The Mole, Avogadro s Number, and Molar Mass

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1 The Mole, Avogadro s Number, and Molar Mass Example: How many atoms are present in 2.0 kg of silver? (1 amu = x10-24 g) Example: How many molecules are present in 10. mg of smelling salts, (NH 4 ) 2 CO 3? First find.. formula (or molecular) mass: mass in amu of one formula unit (or molecule) of cmpd. To calculate.. Formula/molecular mass = sum of atomic masses of all atoms present in cmpd. Problem.. Don t work with individual atoms, molecules, or formula units in lab. Can t even see a sample of chemical until have >10 15 molecules present. Choose to work with collection of molecules on larger scale..moles!! Mole: one mole of any substance contains the same # particles as the atoms in exactly 12 g of 12 C. How many atoms is this? 12 g 12 C x 1 amu x 1 atom 12 C = 6.022x10 23 atoms x10-24 g 12 amu So. 1 mol of anything = 6.022x10 23 things Avogadro s Number (N A ) = 6.022x mol How many moles is 6.091x10 32 molecules of water? How many molecules in 0.75 mol N 2 O 5? 1

2 Subscripts within chemical formula can be used as conversion factors!! In mol Cl 2 O 7, how many atoms of oxygen are present? How many moles of calcium are combined with 7.67 mol N in Ca 3 N 2? Microscale measure chemicals in terms of atoms, molecules, and f.u. (atomic scale) Macroscale measure chemicals in terms of moles or mass (g, lb, kg ) (lab scale) Use Avogadro s number whenever convert macroscale microscale. Use molar mass whenever convert moles mass. Molar Mass Molar Mass: mass (in g) of one mole of a substance. Is numerically equal to the atomic mass (or formula/molecular mass). 1 atom 12 C = 12 amu Atomic Mass 1 mol 12 C = 12 g Molar Mass 1 atom Br = amu 1 mol Br = g 1 f.u. (NH 4 ) 2 CO 3 = amu 1 mol (NH 4 ) 2 CO 3 = g What is the mass of 5.2 mol beryllium? How many moles is 211 g molybdenum? 2

3 What is the mass of mol sodium phosphate? How many moles is g tetraphosphorus decaoxide? What is the mass (in g) of 1 molecule of P 4 O 10? (Give the answer w/4 sf.) In a sample of Fe 3 O 4 there are 11.7 g of oxygen. What mass of iron is combined with the oxygen? Percentage Composition (Theoretical Weight/Mass Percent) As an example..in lab, a student attempted to prepare the compound iron(iii) chloride. The student sent a small portion of the sample away for chemical analysis (Gailbraith Labs). The lab returned the following results of percentages of each element in the compound. Element Exp. % Fe 34.0% Cl 66.0% Did the student prepare iron(iii) chloride?? To decide, calculate the theoretical mass percent of each element in the compound. Theoretical Mass Percent = mass of element in 1 mol x 100 mass of 1 mol of cmpd 3

4 Calculate the theoretical mass percent of carbon in LSD (C 20 H 25 N 3 O). In 7.59 g CO 2, what mass of carbon is present? What mass of oxygen is present? Chemical Formulas: Molecular vs. Empirical Molecular formula - chemical formula with subscripts that give actual whole # ratio of elements in a compound. Molecular formula is a whole # multiple of the empirical formula. Empirical formula chemical formula with subscripts that give the smallest whole # ratio of elements in a compound. Compound Molec. Formula Emp. Formula acetylene C 2 H 2 CH ethane C 2 H 6 CH 3 benzene C 6 H 6 CH butane C 4 H 10 C 2 H 5 Note: Ionic compounds only have empirical formulas due to the definition of the formula unit. 4

5 Calculation of Empirical Formula from Wt% and Mass Data Step 1: Find masses of all elements present. Step 2: Convert masses to moles. Step 3: Divide by smallest # moles found to obtain mole ratios. Step 4: If mole ratios are close enough to whole numbers, round, and use these as subscripts in empirical formula. Step 5: If mole ratios are NOT close enough to whole numbers, multiply by a small whole # to obtain whole numbers. Wt % Data In solution, a student reacted ruthenium(iii) chloride and lithium sulfide. The black precipitate obtained was heated in H 2 S. After heating, the black precipitate was found to contain 61.18% Ru and 38.82%S. What was the empirical formula of the black precipitate? In solution, a student reacted ruthenium(iii) chloride and lithium sulfide. The student was in a hurry and did not heat the black precipitate in H 2 S. After heating, the black precipitate was found to contain 67.75% Ru and 32.25%S. What was the empirical formula of the black precipitate? Mass Data A g sample of sodium pertechnetate was analyzed and found to contain g Na, g Tc, and oxygen. What is the empirical formula of sodium pertechnetate? 5

6 Empirical Formulas From Reaction Data Combustion Analysis Data A g sample of a compound containing only C, H, and O was placed in a combustion furnace. Combustion of the sample yielded g CO 2 and g H 2 O. Calculate the empirical formula of this compound. NOTE: All C from compound ends up in CO 2 and all H in H 2 O. Step 1: Calculate mass C from CO 2 produced. Step 2: Calculate mass H from H 2 O produced. Step 3: Calculate mass O from law of conservation of mass. Step 4: Find empirical formula. Hydrate Analysis A g sample of the hydrate Na 2 HPO 4 xh 2 O was heated to a constant weight of 0.418g. What is the empirical formula of the hydrate? (HINT: Find x) 6

7 Obtaining the Molecular Formula Two pieces of information are needed: 1. Empirical formula 2. Molar mass Remember..molecular formula is whole # multiple of empirical formula. Ex.C x H y (x n) = C nx H ny To find the molecular formula, it is necessary to find the whole #!! Whole # = Molar Mass Empirical Mass A compound has an empirical formula of C 10 H 21 and a molar mass of What is the molecular formula of this compound? A compound has the empirical formula CH. Which of the following molar masses are not possible for this compound: 26.0, 32.6, 39.1, 52.1, and 61.8? 7

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