Stoichiometry Atomic Mass The Mole concept Molar Mass Percent Composition of Compounds Determination of Formula of Compounds Writing and Balancing Chemical.

Stoichiometry• Atomic Mass• The Mole concept• Molar Mass• Percent Composition of Compounds• Determination of Formula of Compounds• Writing and Balancing Chemical Equations• Interpreting balance equations, and• Reaction Stoichiometry and Calculations

Atomic Masses

• Absolute masses of atoms cannot be obtained – too small to measure the mass directly;

• Relative atomic masses are used instead – masses relative to a chosen standard or reference.

• Carbon-12 is used as atomic mass reference – it is assigned an atomic mass of 12 u exactly;

• Other atoms are assigned masses relative to that of carbon-12;

• Relative atomic masses are determined using mass spectrometer;

A Schematic Diagram of Mass Spectrophotometer

Isotope Mass of CO2

Mass Spectrum of Chlorine

Atomic Mass Spectrum of Mercury

Calculation of Relative Atomic Masses

Example-1:

An atomic mass spectrum gives atomic mass ratio of oxygen atom to carbon-12 as 1.3329:1. If the atomic mass of carbon-12 is exactly 12 u, what is the atomic mass of oxygen?

Atomic mass of oxygen = 1.3329 x 12 u

= 15.995 u

Calculation of Average Atomic Masses

Example-2:

Chlorine is composed of two stable naturally occurring isotopes: chlorine-35 (75.76%; 34.9689 u) and chlorine-37 (24.24%; 36.9659 u). What is the average atomic mass of copper?

Atomic mass of chlorine

= (0.7576 x 34.9689 u) + (0.2424 x 36.9659 u)

= 35.45 u (as given in the periodic table)

Calculation of Average Atomic Masses

• Example-3:

Copper is composed of two naturally occurring isotopes: copper-63 (69.09%; 62.93 u) and copper-65 (30.91%; 64.93 u). What is the average atomic mass of copper?

Atomic mass of copper

= (0.6909 x 62.93 u) + (0.3091 x 64.93 u)

= 63.55 u (as given in the periodic table)

Exercise #1: Relative Atomic Mass

A mass spectrometer computed the atomic mass ratio of fluorine to carbon-12 as 1.5832-to-1. If the atomic mass of carbon-12 is 12 u (exactly), what is the atomic mass of fluorine in u?

(Answer: 18.998 u)

Exercise #2: Average Atomic Mass

Natural boron is composed of two isotopes: 19.78% boron-10 (atomic mass = 10.0129 amu) and 80.22% boron-11 (atomic mass = 11.0093 amu). What is the average atomic mass of naturally occurring boron?

(Answer: 10.81 u)

Molar Quantity

• The Mole:A quantity that contains the Avogadro’s number of items;

Avogadro’s number = 6.022 x 1023

12.01 g of carbon contains the Avogadro’s number of carbon atoms.

1 mole of carbon = 12.01 g

1 carbon atom = 12.01 u (or amu)

Gram-Atomic Mass

• Mass of 1 carbon-12 atom = 12 u (exactly);• Mass of 1 mole of carbon-12 = 12 g;• Mass of 1 oxygen atom = 16.00 u • Mass of 1 mole of oxygen = 16.00 g• Gram-atomic mass = mass (in grams) of 1 mole of

an element – that is, the mass (in grams) that contains the Avogadro’s number of atoms of that element.

• gram-atomic mass is the molar mass of an element in grams.

Atomic Mass & Gram-Atomic Mass

• Examples:Element Atomic mass Gram-atomic mass

Carbon 12.01 u 12.01 g/mol

Oxygen 16.00 u 16.00 g/mol

Aluminum 26.98 u 26.98 g/mol

Silicon 28.09 u 28.09 g/mol

Gold 197.0 u 197.0 g/mol

Molecular Mass and Molar Mass

• Molecular mass = the mass of a molecule in u;• Molar mass = the mass of one mole of an element

or a compound, expressed in grams.• Examples:

Molecular Mass Molar Mass

N2 28.02 u 28.02 g/mol

H2O 18.02 u 18.02 g/mol

C8H18 114.22 u 114.22 g/mol

Calculating Molar Mass

• Calculating the molar mass of sucrose, C12H22O11:

(12 x 12.01 g) + (22 x 1.008 g) + (11 x 16.00 g)

