Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 MASS RELATIONSHIPS IN CHEMICAL REACTIONS 1. The mole, Avogadro’s number and molar mass of an element 2. Molecular mass (molecular weight) 3. Percent composition of compounds 4. Empirical and Molecular formulas 5. Stoichiometry 6. Limiting Reagents 7. Reaction Yields 8. Combustion reactions 1 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 THE MOLE (unit mol, symbol n) It is the amount of a substance that contains as many elementary entities (atoms, molecules or other particles) as there are atoms in exactly 12 g of the carbon-12 isotope. Consider: 1 mol = 6.022 x 1023 and 1 mol of C = 12 g of C therefore the actual number of atoms in 12 g of the carbon-12 isotope = 6.022 x 1023 atoms called the Avogadro’s Number 1 mol of C = 12 g = 6.022 x 1023 atoms Converting between moles and number of atoms Example 1. Given: Solution: Example 2. Given: Solution: 1 mol atoms 6.022 x 1023 atoms 3.5 mol He 3.5 mol He x 6.022 x 1023 atoms 1 mol atoms or Find: He atoms 6.022 x 1023 He atoms 1 mol He atoms 1.1 x 1022 Ag atoms 1.1 x 1022 Ag atoms x = 2.1 x 1024 He atoms Find: mols Ag 1 mol Ag atoms 6.022 x 1023 Ag atoms = 1.8 x 10-2 mols Ag 2 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 CONVERTING BETWEEN GRAMS AND MOLES OF AN ELEMENT The mass of 1 mol of atoms of an element is called the molar mass The value of an element’s molar mass in grams per mole is numerically equal to the element’s atomic mass in atomic mass units (amu) For example Copper has a atomic mass of 63.55 amu, therefore 1 mol of copper atoms has a mass of 63.55 g and the molar mass of copper = 63.55 g/mol or g mol-1. 32.07 g of sulfur = 1 mol sulfur 12.01 g of carbon = 1 mol carbon = 6.022 x 1023 S atoms = 6.022 x 1023 C atoms 6.94 g of lithium = 1 mol lithium = 6.022 x 1023 Li atoms Therefore the molar mass of any element becomes a conversion factor between grams of that element and moles of that element: Example for carbon: 12.01 g C 12.01 g = 1 mol C = 1 mol C Example 1. Given: Solution: Find: 0.58 g of C 0.58 g x Mass of element (g) Mass of element (g) 1 mol C or 1 mol C 12.01 g C mols of C = 4.8 x 10-2 mols 12.01 g C ππππππππ ππππππππππ ππππππππ → mols of element (n) n x molar mass ← mols of element (n) N = no of atoms, N A = Avogadro’s number, n = no. of moles n x πππ΄π΄ → N/πππ΄π΄ ← Number of atoms (N) Number of atoms (N) 3 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 COUNTING MOLECULES BY THE GRAM For elements, molar mass is the mass of 1 mol of atoms of that element. For compounds, the molar mass is the mass of 1 mol of molecules or formula units of that compound (also known as molecular mass or molecular weight) If the atomic masses of component atoms, the mass of the molecule can be calculated. For example the molar mass /molecular mass/molecular weight or formula mass of CO 2 is: Molecular mass = 1(atomic mass of C) + 2(atomic mass of O) = 44.01 amu = 1(12.01 amu) + 2(16.00 amu) The molar mass of CO 2 = 44.01 g/mol or g mol-1 CONVERTING BETWEEN GRAMS AND MOLES OF A COMPOUND Given: Solution: Find: 22.5 g of CO 2 22.5 g x 1 mol CO2 44.01 g = 0.511 mol CO 2 mols CO 2 CONVERTING BETWEEN GRAMS OF A COMPOUND AND NUMBER OF MOLECULES Example 1. Given: 22.5 g of CO 2 Solution: 22.5 g x 1 mol CO2 44.01 g x Find: number of CO 2 molecules 6.022 x 1023 CO2 molecules = 3.08 x 1023 CO 2 molecules mol CO2 4 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Example 2 Given: 4.78 x 1023 NO 2 molecules Solution: Find: grams NO 2 Molar mass of NO 2 = 14.01 + 2(16.00) = 46.01 g mol-1 4.78 x 1023 NO 2 molecules X 46.01 g NO2 1 mol NO2 X = 23 6.022 x 10 NO2 molecules 1 mol NO2 36.5 g NO 2 Practice Exercise 1. Calculate the molar mass of the following compounds: (a) N 2 (b) CO (c) MgCl 2 (f) (NH 4 )SO 4. FeSO 4 .6H 2 O (d) CaCl 2 . 