chemical composition. counting atoms by weighing

Chemical Composition

COUNTING ATOMS BY WEIGHING

Problem: The lead in my pencil is graphite-an almost pure carbon compound. I wrote a really long English essay and used up most of a pencil, how many carbon atoms did I use? Can I figure this out.

What is the mass of 1 carbon atom? 1.99 * 10 -23 g Is this a practical number to use for calculations? Scientists have defined atomic mass units or amus to avoid this. 1 amu = 1.66 * 10 -24 g The average atomic mass of 1 carbon atom is 12.01 amu. Any sample of carbon from nature can be treated as though it were composed of identical carbon atoms, each with a mass of 12.01 amu.

Conversion Relationship #1 1 amu = 1.66 * 10 -24 g This equivalency allows conversion between these two measurements of mass. Its just like using 2.2046 lbs = 1 Kg

Practice: g amu What is the mass of 5.00 g Carbon in atomic mass units? What is the mass of 5 million amus of Silver in grams?

Conversion Relationship #2 The mass of a single atom of an element equals its mass on the Periodic Table in atomic mass units. For Carbon:1 C atom = 12.0107 amu For Hydrogen:1 H atom = 1.00795 amu For Chlorine:1 Cl atom = 35.453 amu

Conversion Relationship #2 1 atom = mass on PT in amu The periodic table contains equivalency statements that can be used to convert between mass in amu and number of atoms. For example, What is the mass of 12 Carbon atoms? 1 C atom = 12.01 amu 12 C atoms (12.01 amu / 1 C atom) = 144.1 amu

Practice: # atoms amu Calculate the mass, in amu, of a sample of aluminum that contains 75 aluminum atoms. 1 Al atom = 26.981538 amu

Practice: # atoms amu Calculate the mass of a sample that contains 23 nitrogen atoms. 1 N atom = 14.0067 amu

Practice: # atoms amu Calculate the number of sodium atoms present in a sample that has a mass of 1172.49 amu. 1 Na Atom = 22.98977 amu

Practice: # atoms amu Calculate the number of oxygen atoms in a sample that has a mass of 288 amu. 1 O Atom = 15.9994 amu

Try these Calculate the mass of a sample that contains 2493 Lithium atoms. Which weighs more, 25 Platinum atoms, or 5 iron atoms? How many atoms are in 10462.692 amu of oxygen?

THE MOLE

What is a Dozen? A Dozen is a word that represents a number. 1 Dozen = 12 1 dozen apples = ? = 12 apples 2 dozen cookies = ? = 24 cookies 3.2 dozen eggs = ? = 38.4 eggs (38 eggs)

What is a Mole? A Mole is a word that represents a number. 1 mole = 1 mol = 6.022 x 10 23 This number is called Avogadros number. Avogadros Number = 1 mol = 6.022 x 10 23 A Mole is a lot bigger than a Dozen! 1 mol apples = ? = 6.022 x 10 23 apples 2 mol cookies = ? = 1.2044 x 10 24 cookies 3.2 mol eggs = ? = 1.92704 x 10 24 eggs = 1,927,040,000,000,000,000,000,000 eggs

Conversion Relationship #3 1 mol = 6.022 x 10 23 atoms How many calcium atoms are present in a sample that contains 3.12 mol Ca? How many moles are present in a sample of gold that contains 2.6 x 10 52 atoms?

Why is the mole necessary? Comparing equal masses of chemicals does not compare equal numbers of particles. Consider the synthesis of barium sulfide from its elements: Ba(s) + S(s) BaS If there are 100 amu of each element, how many molecules of BaS will form? Calculate the number of atoms in each 100 amu sample. Are they the same? It is much more efficient to use moles to compare quantities of chemicals. If there are 100 moles of Ba and 100 moles of S, how many moles of BaS will form? 100 moles is the same number of atoms no matter what kind of atom it is. It is a basis for an equal comparison. That is a much easier way of thinking of things.

