# Mass Relations and Stoichiometry

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Mass Relations and Stoichiometry
Topic 3 Mass Relations and Stoichiometry

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

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 H2O 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 amu = amu O: 1 x amu = amu 18.02 amu (mass of 1 molecule of H2O) 2

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. one formula unit (FU) of NaCl: Na: 1 x amu = amu Cl: 1 x amu = amu 58.44 amu (mass of 1 FU NaCl) iron (III) sulfate, Fe2(SO4)3 Fe: 2 x amu = amu S: 3 x amu = amu O: 12 x amu = amu amu (mass of 1 FU Fe2(SO4)3) Glucose, C6 H12 O6 C: 6 x amu = amu H: 12 x amu = amu Note: molecular wt and formula wt are calculated the same way. O: 6 x amu = amu amu (mass of 1 molecule) 2

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 (Na). The value of Avogadro’s number is x 1023. 1 mole = x 1023 X X = ions, particles, atoms, molecules, items, etc. 1 mole Na2CO3  x 1023 FU Na2CO3 1 mole CO2  x 1023 molecules CO2 2

Mass and Moles of a Substance
The molar mass (Mm) of a substance is the mass of one mole (6.022 x 1023 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. 1 molecule of H2O - MW = amu  1 mole of H2O - Mm = g H2O 6.022 x molecules Note: we can use Mm as a conversion factor between grams and mols. Mm of 1 mole of MgSO4 . 7H2O Mg: 1 x g = g S: 1 x g = g Note: must account for mass of water in hydrates O: 4 x g = g H:14 x g = g O: 7 x g = g g/mol MgSO4 . 7H2O 2

Let’s convert 1 Na atom  g/mol
How is it possible that Mm 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? Avogadro’s number and amu are both based on carbon-12 and inverse values of each other. 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.

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. 58.44 g NaCl 1 mol NaCl 1 mol NaCl g NaCl Converting mass to mols or vice versa will require using molar mass. Mm NaCl = g/mol Note: we can use Mm as a conversion factor between grams and mols with g in numerator or denominator. 2

Mass and Moles of a Substance
Mole calculations Suppose we have 5.75 moles of magnesium. What is its mass? Note: we use Mm 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. 2

Mass and Moles of a Substance
Mole calculations Suppose we have grams of H2O. How many moles does this represent? 2

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 20-22 code: moles 2

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, If given the %A by mass, it is useful to put the percentage in ratio form for dimensional analysis calculations. 2

Mass Percentages from Formulas
Let’s calculate the percent composition (%C, %H) of one molecule of butane, C4H10. First, we need the molecular wt of C4H10. Now, we can calculate the percents (basically, part/whole). Note: % is a unit like g, etc. Don’t use the % button on calculator. 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. 2

How many grams of carbon are there in 83
How many grams of carbon are there in 83.5 g of formaldehyde, CH2O, (40.0% C, 6.73% H, 53.3% O)? rewrite % into ratio = 33.4 g C

An unknown acid contains only C, H, O. A 4
An unknown acid contains only C, H, O. A 4.24 mg sample of acid is completely burned. It gives 6.21 mg of CO2 and 2.54 mg H2O. What is mass% of each element in the unknown acid? goal of problem O2 %C, H, O in sample unknown acid  CO2 + H2O has C, H, O 4.24 mg 6.21 mg mg mol to mol ratio needed to convert from one species to another C: 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. 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: %O: 100% % % = 53.4% O %H: Alternatively, we could have just subtracted the percent C and H from 100% to determine the %O.

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. 2

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 HyOz mols 2

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 HyOz 2

Determining Chemical Formulas
Our assumed grams of benzoic acid (68.8%C, 5.0%H, 26.2%O) would contain: 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. Note: 68.8g g g = assumed g sample 2

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 C7H6O2 . 2 x  C7H6O2 C3.5 H3 O1 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. 2

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). C2H3O empirical formula (lowest whole # ratio) C4H6O molecular formula (multiple of 2 x emp) C8H12O molecular formula (multiple of 4 x emp) Which is not an empirical formula meaning not lowest whole #? CH4 CH4O C2H4O2 C2H6O To determine the molecular formula, we must know the molecular weight (molar mass) of the compound. C2H4O2 is divisible by 2; CH2O would be its empirical formula 2

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 2

Acetic Acid contains 39. 9% C, 6. 7% H, 53. 4% O
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? 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. Next, we get them on same scale by dividing each by the smallest mols, 3.33 mols empirical formula = CH2O Mm= g/mol 2 x CH2O  C2H4O2 HW 23 code: formula

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. What we are discussing deals with mol to mol ratios (very important concept) and is the basis of many calculations. 2

Molar Interpretation of a Chemical Equation
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 molecules NH3 28.02 g N (2.02 g) H  2 (17.04 g) NH3 28.02 g g  g 34.08 g = g 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. 2

Molar Interpretation of a Chemical Equation
Suppose we wished to determine the number of moles of NH3 we could obtain from 4.8 mol H2. We will assume N2 is in excess which means H2 is limited and will dictate the amount of product that will be formed; once the H2 is gone, the reaction will stop. 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. 2

Mass Relationships in Chemical Equations
How many grams of HCl are required to react with 5.00 grams MnO2 according to this equation? ? g g Note: To get from one substance to another requires the use of mol to mol ratios. 2

Mass Relationships in Chemical Equations
How many grams of CO2 gas can be produced from 1.00 kg Fe2O3? Fe2O3 (s) CO (g)  2 Fe (s) CO2 (g) 1.00 kg assume excess ? g HW 24 code: stoich 2

10 wheels in excess; therefore, frames are limiting factor
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 wheels 1 frame wheels  1 bike R + R  P Reaction stops when one component , limiting reagent, is exhausted 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. Basically, we must find out which species will run out first because it will dictate how much product will form. 2

Limiting Reagent If 0.30 mol Zn is added to hydrochloric acid containing 0.52 mol HCl, how many grams of H2 are produced? 0.30 mol mol ? g First, we calculate how many mols of H2 is possible for each reactant. 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 We use the mols of H2 possible from the limiting reagent, HCl, to determine the mass of H2. 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. 2

smaller mols; limiting reagent
If 7.36 g Zn was heated with 6.45 g sulfur, what amount of ZnS was produced? 7.36 g g ? g mols produced by each reactant: smaller mols; limiting reagent This is known as the theoretical yield. 2

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). Once again, % is a unit. 2

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? experimental value % is unit, not button on calculator theoretical value; calculated value 2

smaller mols; limiting reagent
If 11.0 g CH3OH are mixed with 10.0 g CO, what is the theoretical yield of HC2H3O2 in the following reaction? If the actual yield was 19.1 g, what is the %yield of HC2H3O2? CH3OH (l) + CO (g)  HC2H3O2 (l) 11.0 g g ? g mols produced by each reactant: smaller mols; limiting reagent theoretical yield experimental value theoretical value; calculated value HW 25 code: limiting 2