6H 2 O (e) C 6 H 5 OH (g) CH 3 CH 2 CH 2 CH 2 CH 2 COOH Percent Composition of Compounds It is the percentage mass of each element in a compound. General formula: % composition of element X = n x molar mass of element X molar mass of compound Where n = number of moles of the element in 1 mole of the compound x 100% 5 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Example 1. Calculate the mass % of H and O in H 2 O 2 . Solution: 1 mol of H 2 O 2 = 34.02 g contains 2 mols of H and 2 mols of O Molar masses (in g mol-1): H 2 O 2 = 34.02, H = 1.008, O = 16.00 %H= %O= 2 x 1.008 H g/mol 34.02 H 2 O 2 g/mol 2 x 16.00 O g/mol 34.02 H 2 O 2 g/mol x 100 = 5.926 % x 100 = 94.06 % Calculation of the percent composition of H and O in the Empirical formula of H 2 O 2 which is HO 1 x 1.008 H g/mol %H= %O= 17.01 HO g/mol 1 x 16.00 O g/mol 17.01 HO g/mol x 100 = 5.926 % x 100 = 94.06 % Both molecular formula and empirical formula gives the same percent composition. Practice Exercise 1. Calculate the percent composition of Cl in CCl 2 F 2 . 3. Calculate the percent composition of K and Mn in KMnO 4 . 2. 4. Calculate the percent composition of each element in C 12 H 23 O 6 Br Calculate the percent composition of H 2 O in CaCl 2 ⋅ 2H 2 O 6 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 CALCULATING EMPIRICAL AND MOLECULAR FORMULAS FROM REACTION DATA (a) Calculating Empirical Formulas Example 1. Calculate the empirical formula of a compound that is made up of 69.58% Ba, 6.090 % C and 24.32 % O only. Solution Mass % →mass of element →moles of each element → mole ratio → empirical formula Assume 100g of the compound Therefore: Ba = 69.58 g, Mass (g) Molar mass (g mol-1) Moles (mols) C = 6.090 g , O = 24.32 g Ba C O 69.58 6.090 24.32 6.090 24.32 137.3 12.01 0.5068 0.5071 0.5068 0.5071 1 1 69.58 137.3 Divide by the smallest mols 0.5068 Round off to the nearest whole number 1 12.01 0.5068 1 Empirical formula = BaCO 3 16.00 16.00 1.520 1.520 0.5068 2.999 3 7 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Practice Exercise 1 . A compound containing nitrogen and oxygen is decomposed in the laboratory and produces 24.5 g of nitrogen and 70.0 g of oxygen. Determine the empirical formula of the compound. Solution: Mass (g) Molar mass (g mol-1) Moles (mols) N 24.5 O 70.0 14.01 16.00 1.75 4.38 24.5 14.01 Divide by the smallest mols 1.75 1.75 1 70.0 16.00 4.38 1.75 2.5 Multiply by a factor# to convert to a whole number # See notes below N 1 O 2.5 x 2 = N 2 O 5 Practice Exercise 2. A laboratory analysis of aspirin determined the following mass percent composition: C = 60.00 %, Find the empirical formula. H = 4.48 % and O = 35.53 % only. Answer: C 9 H 8 O 4 8 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 If subscripts are not whole numbers, multiply all the subscripts by a small whole number to get whole number subscripts Fractional subscript Multiply by this number to get Whole-number subscripts __.10 10 __.20 5 __.33 3 __. 25 __.50 __.66 __.75 Practice Exercise 3. 4 2 3 4 A sample was found to contain 13.42 g of C, 2.25 g of H and 17.88 g of O only. Determine the empirical formula for this compound. Practice Exercise 4. A sample has the following percentage compositions: 40% C, 6.71% H and 53.29% O What is the empirical formula for this compound? Practice Exercise 5 A 3.24 g sample of titanium reacts with oxygen to form 5.40 g of the metal oxide. What is the formula of the oxide? 