Chapter 3: Stoichiometry Oct 6 2:25 AM What is Stoichiometry? The Meaning of the Word The word Stoichiometry derives from two Greek words: stoicheion (meaning "element") and metron (meaning "measure"). Stoichiometry deals with calculations about the masses (sometimes volumes) of reactants and products involved in a chemical reaction. It is a very mathematical part of chemistry, so be prepared for lots of calculator use. Oct 6 2:25 AM 1
3.1 Counting by Weighing Solve problems related to determining the number of atoms you have based on total mass and average mass. Jellybeans can be counted by weighing 3.2 Atomic Mass Calculate average atomic masses from isotope data Calculate relative isotope abundance from pertinent mass spectral data. Mass Spectrometer. 12C is assigned a mass of exactly 12 atomic mass units(amu), and the masses of all other atoms are given relative to this standard. Oct 3 3:44 PM Example 3.2 A Calculation of Average Atomic Masses from Isotopic Data. A sample of metal "M" is vaporized and injected into a mass spectrometer. The mass spectrum tells us that 60.10% of the metal is present as 69 M and 39.90% is present as 71 M. The mass value for 69 M and 71 M are 68.93 amu and 70.92 amu respectively. What is the average atomic mass of the element? What is the element? To calculate Weighted Average use: Oct 6 2:31 AM 2
Example 3.2 B Calculation of Relative Isotope Abundance The element indium exists naturally as two isotopes. 113 In has a mass of 112.9043 amu, and 115 In has a mass of 114.9041 amu. The average atomic mass of indium is 114.82 amu. Calculate the percent relative abundance of the two isotopes of indium. Oct 6 3:14 AM 3.3 THE MOLE Interconvert between mole, mass, and the number of particles of a given element. The mole is the key to many chemical calculations. A mole is defined as the number equal to the number of carbon atoms in exactly 12 grams of pure 12 C. 1mole of anything = 6.022 x 10 23 units of that thing One mole of ANY substance contains Avogardo's number of particles. Key problem solving relationship: The average mass of one atom of a substance expressed in amu is the same number as the mass of one mole of a substance expressed in grams. Chemistry Lovers Celebrate Mole Day 1 atom of 20 The mole unit song Ne = 20.18 amu 1 mole of 20 Ne = 20.18 grams 1 mole of 20 Ne = 6.022 x 10 23 atoms of Ne Oct 3 4:00 PM 3
Oct 17 12:00 PM Samples containing one mole each of copper, aluminum, iron, sulfur, iodine, and mercury Example 3.3 A Conversion Among Grams, Atoms, and AMUs How many grams does a sample containing 34 atoms of neon weight? Example 3.3 B Conversion Between Atoms, Moles, and Mass A sample of elemental silver (Ag) has a mass of 21.46 g. How many moles of silver are in the sample? How many atoms of silver are in the sample? Example 3.3 C Practice with Conversions What is the weight of 7.81 x 10 22 atoms of calcium? Oct 23 10:03 PM 4
3.4 Molar Mass Calculate the molar masses. Interconvert among molar mass, moles, mass, and number of particles in a given sample. The Molar Mass of a substance is the mass in grams of one mole of the compound. Example 3.4 A Calculations of the Molar mass of a compound Calculate the molar mass of potassium dichromate. Example 3.4 B Converting Among Molar Mass, Moles, Mass, and Number of Particles How many micrograms are in 3.82 x 10 7 moles of pyrogallol, C 6 H 6 O 3? Oct 6 7:13 AM Example 3.4 C Practice with Conversions Freon 12, which has the formula of CCl 2 F 2, is used as a refrigerant in air conditions and as a propellant in aerosol cans. Given a 5.6 mg sample of Freon 12: a. Calculate the number of molecules of Freon 12 in that sample. b. How many mg of chlorine are in the sample? Oct 6 3:23 AM 5
3.5 Learning to Solve Problems Solving problems in a flexible, creative way is called conceptual problem solving Become independent problem solver. With a new problem you need: a. Decide on a final goal; b. work backwards from the final goal; c. Ask" Does the answer makes sense?" 3.6 Percent Composition of Compounds Calculate the mass percent of each element in the compound. There are 3 steps to calculating the mass percent of each element in a compound. a. Compute the molecular mass of the compound. b. Calculate how much the molecular mass comes from each element c. Divide each element's mass contribution by the total molecular mass, and multiply by 100 to convert to percent. Example 3.6 A Determination of the mass percent in a Compound Calculate the mass percent of each element in Glucose, C 6 H 12 O 6 Oct 10 10:19 AM Example 3.6 B Practice with Mass Percent Calculate the mass percent of each element in potassium ferricyanide, K 3 Fe(CN) 6? Checking the Figures Adding up the percentages does not add up to 100% due to the rounding to 2 sig. figs after the decimal point for the molar mass which leads to a loss of 0.01%. In such cases we say the answers are correct "within round off error" Oct 10 10:19 AM 6
