Math of Formulas. Chapter 10

Transcription

1 Math of Formulas Chapter 10

2 Macro vs. Micro Chemistry has two worlds: The macroscopic world = what a scien>st can see and weigh The microscopic world = the atomic level, filled with >ny molecules Chemists need a way to convert from the molecular level to one that is usable in the laboratory

3 Enter the Mole Mole (mol) - SI unit for measuring the amount of a substance Avogadro s Number 1 mole = 6.02x10 23 representa>ve par>cles Just as 1 dozen = 12 A mole is 602,000,000,000,000,000,000,000 par>cles

4 Avogadro s Analogies The popula>on of the earth is six billion (6 x 109 people). It would take about 100 trillion Earth popula>ons to sum up to Avogadro's number. One mole of high school textbooks would cover the USA to a depth of about 320 km (200 miles). Water flows over Niagara Falls at about 650,000 kl (172,500,000 gallons) per minute. At this rate it would take 134,000 years for one mole of water drops (6.02 x 1023 drops) to flow over Niagara Falls. Avogadro's number (6.02 x 1023 ) is the approximate number of milliliters of water in the Pacific Ocean (7 x 108 km3 or 7 x 1023 ml). If one mole of par>cles the size of sand grains were released by the erup>on of Mount St. Helens, they would cover the en>re state of Washington to the depth of a ten- story building.

5 How Do I Weigh a Mole? Molar Mass mass, in grams, of one mole of a substance (g/mol) Molar Mass of elements = atomic mass in grams ex: molar mass of Carbon is 12 g/mol Molar Mass of compounds = sum of the par>al masses of the elements within a compound

6 What is the Molar Mass of Water? H 2 O Symbol: # of atoms x atomic mass = par>al mass H O Add up par>al masses to get molar mass: = 18 g/mol

7 Examples Br 2 H 2 SO 4 Al(NO 3 ) 3 Br 2 x 80 = 160 g/mol H 2 x 1 = 2 S 1 x 32 = 32 O 4 x 16 = g/mol Al 1 x 27 = 27 N 3 x 14 = 42 O 9 x 16 = g/mol

8 What is the molar mass of (NH 4 ) 2 CO 3? A.) 144 g/mol B.) 138 g/mol C.) 96 g/mol D.) 78 g/mol N 2 x 14 = 28 H 8 x 1 = 8 C 1 x 12 = 12 O 3 x 16 = 48

9 What is the molar mass of (NH 4 ) 3 PO 4 N 3 x 14 = 42 H 12 x 1 = 12 P 1 x 31 = 31 O 4 x 16 = g/mol

10 Percent ComposiLon % composilon = part x 100 whole Of an element in a compound % composilon = parlal mass of element x 100 molar mass of compound

11 Examples What is the percent by mass of oxygen in the compound P 2 O 5? Phosphorus? P 2 x 31 = 62 O 5 x 16 = g/mol %O = 80 x 100 = 56.3% 142 %P = 62 x100 = 43.7% 142

12 What is the percent composilon of chromium in BaCrO 4? A.) 4.87 % B.) 9.47 % C.) 20.5 % D.) 25.2 % Ba 1 x 137 = 137 Cr 1 x 52 = 52 O 4 x 16 = g/mol %Cr = 52 x 100 = 253

13 What is the percent composilon of nitrogen in the compound (NH 4 ) 2 SO 4? N 2 x 14 = 28 %N = 28 x 100 = 21.2% H 8 x 1 = S 1 x 32 = 32 O 4 x 16 = g/mol

14 Mole- Mass Conversions Write down the given amount Mul6ply by a frac6on Units to cancel must be on bo=om Desired units on top Plug in values for substance s molar mass X grams in 1 mole

15 Examples How many moles are contained in 34.0 g of NH 3? 34.0g 1 x mol = 2.0 mol 17 g N 1 x 14 = 14 H 3 x 1 = 3 17 g/mol What is the mass (in 17 grams) g of 3 moles of = 51 g NH 3? 3 mol X 1 mol

16 What is the mass in grams of 5.90 moles of C 8 H 18? A.) g B.) 19.4 g C.) 389 g D.) 673 g 5.90 mol x 114 g = 673 g 1mol C 8 x 12 = 96 H 1 x 18 = g/mol

17 What is the number of moles in 432 grams of Ba(NO 3 ) 2? A.) mol B.) mol C.) 1.65 mol D.) 3.66 mol 432 g x 1mol = 1.65 mol 261 g Ba 1 x 137 = 137 N 2 x 14 = 28 O 6 x 16 = g/mol

18 Mole Triangle The mole has three values Mass: one mole is equal to the molar mass Par6cles: one mole is 6.02x10 23 par6cles Volume: one mole is 22.4 L (gases only) at STP Molar Mass 1 Mole 22.4 L (gas) 6.02x10 23 par6cles

19 How many atoms are in 3.5 moles of arsenic atoms? A.) 5.8 x atoms B.) 7.5 x 10 1 atoms C.) 2.1 x atoms 3.5 mol x 6.02x10 23 atom = 1 mol D.) 1.7 x atoms

20 How many moles of silver atoms are in 1.8 x atoms of silver? A.) 3.0 x 10-4 B.) 3.3 x 10-3 C.) 3.0 x x10 20 atom x 1 mol = 6.02x10 23 atom D.) 1.1 x 10 44