= 342.3 g/mole

• Molar mass of ammonium hydrogen phosphate, (NH4)2HPO4:

(2 x 14.01 g) + (9 x 1.008 g) + (1 x 30.97 g) + (4 x 16.00 g)

= 132.06 g/mole

Percent Composition of a Compound

• Composition of aluminum sulfate, Al2(SO4)3:

• Molar mass of Al2(SO4)3 =

(2 x 26.98 g) + (3 x 32.06 g) + (12 x 16.00 g) = 342.14 g/mole

Mass percent of Al = (53.96 g/342.14 g) x 100% = 15.77%

Mass percent of S = (96.18 g/342.14 g) x 100% = 28.11%

Mass percent of O = (192.0 g/342.14 g) x 100% = 56.12%

Formula of Compounds

• Empirical FormulaA chemical formula that represents a simple whole number ratio of the number of moles of elements in the compound. Examples: MgO, Cu2S, CH2O, etc.

• Molecular FormulaA formula that shows the actual number of atoms of each type in a molecule.

Examples: C4H10, C6H6, C6H12O6.

Empirical Formula-1

• Empirical formula from composition:Example: A compound containing carbon, hydrogen, and oxygen has

the following composition (by mass percent): 68.12% C, 13.73% H, and 18.15% O, Determine its empirical formula.

• Solution: Use mass percent to calculate mole and mole ratio of C:H:O

• Mole of C = 68.12 g x (1 mol C/12.01 g) = 5.672 mol C• Mole of H = 13.73 g x (1 mol H/1.008 g) = 13.62 mol H• Mole of O = 18.15 g x (1 mol O/16.00 g) = 1.134 mol O

Divide all moles by mole of O (smallest value) to get simple ratio: 5.672 mol C/1.134 mol O = 5; 13.62 mol H/1.134 mol O = 12, and1.134 mol O/1.134 mol O = 1;

Mole ratio: 5C:12H:1O Empirical formula = C5H12O

Empirical Formula-2

• Empirical formula from mass of elements in a sample of compound

Example: When 1.96 g of phosphorus is burned, 4.49 g of a phosphorus oxide is obtained. Calculate the empirical formula of the phosphorus oxide.

• Solution:

Calculate moles of P and O in sample and obtain a simple mole ratio;

Mole of P = 1.96 g P x (1 mol/30.97 g) = 0.0633 mol P;

Mole of O = (4.49 g – 1.96 g) x (1 mol/16.00 g) = 0.158 mol O;

Divide by mole of P (smaller value) to get a simple mole ratio:

0.0633 mol P/0.0633 = 1 mol P; 0.158 mol O/0.0633 = 2.5 mol O

Mole ratio: 1 mol P to 2.5 mol O, OR 2 mol P to 5 mol O

• Empirical formula = P2O5

Empirical Formula-3

• Empirical formula from data of combustion reaction:Example: A compound is composed of carbon, hydrogen, and oxygen. When 2.32

g of this compound is burned in excess of oxygen, it produces 5.28 g of CO2 gas and 2.16 g of water. Calculate the composition (in mass percent) of the compound and determine its empirical formula.

• Solution:• Find mass of C, H, and O in the sample and then calculate their mass

percent:Mass of C = 5.28 g CO2 x (12.01 g C/44.01 g CO2) = 1.44 g Mass % of C = (1.44 g C/2.32 g sample) x 100% = 62.1% Mass of H = 2.16 g H2O x (2 x 1.008 g/18.02 g H2O) = 0.24 g Mass % of H = (0.242 g H/2.32 g sample) x 100% = 10.4% Mass of O = 2.32 g sample – 1.44 g C – 0.24 g H = 0.64 gMass % of O = 100 – 62.1% C – 10.4% H = 27.5%

• Derive empirical formula from these mass percent composition • (next slide)

Empirical Formula-3

• Empirical formula from data of combustion (continued):

• Calculate mole and simple mole ratio from calculated mass of each element:

Mole of C = 1.44 g C x (1 mol/12.01 g) = 0.12 mol

Mole of H = 0.242 g x (1 mol/1.008 g) = 0.24 mol

Mole of O = 0.64 g x (1 mol/16.00 g) = 0.04 mol

• Divide all moles by mole of O (smallest mole) to obtain a simple ratio:

0.12 mol C/0.04 = 3 mol C; 0.24 mol H/0.04 = 6 mol H;

0.04 mol O/0.04 = 1 mol O

• Simple molar ratio: 3 mol C : 6 mol H : 1 mol O

• Empirical formula: C3H6O

Molecular Formula

• Molecular formula is derived from empirical formula and molecular mass, which is obtained independently

• Empirical formula = CxHyOz; molecular formula = (CxHyOz)n, where n = (molecular mass/empirical formula mass)

• Example:

A compound has an empirical formula C3H6O and its molecular formula is 116.2 u. What is the molecular formula?

