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Topic 3 Mass Relations and Stoichiometry

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Mass and Moles of a Substance Chemistry requires a method for determining the numbers of molecules in a given mass of a substance which has lead to the development of the mole (quantity of substance to be discussed later). –This allows the chemist to carry out “recipes” for compounds based on the relative numbers of atoms involved. –stoichiometry - the calculation involving the quantities of reactants and products in a chemical equation. 2

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Molecular Weight and Formula Weight The molecular weight (for molecular substances) of a substance is the sum of the atomic weights of all the atoms in a molecule of the substance. –For, example, a molecule of H 2 O contains 2 hydrogen atoms (at 1.01 amu each) and 1 oxygen atom (16.00 amu), giving a molecular weight of amu. H: 2 x 1.01 amu = 2.02 amu O: 1 x amu = amu amu (mass of 1 molecule of H 2 O) 3

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Molecular Weight and Formula Weight The formula weight of a substance is the sum of the atomic weights of all the atoms in one formula unit of the compound, whether molecular or not. Na: 1 x amu = amu Cl: 1 x amu = amu amu (mass of 1 FU NaCl) 4 iron (III) sulfate,Fe 2 (SO 4 ) 3 Fe: 2 x amu = amu S: 3 x amu = amu O: 12 x amu = amu amu (mass of 1 FU Fe 2 (SO 4 ) 3 ) Glucose, C 6 H 12 O 6 C: 6 x amu = amu H: 12 x 1.01 amu = amu O: 6 x amu = amu amu (mass of 1 molecule) one formula unit (FU) of NaCl: Note: molecular wt and formula wt are calculated the same way.

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Mass and Moles of a Substance The Mole Concept –A mole is defined as the quantity of a given substance that contains as many molecules or formula units as the number of atoms in exactly 12 grams of carbon–12. –The number of atoms in a 12-gram sample of carbon–12 is called Avogadro’s number (N a ). The value of Avogadro’s number is x mole = x X X = ions, particles, atoms, molecules, items, etc. 1 mole Na 2 CO 3 x FU Na 2 CO 3 1 mole CO 2 x molecules CO 2 5

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Mass and Moles of a Substance The molar mass (M m ) of a substance is the mass of one mole (6.022 x FU or molecules) of a substance. This is the term we will use the most in the course and is done the same way as formula wt. except using gram instead of amu. –For all substances, molar mass, in grams per mole, is numerically equal to the formula weight in atomic mass units. –That is, one mole of any element weighs its atomic mass in grams. 6 1 molecule of H 2 O - MW = amu 1 mole of H 2 O - M m = g H 2 O M m of 1 mole of MgSO 4. 7H 2 O Mg: 1 x g = g S: 1 x g = g O: 4 x g = g g/mol MgSO 4. 7H 2 O H:14 x 1.01 g = g O: 7 x g = g Note: we can use M m as a conversion factor between grams and mols. Note: must account for mass of water in hydrates x molecules

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How is it possible that M m and FW/MW are the same value but different units? A.)What is the mass in grams of one Cl atom? B.)in one HCl molecule? 7 Let’s convert 1 Na atom g/mol Notes: Converting mass to mols or vice versa will require using molar mass. Converting mass to atoms, molecules, ions, etc. or vice versa will require going through mols by using Avogadro’s number. Avogadro’s number and amu are both based on carbon-12 and inverse values of each other.

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Mass and Moles of a Substance Mole calculations –Converting the number of moles of a given substance into its mass, and vice versa, is fundamental to understanding the quantitative nature of chemical equations g NaCl1 mol NaCl 1 mol NaCl58.44 g NaCl 8 M m NaCl = g/mol Converting mass to mols or vice versa will require using molar mass. Note: we can use M m as a conversion factor between grams and mols with g in numerator or denominator.

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Mass and Moles of a Substance Mole calculations Suppose we have 5.75 moles of magnesium. What is its mass? 9 Note: we use M m as a conversion factor between grams and mols with mol in this case being placed in the denominator to cancel with the 5.75 mols we are converting to g.

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Mass and Moles of a Substance Mole calculations Suppose we have grams of H 2 O. How many moles does this represent? 10

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Mass and Moles and Number of Molecules or Atoms The number of molecules or atoms in a sample is related to the moles of the substance by Avogadro’s #: How many molecules are there in 56 mg HCN? HW code: moles

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Determining Chemical Formulas The percent composition of a compound is the mass percentage of each element in the compound. –We define the mass percentage of “A” as the parts of “A” per hundred parts of the total, by mass. That is, 12 If given the %A by mass, it is useful to put the percentage in ratio form for dimensional analysis calculations.

