 + (aq) + Cl - (aq) + Na + (aq) + OH - (aq) NH 3 (g) + Na+(aq) + Cl - (aq) + H 2 O(l) = NH 4 + (aq) + OH - (aq) NH 3 (g) + H 2 O(l) acids ionize in water to form H + ions more precisely, the H from the acid molecule is donated to a water molecule to form hydronium ion, H 3 O +. A proton (H + ) cannot exist on its own in water! bases dissociate in water to form OH ions bases, such as NH 3, that do not contain OH ions, produce OH by pulling H off water molecules acid + base salt + water titration - a solution s concentration is determined by reacting it with another material and using stoichiometry (involving a chemical equation and calculation). An indicator permanently changes colour at the end-point (just finished). For example, if we know the concentration and precise volume of the alkali but only the volume of acid of unknown concentration, we can determine its concentration. Titration can be used for many ionic reactions. n 1 A + n 2 B products (e.g. salt + water) C 1 x V 1 = n 1 C 1 x V 1 x n or 2 C C 2 x V 2 n 2 = 2 n 1 x V 2

5 ml of M NaOH(aq) reacts ml of HCl(aq) solution. What is the concentration of the acid? The formula can be used with ml (for both solutions) or converted to L for both solutions. NaOH(aq) + HCl(aq) NaCl(aq) + H 2 O(l) C 1 concentration = M NaOH(aq); C 2 =? V 1 volume = ml NaOH(aq); V 2 = ml n 1 stoichiometric value = 1 for NaOH; n 2 = 1 for HCl C 2 = x x 1 / 1 x = M HCl(aq) Some neutralization reactions evolve gases; the intermediate carbonic acid (H 2 CO 3 ) thus decomposes, e.g. Na 2 CO 3 (aq) + 2HNO 3 (aq) 2NaNO 3 (aq) + CO 2 (g) + H 2 O(l) PRACTICE EXAMPLE FIVE A ml sample of an unknown H 3 PO 4 solution is titrated with a M NaOH solution. The end-point (equivalence point) is reached when ml of NaOH solution is added. What is the concentration of the unknown H 3 PO 4 solution? 3NaOH(aq) + H 3 PO 4 (aq) Na 3 PO 4 (aq) + 3H 2 O(l) Stoichiometry: n 1 = 3; n 2 = 1 so C 2 = x x 1 / x 3 = M H 3 PO 4 REDOX REACTIONS REDOX (oxidation-reduction) reactions = transferring electrons from one atom to another Many involve the use of O 2, Cl 2 etc. 4 Fe(s) + 3O 2 (g) 2 Fe 2 O 3 (s); the iron has transferred its electrons to the oxygen atoms Combustion (molecular - involve the use of O 2 ) is also REDOX, e.g. H 2 (g) + O 2 (g) 2H 2 O(l) oxidation occurs when an atom s oxidation state increases during a reaction (Fe(0) to Fe +3). LOSS OF ELECTRONS reduction occurs when an atom s oxidation state decreases during a reaction (O (0) to O (- 2). GAIN OF ELECTRONS In a REDOX reaction, the oxidizing agent is always reduced and the reducing agent always oxidized.

6 6 C +2S CS 2 carbon is the reducing agent (0 to +4) and sulphur the oxidizing agent (0 to -2). Oxidation state and ionic charges are not to be confused; see the table in book p.164. for single atoms with a charge (e.g. Fe 3+, O 2- ) the oxidation state is often the charge! oxygen is nearly always -2 (exception KO 2 ). Group I = +1; Group 2 = +2 Transition metals have variable oxidation states (e.g. chromium from +2 to +6) K 2 Cr 2 O 7 : Cr = +6 = potassium chromate(vi) elements (e.g. O 2 oxidation state = zero (0). Metals have positive oxidation states. In a neutral atom or formula the sum ( ) of the oxidation states = 0. An ion is equal to the charge of the ion. SO 4 2-, and H 2 SO 4 sulphur has oxidation state of +6. PRACTICE EXAMPLE SIX What is the oxidation state of Cl in each ion? 1. a) ClO - +1 b)clo c)clo d)clo Determine the oxidizing and reducing agent: a) Al(s) + 3Ag+(aq) Al 3+ (aq) + 2Ag(s) b) NaI 2 (aq) + Cl 2 (g) 2NaCl(aq) + I 2 (aq) a) oxidizing agent = reduced (gain in electrons); reducing agent = oxidized (loss of electrons) so reducing agent = Al; oxidizing agent = Ag +. b) I - = reducing agent; Cl 2 = oxidizing agent. COMBUSTION REACTIONS We have encountered several combustion reactions so far. Common ones include burning elemental carbon, hydrogen, sulphur, phosphorous, hydrocarbons (e.g. methane) or alcohol in air or oxygen. They give off heat (exothermic, H < 0 typically about 2000 KJmol -1 ) and light. See book, p for equations. Equations must be balanced in an exam (number of atoms on the left = number of atoms on the right).

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