The Mole is the Most Important Quantity in Chemistry!!!! Comparing quantities in chemistry using moles allows an equal basis of comparison. Comparing quantities in chemistry using grams does not.

Conversion Relationship #4 The Mass of a Mole The Periodic Table of Elements tells us the mass of 1 mole of each of the atoms. 1 mole of an element = mass on Periodic Table in grams. To Clarify between the mass of 1 atom and the mass of one mole of atoms: 1 atom = atomic mass in amu The mass of 1 carbon atom is 12.0107 amu 1 mole of atoms = atomic mass in grams The mass of 1 mole of carbon atoms is 12.0107 g

Practice: g-mol & mol-#atoms How many moles Al is contained in 10.0 g Al? How many atoms does this sample contain?

Practice: grams-moles-#atoms A silicon chip used in an integrated circuit of a microcomputer has a mass of 5.68 mg. How many Si atoms are present in this chip

Practice: #atoms-moles-grams Calculate both the number of moles in, and the mass of, a sample of chromium containing 5.00 x 10 20 atoms.

8.4 MOLAR MASS Goals: 1. To define Molar Mass. 2. To determine the molar mass of a polyatomic substance. 3. To convert between moles and mass of a substance.

The Molar Mass of Atoms The molar mass of an atom is its atomic mass from the Periodic Table in grams. What is the molar mass of an atom of Oxygen? 15.9994 g/mol What is the molar mass of elemental oxygen? O 2 (g) 2 x 15.9994 g/mol = 31.9988 g/mol

The Molar Mass of Polyatomic Substances A polyatomic substance is a collection of atoms. The molar mass of a polyatomic substance is simply the sum of the molar masses of all the atoms of which the substance is made. Example: Find the molar mass of methane (CH 4 ) 1.Determine the chemical composition: CH 4 = 1 C + 4 H 2.Then add up the masses of all the atoms. CH 4 = 1(12.0107) + 4(1.00794) = 16.04246 The molar mass is the mass of 6.022 x 10 23 molecules of CH 4, in grams. The molar mass of methane = 16.0425 g/mol CH 4

Summary of Molar Mass Molar Mass The Molar Mass of a substance is the mass (in grams) of 1 mole of the substance. 1.For Elements, the molar mass is equal to the atomic mass on the periodic table (in grams). 2.For Diatomic & Polyatomic Substances, the molar mass is equal to the sum of the atomic weights of all the atoms in the substance (in grams).

Practice: Calculating Molar Mass Calculate the molar mass of sulfur dioxide. 1.Chemical Composition: SO 2 = S + 2O 2.Add the molar mass of all the atoms: SO 2 = 1(32.065) + 2(15.9994) Answer: 64.0638 = 64.064 g/mol SO 2

Practice: Calculating Molar Mass Polyvinyl chloride (called PVC) which is widely used for floor coverings (vinyl) and for plastic pipes in plumbing systems, is made from a molecule with the formula C 2 H 3 Cl. Calculate the molar mass of this substance. 1.Chemical Composition: C 2 H 3 Cl = 2C + 3H + 1Cl 2.Sum of molar masses: C 2 H 3 Cl = 2(12.0107) + 3(1.00794) + 1(35.453) Answer: 62.49822 = 62.498 g/mol C 2 H 3 Cl

Conversion Relationship #4 The Mass of a Mole (Revisited) Once the molar mass of a substance is known, it can be used to convert between moles and masses of the substance. The molar mass of methane (CH 4 ) is 16.04246 g/mol. This gives an equivalency statement that can be used as a conversion factor: 1 mol CH 4 = 16.04246 g CH 4 1.What is the mass of 3.2 moles of methane? 2.How many moles are in 5.93 g methane?

Practice: grams-moles (with molecules this time) Calcium Carbonate, CaCO 3 (also called calcite), is the principal mineral found in limestone, marble, chalk, pearls, and the shells of marine animals such as clams. a.Calculate the molar mass of calcium carbonate. b.What is the mass in grams of 4.86 mol CaCO 3 ?