3.7 Determining the Formula of a Compound Determine the empirical formula of a compound Calculate the molecular formula of a compound The empirical formula is represented by the simplest whole number ratio of atoms in a compound. Examples: CH, CH 4, CH 2 O, K 2 Cr 2 O 7 The molecular formula is the actual ratio of atoms in a compound. Examples: C 6 H 6, C 6 H 12 O 6, N 2 H 4 The empirical and molecular formulas can be the same. Examples of substances whose empirical and molecular formulas differ. Notice that: molecular formula = (empirical formula) n, where n is an integer. Oct 10 10:19 AM Example 3.7 A Determination of the Empirical Formula of a Compound The analysis of rocket fuel showed that it contained 87.4% nitrogen and 12.6% hydrogen by weight. Mass spectral analysis showed the fuel to have a molar mass of 32.05 g/mol. What are the empirical and molecular formulas of the compound? To solve empirical formula problems that do not involve combustion (added oxygen) 1. Assume the compound has a mass of exactly 100 grams. You can therefore convert percentage to grams. 2. Calculate the moles of each kind of atom present 3. Determine the simplest whole number ratios by dividing the moles of each element by the smallest calculated mole value Numbers very close to whole numbers, such as 9.92 and 1.08, should be rounded to whole numbers. Numbers such as 2.25, 4.33, and 2.72 should NOT be rounded to whole numbers. Read the summary of methods for obtaining empirical and molecular formulas. p. 96 Oct 11 12:37 PM 7
Example 3.7 B Determination of the Empirical Formula of a Compound Determine the empirical formula and molecular formulas for a deadly nerve gas that gives the following mass percent analysis: C = 39.10% H = 7.67% O = 26.21% P = 16.82% F = 10.30% The total mass is known to be 184.1 grams. Determination of the Empirical Formula of a Hydrate In an experiment, 4.31 g of sodium carbonate hydrate are heated. Following the heating the dry remains (called anhydrate) weigh 3.22 g. What is the formula for the hydrate sodium carbonate? Oct 12 12:31 PM Example 3.7 C Determining the Empirical Formula From Combustion Data A combustion device was used to determine the empirical formula of a compound containing ONLY carbon, hydrogen and oxygen. A 0.6349 g sample of the unknown produced 1.603g of CO 2, and 0.2810 g of H 2 O. Determine the empirical formula of the compound. Solution tips: 1. Assume that the combustion was complete. Therefore, all the carbon was converted to CO 2 and all the hydrogen was converted to H 2 O. 2. Calculate the grams of carbon in the given mass of CO 2 and the grams of hydrogen in the given mass of water. 3. Based on the law of conservation of mass and the given mass of the original compound you know that grams O = total grams (grams C + grams H) 4. Follow the steps for finding the empirical formula Oct 12 12:31 PM 8
3.8 Chemical Equations State the meaning of each part of a chemical reaction State a variety of different relationships that are inferred from a chemical equation. Chemical equation are all of the form CH 4 + 2O 2 Reactants CO 2 + 2H 2 O Products In a chemical reactions atoms have been reorganized. Bonds have been broken and new ones have been formed. Atoms are neither created nor destroyed. All atoms present in the reactants must be accounted for among the products. Oct 10 10:19 AM Oct 13 8:50 PM 9
Example 3.8 A Interpreting a Chemical Equation State, completely, what is happening in the reaction given below. Include in your answer the physical states of each component of the reaction. Na 2 CO 3(aq ) + 2HCl (aq ) CO 2(g) + H 2 O (l) + 2NaCl (aq ) Example 3.8 B Relating Reactions and Products of a Chemical Equations Show, by means of molar masses, that the matter is neither created nor destroyed in the equation given below. C 2 H 6(l) + 3O 2(g) 2CO 2(g) + 3H 2 O (g) Oct 13 8:50 PM 3.9 Balancing Chemical Equations Balance many chemical equations A balanced chemical equation means that the number of atoms of each element on the reactants' side equals the number of atoms of each element of atoms of each element on the products' side. Balancing an Equation with the Jigsaw Oct 13 8:50 PM 10