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Mass Percentages from Formulas Let’s calculate the percent composition (%C, %H) of one molecule of butane, C 4 H 10. First, we need the molecular wt of C 4 H 10. Now, we can calculate the percents (basically, part/whole). 13 What if we wanted the %C & %H for 1 mol of butane? Same calculation and results except we would use molar mass, g/mol, instead of amu/atom. Note: % is a unit like g, etc. Don’t use the % button on calculator.

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How many grams of carbon are there in 83.5 g of formaldehyde, CH 2 O, (40.0% C, 6.73% H, 53.3% O)? 14 rewrite % into ratio = 33.4 g C

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An unknown acid contains only C, H, O. A 4.24 mg sample of acid is completely burned. It gives 6.21 mg of CO 2 and 2.54 mg H 2 O. What is mass% of each element in the unknown acid? 15 %C, H, O in sample unknown acid CO 2 + H 2 O O2O2 has C, H, O 4.24 mg 6.21 mg 2.54 mg C: H: O: Total mass = 4.24 mg = mass C + mass H + mass O = 1.69 mg mg + mass O mass O = 4.24 mg – 1.69 mg – mg = 2.26 mg O %C: %H: %O: 100% % % = 53.4% O goal of problem Note: We did the same calculation for H as we did for C except we did it in terms of mg and mmol to demonstrate how taking advantage of the prefix can simplify your work by adding m to the mols and g of the molar mass conversion factor (mmol/mg) and mol to mol ratio (mmol/mmol). This eliminates the useless conversion from mg to g and back again. mol to mol ratio needed to convert from one species to another Alternatively, we could have just subtracted the percent C and H from 100% to determine the %O.

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Determining Chemical Formulas We can determine the formula of a compound from the percent composition. –The percent composition of a compound leads directly to its empirical formula. –An empirical formula (or simplest formula) for a compound is the formula of the substance written with the smallest integer (whole number) subscripts. –From the empirical formula, we can find the molecular formula of a substance which will be a multiple of the empirical formula based on its molar mass. 16

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Determining Chemical Formulas Benzoic acid is a white, crystalline powder used as a food preservative. The compound contains 68.8% C, 5.0% H, and 26.2% O by mass. What is its empirical formula? In other words, give the smallest whole-number ratio of the subscripts in the formula based on mols (C:H:O) Cx HyOzCx HyOz 17 mols

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Determining Chemical Formulas For the purposes of calculations of this type, we will assume we have grams of sample; therefore, benzoic acid at 68.8% C means which means the mass of each element equals the numerical value of the percentage. Since x, y, and z in our formula represent mole-mole ratios, we must first convert these masses to moles. Cx HyOzCx HyOz 18

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Determining Chemical Formulas This isn’t quite a whole number ratio, but if we divide each number by the smallest of the three, a better ratio will emerge. We are dividing by the smallest number to get the species all on the same scale – “normalizing” the values. Our assumed grams of benzoic acid (68.8%C, 5.0%H, 26.2%O) would contain: 19 Note: 68.8g g g = assumed g sample

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Determining Chemical Formulas Next step is to get all species on the same scale, basically normalizing to moles of smallest species (in this case, 1.63 mols of O) for the purpose of getting values that can easily be converted to whole number ratios. now it’s not too difficult to see that the smallest whole number ratio is 7:6:2 (multiple everything by 2 to get whole number. The empirical formula is C 7 H 6 O 2. 2 x C 7 H 6 O 2 20 C 3.5 H 3 O 1 This is the empirical as well as molecular formula of benzoic acid because the molar mass of the empirical formula is the same as the molecular formula of benzoic acid.

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Determining Chemical Formulas An empirical formula gives only the smallest whole-number ratio of atoms in a formula. The molecular formula should be a multiple of the empirical formula (since both have the same percent composition). C 2 H 3 O 2 empirical formula (lowest whole # ratio) C 4 H 6 O 4 molecular formula (multiple of 2 x emp) C 8 H 12 O 8 molecular formula (multiple of 4 x emp) Which is not an empirical formula meaning not lowest whole #? CH 4 CH 4 OC 2 H 4 O 2 C 2 H 6 O To determine the molecular formula, we must know the molecular weight (molar mass) of the compound. 21 C 2 H 4 O 2 is divisible by 2; CH 2 O would be its empirical formula

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Determining Chemical Formulas Determining the molecular formula from the empirical formula. molar mass = n x empirical formula mass where n is the multiple factor n = molar mass empirical mass 22