Calculate the molar mass for sodium sulfate, Na 2 SO 4. A sample of sodium sulfate with a mass of 300.0 g represents what number of moles of sodium sulfate? a.Calculate the molar mass of Sodium Sulfate. b.Convert mass Na 2 SO 4 moles Na 2 SO 4 Practice: grams-moles

Practice: moles-grams Juglone, a dye known for centuries, is produced from the husks of black walnuts. It is also a natural herbicide (weed killer) that kills off competitive plants around the black walnut tree but does not affect grass and other noncompetitive plants. The formula for juglone is C 10 H 6 O 3. a.Calculate the molar mass of Juglone: b.How many moles are contained in a 1.56 g sample of juglone?

Conversion Relationship #3 (Revisited) Remember Avogadros Number? 6.022 x 10 23 Avogadros number represents 1 mole of anything. 1 mole of any substance contains 6.022 x 10 23 units of that substance. This relationship is an equivalency factor that can be used to make conversions between moles and # of molecules. 1 mol = 6.022 x 10 23 molecules

Practice: mass-moles-#molecules Isopentyl Acetate, C 7 H 14 O 2, the compound responsible for the scent of bananas, can be produced commercially. Interestingly, bees release about 1 g (1x10 -6 g) of this compound when they sting. This attracts other bees, which then join the attack. How many moles and how many molecules of isopentyl acetate are released in a typical bee sting? a.Determine the molar mass of C 7 H 14 O 2 : b.Convert mass C 7 H 14 O 2 moles C 7 H 14 O 2 # of molecules C 7 H 14 O 2 :

Practice: mass-moles-#molecules The substance Teflon, the slippery coating on many frying pans, is made from the C 2 F 4 molecule. Calculate the number of C 2 F 4 units present in 135 g of Teflon. a.Calculate the molar mass of C 2 F 4 : b.Convert mass moles # molecules

MOLAR RELATIONSHIPS

RELATIONSHIP #1 PARTICLES IN A MOLE

Particles in a Mole A chemical mole is defined as the number of atoms present in a sample of Carbon- 12 that weighs exactly 12.0107g. A Mole is a word that represents a Number, and that number is also known as Avogadros Number. 1 mole = 6.022 x 10 23 particles Particles are either atoms or molecules.

Practice: Moles - # Particles How many carbon atoms are in a sample that contains 5.16 moles C? How many moles are present in a sample of nitric acid that contains 5 billion molecules?

RELATIONSHIP #2 ATOMS IN A MOLECULE

Atoms in Molecules Consider a single water molecule: What is the composition by type of atom? Using moles, 1 mole H 2 O contains 2 moles H and 1 mole O. The following equivalencies can be made: 1 mol H 2 O = 2 mol H 1 mol H 2 O = 1 mol O How many moles of hydrogen are in 2.53 mole H 2 O?

Practice: Atoms in Molecules How many moles of carbon are in a 6.57 mol sample of Aluminum Acetate?

PERCENT COMPOSITION BY MASS 8.5 Pages 226 - 228

Mass Percent

Calculating Mass Percent Consider the compound Ethanol (C 2 H 5 OH) Follow these steps to determine the mass percent of Carbon in Ethanol: 1.Determine the number of moles of C in one mole of ethanol: There are 2 moles of Carbon, so n = 2. 2.Determine the mass of C in ethanol: 2 mol C x (12.0107 g C / 1 mol C) = 24.0214 g C 3.Determine the molar mass of ethanol: 2(12.0107) + 6(1.00794) + 1(15.9994) = 46.0684 g C 2 H 5 OH 4.Divide molar mass C in ethanol by molar mass ethanol and multiply by 100: (24.0214 g)/(46.0684 g) x 100 = 52.14 % C

Practice: Calculating Mass Percent Carvone is a substance that occurs in two forms, both of which have the same molecular formula (C 10 H 14 O) and molar mass. One type of carvone gives caraway seeds their characteristic smell; the other is responsible for the smell of spearmint oil. Compute the mass percent of each element in Carvone.