21 What is the number of moles in 500 Liters of Helium gas at STP? A.) 0.05 mol B.) 0.2 mol C.) 22 mol 500L x 1 mol = 22.4 L D.) 90 mol

22 MulPstep Conversions Convert to moles and then to desired How many molecules of water are present in a 30 gram sample? 30g x 1 mol 18 g x 6.02x mol molecules = 1x10 24 molecules What is the mass of a sample that contains 3.12 x carbon atoms? 3.12x10 24 atom x 1mol x 12g = 6.22 g 6.02x10 23 atom 1mol

23 Empirical Vs. Molecular Formulas Empirical Formula shows the smallest whole- number ra9o of the atoms in the compound ex: NO 2 (1:2) Molecular Formula exactly how many atoms are present in the molecule (may be the empirical formula or not) ex: NO 2 or N 2 O 4

24 Empirical or Molecular? If molecular give its corresponding empirical formula E H 2 O M H 2 O 2 E N 2 O 5 M C 6 H 12 O 6 M C 2 H 4 E PI 3 HO CH 2 O CH 2 Press: A for empirical B for molecular

25 Which of the following is NOT an empirical formula? A.) Sb 2 S 3 B.) C 2 H 8 O C.) C 2 N 2 H 8 D.) BeCr 2 O 7 CNH 4

26 Which of the following have the same empirical formula? A.) CO 2 and SO 2 B.) C 7 H 14 and C 10 H 20 C.) C 4 H 10 and C 10 H 4 D.) C 6 H 12 and C 6 H 14 CO 2 and SO 2 CH 2 and CH 2 C 2 H 5 and C 5 H2 CH 2 and C 3 H 7

27 Chemical Formulas and Moles Al 2 O 3 Subscripts tell you the number of moles of atoms in a formula 2 moles Al and 3 moles O PI 3? 1 mol Phosphorous and 3 moles Iodine

28 Determining Empirical Formulas From Percent Composi9on Empirical formulas have a simple whole number ra9o of atoms 1) Assume that you have 100 grams of substance (replace percent with grams) 2) Change grams to moles 3) Find lowest whole number ra9o (divide all numbers by the lowest value for moles) 4) Use value from step 3 as your subscripts for the respec9ve elements (if all values are not within 0.1 of a whole number, alter by mul9plying by a whole number)

29 Examples A compound is analyzed and found to contain 50% sulfur and 50% oxygen. What is its empirical formula? S 50g x 1mol 32g = mol = 1 SO 2 O 50g x 1mol 16g = 3.125mol = 2

30 A compound is analyzed and found to contain 25.9% nitrogen and 74.1% oxygen. What is its empirical formula? N 25.9g x 1mol = 1.85mol 14g 1.85 O 74.1g x 1mol = 4.63mol 16g 1.85 = 1 = 2.5 x 2 = 2 x 2 = 5 N 2 O 5

31 What is the empirical formula of a compound that is 40% sulfur and 60% oxygen by weight? A.) SO B.) SO 2 C.) SO 3 S 40g x 1mol = 1.25mol = 1 32g 1.25 O 60g x 1mol = 3.75mol = 3 16g 1.25 D.) S 6 O 4

32 Combined Problem A compound contain 64.9% C, 13.5% H, and 21.6% O. Its molecular mass is 74 g/mol. Find the molecular formula. C 64.9g x 1mol = 5.408mol = 4 12g 1.35 H 13.5g x 1mol = 13.5mol = 10 1g 1.35 O 21.6g x 1mol = 1.35mol = 1 16g 1.35 C 4 H 10 O C 4 x 12 = 48 H 10 x 1 = 10 O 1 x 16 = g/mol 74 = 1 74 C 4 H 10 O

33 Zeanxanthin is one of the compounds found to cause the colors in maple leaves in the fall. It has a molecular weight of 544 and is 83.82% carbon, 10.29% hydrogen, and 5.88% oxygen. Find the molecular formula of zeanxanthin. C 83.82g x 1mol = = 19 12g H 10.29g x 1mol = = 28 1g C 19 H 28 O C 19 x 12 = 228 H 28 x 1 = 28 O 1 x 16 = g/mol 544 = O 5.88g x 1mol = = 1 16g C 38 H 56 O 2

34 Chapter 5/6 Test To do well on this test you should be able to comfortably do the following: Name compounds if given formula Give formula of a compound if given its name Mole concept and relauonships (molar mass = 1 mol = 6.02x10 23 parucles) Determine the molar masses of elements and compounds Determine percent composiuon of elements within a compound Molar conversions (mass mole & mass parucles) IdenUfy empirical and molecular formulas Determine the empirical formula of a compound from percent composiuon or lab data Determine the molecular formula of a compound from percent composiuon (or enough informauon to determine it) and molar mass

35 Hydrates A crystalline form of an ionic substance that contains a definite number of water molecules (loosely bound by intermolecular forces).

36 Anhydrous vs. Hydrated Salts Anhydrous (no water) is a term used to describe the ionic compound once water has been removed Heat can be used to remove the water from the hydrated salt CuSO 4 5H 2 O + heat CuSO 4 + 5H 2 O Hydrate Lab