9 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 CALCULATING MOLECULAR FORMULAS FOR COMPOUNDS To calculate the molecular formula, the following must be known: (i) (ii) molar mass of the compound empirical formula of the compound Note: The formula calculated from percent composition is always the empirical formula Molecular formula = Empirical formula × n, where n = 1,2,3…… Example: Find the molecular formula for fructose (a sugar formed in fruit) from its empirical formula CH 2 O and its molar mass, 180.2 g mol-1. Solution: Molar mass is a whole-number multiple of the empirical formula mass, the sum of the masses of all atoms in the empirical formula. Therefore molar mass = Empirical formula × and n = n Molar mass Empirical formula molar mass Empirical formula molar mass for fructose = 1(12.01) + 2(1.01) + 16 = 30.03 g mol-1 Therefore, n= 180.2 g/mol 30.03 g/mol = 6, hence molecular formula = CH 2 O × 6= C 6 H12 O 6 Practice Exercise 1: Given that the empirical formula of a compound is CH and the molar mass is 104 g mol-1, determine the molecular formula. 10 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Solution: Empirical formula mass = 12.01 g mol-1 + 1.01 g mol-1 = 13.01 g mol-1 Divide the molar mass of the compound by the empirical formula mass: No of CH units = 104 ππ ππππππ−1 13.01 ππ ππππππ−1 = 8.00 Therefore molecular formula = CH × 8 = C 8 H 8 Practice Exercise 2. Naphthalene , a compound containing carbon, and hydrogen only, is often used in moth balls. Its empirical formula is C 5 H 4 and its molar mass is 128.16 g mol-1. Find its molecular formula. Solution: C 10 H 8 STOICHIOMETRY Greek: Stoicheon = element metron = element measuring Stoichiometry is the science of measuring the quantitative proportions or mass ratios in which chemical elements stand to one another Molar Ratios: xA + yB → aA + zD Stoichiometric relationship: nA x = nB y = nπΆπΆ a = nπ·π· z 11 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Example 1: Consider the following balanced equation and write the stoichiometric relationship for all reactants and products 2 C 2 H 6 (g) + 7 O 2 (g) → 4 CO 2 (g) + 6 H 2 O (l) Solution: nC2 H6 (g) 1. 2 = nO2 (g) 7 = nCO2 (g) 4 nH2 O(g) = 6 Mole to Mole conversions: mol → mol 3 H 2 (g) + N 2 (g) → 2 NH 3 (g) 3 H 2 molecules ≡ 1 N 2 molecule ≡ 2 NH 3 molecules 3 mols H 2 ≡ 1 mol N 2 ≡ 2 mol NH 3 Example 1. If 2.0 mol of N 2 (g) reacts with sufficient H 2 (g), how many mols of NH 3 (g) will be produced? Solution: nN2 1 nNH = 3 nNH3 2 ⇒ 2.0 mols 1 = nNH3 = 2.0 mols x 2 = 4.0 mols 2 Example 2. If 4.25 mols of H 2 (g) reacted with sufficient N 2 (g), calculate the number of moles of NH 3 (g) that would be produced. 12 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2. 2011 Mole to mass conversions: mol → grams Example 1: How many grams of oxygen are produced when 1.50 mols of KClO 3 (s) are decomposed according to the balanced equation? β 2 KClO 3 (s) nKClO3 nO2 = 2 3 2 KCl(s) + 3 O 2 (g) ⇒ 1.5 mols 2 Therefore nO 2 = 1.50 mols × nO 2 3. = mass of O 2 3 = nO2 3 = 2.25 mols 2 ⇒ mass of O 2 = 2.25 mols × 32.00 g mol-1 Molar mass of O 2 = 72.0 g Mass to mole conversions β 2 KClO 3 (s) Example: 2 KCl(s) + 3 O 2 (g) If 80.0 g of O 2 (g) was produced in the above reaction, calculate the number of moles of KClO 3 decomposed. Solution: Stoichiometry from balanced equation is: nKClO3 nO2 2 = 3 ⇒ nKClO3 = nO 2 × 2 3 = 80 g 32.00 g/mol × 2 3 = 1.67 mols of KClO 3 decomposed 13 