Practice: Calculating Mass Percent Penicillin F has the formula C 14 H 20 N 2 SO 4. Calculate the mass percent of each element in Penicillin F.

Using Mass Percent A sample of Calcium Carbonate has a mass of 5.69 g. What is the mass of Oxygen present in the sample?

Using Mass Percent What mass of carbon is present in 15.39 mol C 6 H 12 O 6 ?

THE EMPIRICAL FORMULA 8.6 Pages 228 - 230

Combustion Analysis When a compound containing only C, H, & O is burned in the presence of excess oxygen, the composition by mass of C, H, & O can be determined by measuring the mass of CO 2, and H 2 O produced. 0.2015 g of a substance containing C, H, & O is found to contain 0.0806 g C, 0.01353 g H, and 0.1074 g O. What is the ratio of C:H:O atoms in the compound?

Step 1: Convert mass to moles 0.0806 g C (1 mol C / 12.0107 g C) = 0.006710683 mol C =.00671 mol C 0.01353 g H (1 mol H / 1.00794 g H) = 0.0134234181 mol H = 0.01342 mol H 0.1074 g O (1 mol O / 15.9994 g O) = 0.0067127517 mol O = 0.006713 mol O

Step 2: Convert Moles to Atoms 0.00671 mol C (6.022 x 10 23 atoms C / 1 mol C) = 4.04 x 10 21 atoms C 0.01342 mol H (6.022 x 10 23 atoms H / 1 mol H) = 8.084 x 10 21 atoms H 0.006713 mol O ((6.022 x 10 23 atoms H / 1 mol H) = 4.042 x 10 21 atoms O

Step 3: Determine the Ratio of C, H, & O C:H:O (4.04 x 10 21 atoms C) : (8.084 x 10 21 atoms H) : (4.042 x 10 21 atoms O) 1:2:1 Notice that the mole ratio is the same (0.00671 mol C) : (0.01342 mol H) : (0.006713 mol O)

Is this ratio the molecular formula? The ratio of C:H:O is 1:2:1 Does this mean the molecular formula is CH 2 O? What about the molecular formulas of the following compounds? C 2 H 4 O 2, C 3 H 6 O 3, C 5 H 10 O 5 All of the above have a ratio of C:H:O of 1:2:1.

Empirical Formulas The Empirical Formula of a compound is the smallest whole-number (integer) ratio of atoms. All four of the compounds CH 2 O, C 2 H 4 O 2, C 3 H 6 O 3, & C 5 H 10 O 5 have the same empirical formula; CH 2 O. The Empirical Formula of a compound is the most simplified formula.

Determining Empirical Formulas Determine the empirical formula for each compound: 1.C 6 H 6 2.C 12 H 4 Cl 4 O 2 3.C 6 H 16 N 2 Answers: 1.CH 2.C 6 H 2 Cl 2 O 3.C 3 H 8 N

CALCULATING EMPIRICAL FORMULAS 8.7 Pages 230 - 235

Calculating Empirical Formulas 1. Determine the number of moles of each element present in the compound. (This can be done 1 of 2 ways) a)If the amounts are given in grams, simply convert them to moles using the molar masses of the elements from the periodic table of elements. b)If the amounts are give in percent composition by mass, simply base your calculations on a sample of mass = 100. g of the compound. The percent mass of each element will represent the mass in grams of that element. 2. Divide each value of the number of moles by the smallest of the values. If each resulting number is a whole number (after appropriate rounding) these numbers represent the subscripts of the elements in the empirical formula. 3. If the numbers obtained in the previous step are not whole numbers, multiply each number by an integer so that the results are all whole numbers, which are the subscripts of the elements in the empirical formula.