GUIDELINES FOR BALANCING A CHEMICAL EQUATION 1. Use Correct formulas. Never change a molecular structure. Only use coefficients. 2. Place a coefficient in front of each formula. The coefficients must be whole numbers. 3. Find the atoms that are in only one compound on the reactants' side. Balance those first. 4. Balance polyatomic ions as a single unit. 5. In general leave O and H until the very end. 6. Always double check AFTER balancing!!! Example 3.8A Balancing Chemical Equation Balance the following chemical equation. NaOH (aq ) + H 3 PO 4(aq ) Na 3 PO 4(aq ) + H 2 O (l) Example 3.8B Practice with Balancing Balance the following chemical equation. C 4 H 10( g) + O 2(g) CO 2(g) + H 2 O (g) Oct 13 8:50 PM 3.10 Stoichiometric Calculations: Amounts of Reactants & Products Calculate the amount of products obtained from a given amount of reactant Calculate the amount of reactants required to generate a desired amount of product. Calculating Masses of Reactants and Products in Chemical reactions 1. Balance the equation for the reaction. 2. Convert the known mass of the reactant or the product to moles of that substance. 3. Use the balanced equation to set up the appropriate mole ratios. 4. Use the appropriate mole ratio to calculate the number of moles of the desired reactant or product. 5. Convert from moles back to grams if required by the problem. Remember... Double check the balanced chemical equation. Don't multiply the molar mass of a substance by the coefficient in the problem BEFORE using it in one of the steps above. For example, if the formula says 2H 2 O, DON'T use 36.0 g/mol, use 18.0 g/mol. Round off only once after all calculations are done. Oct 13 8:50 PM 11
Analogies in Stoichiometry Bike by Parts Consider the following Analogy: 2 Wheels + 1 Body + 1 Handle bar + 1 Gear Chain = 1 bike How many bikes can be produce given, 8 wheels, 5 bodies, 6 handle bar and 5 gear chain. Jan 31 5:49 PM Example 3.10A Amount of product from a Given Amount of Reactant Given the following reaction: Na 2 S (aq ) + AgNO 3(aq ) Ag 2 S (g) + NaNO 3(aq ) How many grams of Ag 2 S can be generated from the reaction of 3.94 g of AgNO 3 with excess Na 2 S? Strategy 1. Always balance the chemical equation! The mole ratio conversion factor acts as the bridge between AgNO 3 and Ag 2 S. This leads to the following strategy: molar mass g AgNO 3 moles AgNO 3 mole ratio moles Ag 2 S molar mass g Ag 2 S Oct 13 8:50 PM 12
Example 3.10 B Amount of Reactant Needed to Produce a Product Aspirin is prepared by the reaction of salicylic acid (C 7 H 6 O 3 ) and acetic acid anhydride (C 4 H 6 O 3 ). How many grams of salicylic acid (sal) are needed to make 500 aspirin tablets weighing 1.00 g each (assuming 100% yield)? Strategy number of aspirin tablets C 7 H 6 O 3 + C 4 H 6 O 3 C 9 H 8 O 4 + HC 2 H 3 O 2 Salicylic acid mass of tablets g of aspirin acetic anhydrate molar mass moles of aspirin aspirin mole ratio acetic acid moles of salicylic acid molar mass g of salicylic acid Oct 15 10:01 AM 3.11 Calculations Involving a Limiting Reactant Identify the limiting reactant. Solve problems involving a limiting reactant. Calculate percent yield of a product Solving Stoichiometry Problems Involving Masses of Reactants and Products. 1. Write and balance the equation for the reaction. 2. Convert the known mass of the substances to moles. 3. Determine which reactant limiting. 4. Using the amount of the limiting. reactant and the appropriate mole ratios, compute the number of moles of the desired product. 5. Convert from moles to grams using molar mass. Oct 20 10:19 PM 13
Example 3.11A A Calculations Involving a Limiting Reactant Sodium hydroxide reacts with phosphoric acid to give sodium phosphate and water. If 17.80 g of NaOH is mixed with 15.40 g of H 3 PO 4, a. How many grams of Na 3 PO 4 can be formed? b. How many grams of the excess reactant remain un reacted? c. If the actual yield of Na 3 PO 4 was 15.00 g, what is the percent yield of Na 3 PO 4? Strategy 1. Write a balanced chemical equation for this reaction 3NaOH (aq ) + H 3 PO 4(aq ) Na 3 PO 4(aq ) + 3H 2 O (l) 2. Determine which reactant limits the amount of product formed by calculating the amount of product formed by each reactant. The reactant that forms less product is limiting. g of reactant molar mass moles of reactant mole ratio moles of product molar mass g of product 3. To determine grams of excess reactant, you must calculate how many moles of excess reactant were actually used. # moles excess = # moles original # moles used Then convert moles to grams. 4. The percent yield = actual yield theoretical yield x 100% Oct 13 8:50 PM Example 3.11B Tying it all together. The space shuttle environmental control system handles excess CO 2 (which the astronauts breathe out it is 4% by mass of exhaled air) by reacting it with lithium hydroxide pellets to form lithium carbonate and water. If there were 7 astronauts on board the shuttle, and each exhales 20 liters of air minute, how long could clean air be generated if there were 25,000 g of lithium hydroxide pellets available for each shuttle mission? Assume the density of air is 0.0010 g/ml. Oct 21 12:23 AM 14