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Practice Exercise: Consider the following equation: (a) 2H 2 (g) + O 2 (g) → 2H 2 O How many grams of H 2 O are produced when 2.50 moles of O 2 (g) is reacted? (b) If 3.00 moles of H 2 O is produced, calculate the mass of O 2 (g) that was used. 4. Mass to mass conversions (c) How many grams of H 2 (g) must be used, given the data in (b) above? Example 1 How many grams of Cl 2 (g) can be liberated from the decomposition of 64.0 g of AuCl 3 in the following reaction: 2 AuCl 3 (aq) → 2 Au(s) + 3 Cl 2 Solution: From stoichiometry nAuCl3 2 nAuCl3 2 nCl 2 = = = nAu nCl2 2 nCl2 3 nAuCl3 2 mass of Cl 2 (g) = 3 x 3 = 64.0 g 303.32 g/mol = 0.211 mols × = 22.40 g × 3 2 = 0.211 mols 70.9 g mol-1 14 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Practice Exercises 1. 2. Calculate the mass of AuCl 3 that can be produced from 100 g of Cl 2 in the following reaction: 2 Au(s) + 3 Cl 2 → 2 AuCl 3 (aq) Calculate the mass of AgCl(s) that can be produced by reacting 200.0 g of AlCl 3 and sufficient AgNO 3 , using the following reaction: 3 AgNO 3 (aq) + AlCl 3 (aq) → 3 AgCl(s) + Al(NO 3 ) 3 (aq) 3. 4. Using the following reaction: 2 KI(aq) + Pb(NO 3 ) 2 (aq) → PbI 2 (s) + 2 KNO 3 (aq) Calculate the mass of PbI 2 (s) by reacting 30.0 g of KI with excess Pb(NO 3 ) 2 . How many grams of Na(s) are required to react completely with 75.0 g of Cl 2 (g) using the following equation: 2 Na(s) + Cl 2 (g) → NaCl (unbalanced) 5. A component of acid rain is sulfuric acid which forms when SO 2 (g), a pollutant reacts with oxygen and rain water according to the following reaction: 2 SO 2 (g) + O 2 (g) + H 2 O(β) → H 2 SO 4 (aq) Assuming that there is plenty of O 2 (g) and H 2 O(β), how much H 2 SO 4 in kilograms forms from 2.6 x 103 kg of SO 2 (g)? 15 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 5. 2011 Limiting Reagents The limiting reagent (or reactant) is the reactant that is completely consumed in a chemical reaction. The maximum amount of product formed depends on how much of this (limiting) reactant was originally present. Excess reagents are present in quantities greater than necessary to react with the quantity of the limiting reagent. Theoretical yield - the amount of product that can be made in a chemical reaction based on the amount of limiting reagent. Actual or (experimental) yield – the amount of product actually produced by a chemical reaction. Percentage Yield = Actual Yield Theoretical Yield x 100 Consider a recipe to bake pancakes: 1 cup flour + 2 eggs + ½ tsp baking powder → 5 pancakes Suppose we have: 3 cups flour + 10 eggs + 4 tsp baking powder → ? pancakes We can make: 3 cups flour → 15 pancakes 10 eggs → 25 pancakes 4 tsp baking powder → 40 pancakes Flour is the limiting reagent as it produces the least amount of pancakes 16 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Practice Exercise 1. Consider the following reaction: Ti(s) + 2Cl 2 (g) → TiCl 4 (s) If we begin with 1.8 mol of Ti and 3.2 mol of Cl 2 , what is the limiting reagent and calculate the theoretical yield of TiCl 4 in moles? Solution: Given: Find: limiting reagent 1.8 mol Ti 3.2 mol Cl 2 Stoichiometry: nTiCl4 1 nTiCl4 1 = = nCl2 2 nTi 1 = Theoretical yield 3.2 mols 2 = 1.8 mols = 1.6 mols Since smaller amount of mols of TiCl 4 is produced from Cl 2 , Therefore Cl 2 is the limiting reagent while Ti is the excess reagent. Therefore theoretical yield of TiCl 4 (s) = 1.6 mols Practice Exercise 1. Consider the following reaction: 2 Al(s) + 3Cl 2 (g) → 2 AlCl 3 (s) If we begin with 0.552 mol of aluminium and 0.887 mol of chlorine, what is the limiting reagent and the theoretical yield? 