Practice: Calculating Empirical Formulas An oxide of aluminum is formed by the reaction of 4.151 g Al with 3.692 g O. Calculate the empirical formula of the compound. 1. Determine the mass of each element: Given 2. Determine the moles of each: 4.151 g Al (1 mol Al / 26.981538 g Al) = 0.1538 mol Al 3.692 g O (1mol O / 15.9994 g O) = 0.2308 mol O 3. Divide each by the least number of moles: Al: 0.1538 / 0.1538 = 1 O: 0.2308 / 0.1538 = 1.5 4. Multiply to get whole numbers to determine the formula: Al:O = (1:1.5) x 2 = 2:3 Answer: Al 2 O 3 Aluminum Oxide

Practice: Calculating Empirical Formulas When a 0.3546 g sample of vanadium metal is heated in air, it reacts with oxygen to achieve a final mass of 0.6330 g. Calculate the empirical formula of this vanadium oxide. 1. Determine the mass of each element present: mV = 0.3546 g mO = 0.6330 0.3546 = 0.2784 g 2. Determine the moles of each element present: molV = 0.3546 g (1 mol / 50.9415 g) = 0.0069609258 mol V mol O = 0.2784 g (1 mol / 15.9994 g) = 0.0174006525 mol O 3. Determine the mole:mole ratio of elements: V: 0.0069609258 / 0.0069609258 = 1 O: 0.0174006525 / 0.0069609258 = 2.499761242 2.5 4. Determine the lowest whole number ration of elements: V:O = (1:2.5) x 2 = 2:5 Answer: V 2 O 5 Vanadium (V) Oxide

Practice: Calculating Empirical Formulas A sample of lead arsenate, an insecticide used against the potato beetle, contains 1.3813 g of lead, 0.00672 g of hydrogen, 0.4995 g arsenic, and 0.4267 g oxygen. Calculate the empirical formula for lead arsenate. 1. Determine the mass of each element: given 2. Determine moles of each element: 1.3813 g Pb (1 mol / 207.2 g) = 0.0066665058 mol Pb 0.00672 g H (1 mol / 1.00794 g) = 0.0066670635 mol H 0.4995 g As (1 mol / 74.9216 g) = 0.0066669692 mol As 0.4267 g O (1 mol / 15.9994 g) = 0.0266697501 mol O 3. Determine the mole ratios: Pb: 0.0066665058 / 0.0066665058 = 1 H: 0.0066670635 / 0.0066665058 = 1.000083657 1 As: 0.0066669692 / 0.0066665058 = 1.000069512 1 O: 0.0266697501 / 0.0066665058 = 4.000559048 4 4. Multiply the mole ratios to get the lowest whole # integers: Pb:H:As:O = 1:1:1:4 already done Answer: PbHAsO 4

Practice: Calculating Empirical Formulas Analysis of the chemical carbamic acid finds that it is composed of 0.8007 g C, 0.9333 g N, 0.2016 g H, and 2.133 g O. Determine the empirical formula of carbamic acid. 1. Determine the mass of each element: given 2. Determine moles of each element: 0.8007 g C (1 mol / 12.0107 g) = 0.0666655565 mol C 0.9333 g N (1 mol / 14.0067 g) = 0.0666323974 mol N 0.2016 g H (1 mol / 1.00794 g) = 0.2000119055 mol H 2.133 g O (1 mol / 15.9994 g) = 0.1333174994 mol O 3. Determine the mole ratios: C: 0.0666655565 / 0.0666323974 = 1.00497642 1 N: 0.0666323974 / 0.0666323974 = 1 H: 0.2000119055 / 0.0666323974 = 3.001721584 3 O: 0.1333174994 / 0.0666323974 = 2.000790976 2 4. Multiply the mole ratios to get the lowest whole # integers: C:N:H:O = 1:1:3:2 already done Answer: CNH 3 O 2