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Acetic Acid contains 39.9% C, 6.7% H, 53.4% O. Determine empirical formula. The molecular mass of acetic acid is 60.0 g/mol. What is the molecular formula? HW We assume g sample meaning we have 39.9 g C, 6.7 g H, 53.4 g O and calculate the mols of each. empirical formula = CH 2 OM m = g/mol 2 x CH 2 O C 2 H 4 O 2 Next, we get them on same scale by dividing each by the smallest mols, 3.33 mols code: formula

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Stoichiometry: Quantitative Relations in Chemical Reactions Stoichiometry is the calculation of the quantities of reactants and products involved in a chemical reaction. –It is based on the balanced chemical equation and on the relationship between mass and moles (molar mass is an important concept here; g mol, mol g) and mol to mol ratios. –Such calculations are fundamental to most quantitative work in chemistry. 24 What we are discussing deals with mol to mol ratios (very important concept) and is the basis of many calculations.

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The balanced chemical equation can be interpreted in numbers of molecules, but generally chemists interpret equations as “mole-to-mole” relationships. Lets look at the following reaction: 1 molecule N molecules H 2 2 molecules NH g N 2 + 3(2.02 g) H 2 2 (17.04 g) NH g g g g = g Molar Interpretation of a Chemical Equation 25 If the number of each particular atom is the same on both sides, the Law of Conservation of Mass will be preserved and the mass of reactants will be equal to the mass of the products.

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Molar Interpretation of a Chemical Equation Suppose we wished to determine the number of moles of NH 3 we could obtain from 4.8 mol H 2. We will assume N 2 is in excess which means H 2 is limited and will dictate the amount of product that will be formed; once the H 2 is gone, the reaction will stop. 26 We should realize that we have conversion factors that exist from the mol to mol ratios available from the balanced equation to go from one species to another.

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Mass Relationships in Chemical Equations How many grams of HCl are required to react with 5.00 grams MnO 2 according to this equation? 27 ? g 5.00 g Note: To get from one substance to another requires the use of mol to mol ratios.

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Mass Relationships in Chemical Equations How many grams of CO 2 gas can be produced from 1.00 kg Fe 2 O 3 ? Fe 2 O 3 (s) + 3 CO (g) 2 Fe (s) + 3 CO 2 (g) HW kg assume excess ? g code: stoich

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Limiting Reagent The limiting reactant (or limiting reagent) is the reactant that is entirely consumed when the reaction goes to completion. The limiting reagent ultimately determines how much product can be obtained. –For example, bicycles require one frame and two wheels. If you have 20 wheels but only 5 frames, how many bicycles can be made? o o o o o o o o o o o o o o o o o o o o 20 wheels 1 frame + 2 wheels 1 bike 29 R + R P 10 wheels in excess; therefore, frames are limiting factor Smaller value is correct answer or you can determine which is the limiting reagent and only calculate that value. Reaction stops when one component, limiting reagent, is exhausted Basically, we must find out which species will run out first because it will dictate how much product will form.

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Limiting Reagent If 0.30 mol Zn is added to hydrochloric acid containing 0.52 mol HCl, how many grams of H 2 are produced? mol 0.52 mol ? g The maximum product possible is based on the limiting reagent; smaller mols of product is maximum possible based on the limiting reagent which is HCl in this case. limiting reagent HCl First, we calculate how many mols of H 2 is possible for each reactant. We use the mols of H 2 possible from the limiting reagent, HCl, to determine the mass of H 2. Note: The limiting reagent is not necessarily the species with the smaller mass or #mols; you must account for the mol-to-mol ratio as demonstrated in this problem.

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If 7.36 g Zn was heated with 6.45 g sulfur, what amount of ZnS was produced? g 6.45 g ? g smaller mols; limiting reagent This is known as the theoretical yield. mols produced by each reactant:

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Theoretical and Percent Yield The theoretical yield of product is the maximum amount of product that can be obtained from given amounts of reactants. The percentage yield is the actual yield (experimentally determined) expressed as a percentage of the theoretical yield (calculated like in previous example). 32 Once again, % is a unit.

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Theoretical and Percent Yield To illustrate the calculation of percentage yield, recall that the theoretical yield of ZnS in the previous example was 11.0 g ZnS. If the actual yield experimentally for the reaction is 9.32 g ZnS, what is the %yield? 33 experimental value theoretical value; calculated value % is unit, not button on calculator

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If 11.0 g CH 3 OH are mixed with 10.0 g CO, what is the theoretical yield of HC 2 H 3 O 2 in the following reaction? If the actual yield was 19.1 g, what is the %yield of HC 2 H 3 O 2 ? CH 3 OH (l) + CO (g) HC 2 H 3 O 2 (l) g 10.0 g ? g smaller mols; limiting reagent theoretical yield experimental value theoretical value; calculated value HW 25 mols produced by each reactant: code: limiting

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