17 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 6. 2011 Limiting Reagent, Theoretical Yield, and Percent Yield from Initial masses of Reactants Consider the following reaction: 2 Na(s) + Cl 2 (g) → 2 NaCl(s) If we begin with 53.2 g of Na and 65.8 g of Cl 2 , what is the limiting reactant and theoretical yield? 53.2g nNa = 22.99g/mol = 2.31 mols, nNaCl nNa 2 nNaCl 2 = = 2 nCl2 1 nCl = 2.31 mols ⇒ 2 = 65.8g 70.90g/mol = 0.928 mols nNaCl = 0.928 mols x 2 = 1.856 mols Therefore the limiting reagent is Cl 2 Theoretical yield (calculated from Cl 2 ) Mass of NaCl = 1.856 mols x 58.44 g mol-1 = 108 g NaCl Suppose when the synthesis was carried out, the actual yield of NaCl was found to be 86.4 g. What is the percent yield? Percentage Yield = = = Actual Yield Theoretical Yield 86.4 g 108 g x 100 80.0 % x 100 18 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Practice Exercise 1. 2. Ammonia can be synthesized by the Haber Process according to the following reaction: 3 H 2 (g) + N 2 (g) → 2 NH 3 (g) (a) What is the maximum amount of ammonia in grams that can be synthesized from 25.2g of N 2 (g) and 8.42g of H 2 (g)? (b) What is the maximum amount of ammonia in grams that can be synthesized from 5.22g of H 2 (g) and 31.5 of N 2 (g)? Consider the following reaction: Cu 2 O(s) + C(s) → 2 Cu(s) + CO 2 (g) When 11.5 g of C are allowed to react with 114.5 g of Cu 2 O(s), 87.4 g of Cu are obtained. Find the limiting reagent , theoretical yield and percent yield. 19 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 COMBUSTION REACTIONS A combustion reaction is one in which the elements in a compound react with molecular oxygen to form the oxides of those elements. For example C in a carbon-containing compound will be converted to CO 2 and if there is hydrogen it will be converted to H 2 O Notice that by accurately measuring the mass of CO 2 obtained by combustion of the carbon-containing compound, the mass of carbon in the original sample can be calculated. Similarly, by measuring the mass of H 2 O formed in the reaction, the mass of hydrogen in the original sample can be calculated. These calculations assume that all the carbon in the sample is captured in the CO 2 and that all the hydrogen is captured in the H 2 O EXAMPLE 1: Combustion reaction involving C,H and O only Vitamin C is a compound that contains the elements C. H and O. Complete combustion of a sample of mass 0.2000 g of vitamin C produced 0.2998 g of CO 2 and 0.08185 g of H 2 O. Determine the empirical formula of vitamin C. Molar masses (in g mol-1) : CO 2 = 44.01 H 2 O = 18.02 ; C = 12.01 H = 1.008 O = 16.00 CxH yOz +O2 → x CO2 + y 2 H2O All the C is converted to CO 2 and all the H is converted to H 2 O. 20 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Solution: Step1: Determine the mass of C in CO 2 12.01 g mol −1 Step 2: 44.01 g mol −1 x 0.2998 g CO 2 = 0.08181 g of C Calculate the mass of water hydrogen in water 2 x 1.008 g mol −1 18.02 g mol −1 Step 3: (note: there are 2 mols of hydrogen in water) Calculate the mass of O which is obtained by difference Mass of O Step 4: Moles x 0.08185 g H 2 O = 0.009157g of H = Mass of sample – (mass of C + mass of H) = 0.2000 g – (0.08181 g + 0.00915 g) = 0.1090 g of O mass Convert to moles (Atomic mass ) 0.006812 0.009084 0.006814 0.009084 0.006814 1.33 1 C H ÷ by smallest number of moles 0.006812 0.006812 1 0.006812 O 0.006812 convert to whole numbers by multiplying by 3 1x3 3 1.33 x 3 4 1x3 3 Therefore the empirical formula of vitamin C is C 3 H 4 O 3 21 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur EXAMPLE 2. 