Practice: Calculating Empirical Formulas Cisplatin, the common name for a platinum compound that is used to treat cancerous tumors, has the composition (mass percent) 65.02 % Pt, 9.34 % N, 2.02 % H, and 23.63 %Cl. Calculate the empirical formula for cisplatin. 1. Determine the mass of each element: given in % so use a 100.g sample: 65.02 g Pt + 9.34 g N + 2.02 g H + 23.63 g Cl = 100.00 g sample 2. Determine moles of each element: 65.02 g Pt (1 mol / 195.08 g) = 0.3332991593 mol Pt 9.34 g N (1 mol / 14.0067 g) = 0.6668237344 mol N 2.02 g H (1 mol / 1.00794 g) = 2.004087545 mol H 23.63 g Cl (1 mol / 35.453 g) = 0.6665162328 mol Cl 3. Determine the mole ratios: Pt: 0.3332991593 / 0.3332991593 = 1 N: 0.6668237344 / 0.3332991593 = 2.000676317 2 H: 2.004087545 / 0.3332991593 = 6.012879088 6 Cl: 0.6665162328 / 0.3332991593 = 1.999753717 2 4. Multiply the mole ratios to get the lowest whole # integers: Pt:N:H:Cl = 1:2:6:2 already done Answer: PtN 2 H 6 Cl 2

Practice: Calculating Empirical Formulas The most common form of nylon (nylon 6) is 63.68% C, 12.38% N, 9.80% H, and 14.14% O. Calculate the empirical formula of nylon 6. 1. Determine the mass of each element: given in % so use a 100.g sample: 63.68 g C + 12.38 g N + 9.80 g H + 14.14 g O = 100.00 g sample 2. Determine moles of each element: 63.68 g C (1 mol / 12.0107 g) = 5.301939104 mol C 12.38 g N (1 mol / 14.0067 g) = 0.8838627228 mol N 9.80 g H (1 mol / 1.00794 g) = 9.7228096 mol H 14.14 g O (1 mol / 15.9994 g) = 0.883731419 mol O 3. Determine the mole ratios: C: 5.301939104 / 0.883731419 = 5.999491463 6 N: 0.8838627228 / 0.883731419 = 1.000148579 1 H: 9.7228096 / 0.883731419 = 11.00199607 11 O: 0.883731419 / 0.883731419 = 1 4. Multiply the mole ratios to get the lowest whole # integers: C:N:H:O = 6:1:11:1 already done Answer: C 6 NH 11 O

8.8 CALCULATION OF MOLECULAR FORMULAS Pages 235 237

Calculating Molecular Formulas Knowing the percent composition or knowing the mass ratios of a compound allows us to calculate the empirical formula of the compound. But this does not determine the identity of the compound In order to calculate the molecular formula of a compound, the molar mass must also be known. n = molar mass of compound molar mass of empirical formula If n can be found, then the identity of the compound can be determine as [n x (empirical formula)].

Practice: Calculating Molecular Formulas A white powder is analyzed and found to have an empirical formula of P 2 O 5. The compound has a molar mass of 283.88 g. What is the compounds molecular formula? 1. Determine molar mass of the empirical formula: P 2 O 5 = 141.94452 g/mol 2. Determine the value of n: n = 283.88 / 141.94452 = 1.999936313 2 3. Determine the molecular formula: n(P 2 O 5 ) = 2(P 2 O 5 ) Answer: P 4 O 10

Practice: Calculating Molecular Formulas A compound used as an additive for gasoline to help prevent engine knock shows the following percentage composition: 71.65% Cl, 24.27% C, 4.07% H. The molar mass is known to be 98.96 g. Determine the empirical and the molecular formula for this compound. Determine the empirical formula: Mass of each, moles of each, mole ratio, lowest whole number mole ratio = empirical formula The empirical formula is ClCH 2 Determine the molar mass of the empirical formula: ClCH 2 = 49.47958 g/mol Determine the value of n: 98.96 g / 49.47958 g = 2.000016977 2 Determine the molecular formula: n(ClCH 2 ) = 2(ClCH 2 ) Answer: Cl 2 C 2 H 4

chemical composition. counting atoms by weighing

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