2011 Combustion reaction involving C,H,O and N only The compound caffeine contains the elements C, H, N and O. Combustion analysis of a 1.500 g sample of caffeine produces 2.737g of CO 2 and 0.6814 g of H 2 O. A separate further analysis of another sample. of mass 2.500 g of caffeine produces 0.8677 g of NH 3 . Determine the empirical formula of caffeine. Molar masses(in g mol-1) : H = 1.008 C = 12.01 ; N = 14.01 ; O = 16.00 CO 2 = 44.01 ; H 2 O = 18.02 ; NH 3 = 17.04. Important features of this problem are that: 1. 2. You are analysing for 4 elements – C, H, N and O. The analysis is performed on two samples (for example sample 1 and 2) which have different masses. NOTE: In the one sample you analyse for carbon and hydrogen. In the other you analyse for nitrogen. Remember that the oxygen is always obtained by difference. 22 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 Solution: In sample 1 - 1.500g of caffeine Step1: Determine the mass of C in CO 2 12.01 g mol −1 Step 2: 44.01 g mol −1 x 2.737 g CO 2 = 0.7469 g of C Calculate the mass of water hydrogen in water 2 x 1.008 g mol −1 18.02 g mol −1 In sample 2 - 2.500 g of caffeine Step 3. x 0.06814 g H 2 O = 0.07623 g of H Determine the mass of N in NH 3 14.01 g mol −1 Step 4: Note: 17.04 g mol −1 x 0.8677 g NH 3 = 0.7134 g of N Calculate % N in sample 2 = % N in sample 1 The % composition of a pure compound is constant. If you know the percentage of N in sample 1 then the percentage of nitrogen in sample 2 is exactly the same. Therefore % N in sample 2 = Step 5. 0.7134 g 2.500 g x 100 = 28.54 % You must determine the masses of all the elements in the compound in a common sample therefore find the mass of N in sample 1 i.e. 28.54 g 100 g X 1.500 g = 0.4280 g mass of N 23 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur Step 6. 2011 The mass of O in sample 1 is obtained by difference Mass of O = Mass of sample 1 – (mass of C + mass of H + mass of N) = 1.500 g – (0.7469 g + 0.07623 g + 0.4280 g) = 0.2489 g Determine the empirical formula C H N O Mass (g) 0.7469 0.07623 0.4280 0.2489g moles: 0.06219 0.07563 0.03057 0.01555 Atomic mass (g mol-1) 12.01 1.008 14.01 16.00 Divide by the smallest number of mol = 0.01555 4 4.9 ~5 ∴ Empirical formula is 2 1 = C4H5N2O 24 Chemistry for Engineers 1A (CHEM 181) – UKZN – School of Chemistry , Howard College Campus, compiled by A.Bissessur 2011 PRACTICE EXERCISES 1. An 0.1888g sample of a hydrocarbon produces 0.6260g of CO 2 and 0.1602g of H 2 O in combustion analysis. Its molecular weight is found to be 106 amu. For this hydrocarbon determine (a) its mass percent composition (c ) its molecular formula (b) 2. its empirical formula Ans. 90.47% C. 9.50% H Ans. C 4 H 5 Ans. C 8 H 10 Dimethylhydrazine is a carbon–hydrogen-nitrogen containing compound. Combustion analysis of a 0.312g sample of the compound produces 0.458 g of CO 2 . From a separate 0.525 g sample the nitrogen content is converted to 0.244 g N 2 . (a) (b) 3. What is the empirical formula of dimethylhydrazine? Ans. CH 4 N If the molecular weight was found to be 60.02 what is the molecular formula of the compound? Ans. C 2 H 8 N 2 A 1.35 g sample of a substance containing C. H. N and O is burned in air to produce 0.810 g of H 2 O and 1.32 g of CO 2 . In a separate analysis of the same substance all of the N in a sample of mass 0.735 g is converted to 0.284g NH 3 . Determine the empirical formula of the substance. Ans. CH 3 NO 25