• Solution:Empirical formula mass = (2 x 12.01 u) + (6 x 1.008 u) + 16.00 u

= 58.1 u

Molecular formula = (C3H6O)n; where n = (116.2 u/58.1 u) = 2

Incorrect molecular formula = (C3H6O)2;

• Correct molecular formula = C6H12O2

Exercise #3: Determination of Formulas

A 2.00-gram sample of phosphorus is completely reacted with oxygen gas, which yields 4.58 g of product that is composed of only phosphorus and oxygen. In separate analyses, the compound is found to have molar mass of about 284 g/mol.

(a) Determine the empirical and molecular formulas of the compound. (b) Write an equation for the reaction of phosphorus with oxygen gas.

(Answer: P2O5; P4O10; 4P + 5 O2 P4O10)

Chemical Equation #1

• Description of reaction:

Iron reacts with oxygen gas and forms solid iron(III) oxide:

• Identity: reactants = iron (Fe) and oxygen gas (O2); product = iron(III) oxide

• Chemical equation: Fe(s) + O2(g) Fe2O3(s)

• Balanced equation:

4Fe(s) + 3 O2(g) 2Fe2O3(s)

Chemical Equation #2

• Description of reaction:

Phosphorus reacts with oxygen gas to form solid tetraphosphorus decoxide.

Equation: P(s) + O2(g) P4O10(s)

Balanced eqn.: 4P(s) + 5 O2(g) P4O10(s)

Chemical Equation #3

• Description of reaction:

Propane gas (C3H8) is burned in air (excess of oxygen) to form carbon dioxide gas and water vapor;

• Identity: reactants = C3H8(g) and O2(g);

products = CO2(g) and H2O(g);

• Equation: C3H8(g) + O2(g) CO2(g) + H2O(g);

• Balanced equation: C3H8(g) + 5 O2(g) 3CO2(g) + 4H2O(g)

Chemical Equation 4

• Description of reaction:

Ammonia gas (NH3) reacts with oxygen gas to form nitrogen monoxide gas and water vapor;

• Equation: NH3(g) + O2(g) NO(g) + H2O(g);

• Balancing the equation:

2NH3(g) + 5/2 O2(g) 2NO(g) + 3H2O(g);

• Multiply throughout by 2 to get rid of the fraction:

• 4NH3(g) + 5 O2(g) 4NO(g) + 6H2O(g);

Balancing Chemical Equations

Rules for balancing equations:1. Use smallest integer coefficients in front of each reactants and

products as necessary; coefficient “1” need not be indicated;2. The formula of the substances in the equation MUST NOT be

changed.

Helpful steps in balancing equations:1. Begin with the compound that contains the most atoms or types of

atoms.2. Balance elements that appear only once on each side of the arrow.3. Next balance elements that appear more than once on either side.4. Balance free elements last.5. Finally, check that smallest whole number coefficients are used.

Stoichiometry

• Stoichiometry = the quantitative relationships between one reactant to another, or between a reactant and products in a chemical reaction.

• Interpreting balanced equations:

Example: C3H8(g) + 5 O2(g) 3CO2(g) + 4H2O(g);

• The equation implies that:

1 C3H8 molecule reacts with 5 O2 molecules to produce 3 CO2 molecules and 4 H2O molecules; OR

1 mole of C3H8 reacts with 5 moles of O2 to produce 3 moles of CO2 and 4 moles of H2O.

Stoichiometric Calculations

Mole-to-mole relationship:• Example: In the following reaction, if 6.0 moles of octane, C8H18, is

completely combusted in excess of oxygen gas, how many moles of CO2 and H2O, respectively, will be formed? How many moles of O2 does it consumed?

Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g)

Calculations:• Mole CO2 formed = 6.0 mol C8H18 x (16 mol CO2/2mol C8H18) = 48 moles

• Mole H2O formed = 6.0 mol C8H18 x (18 mol H2O/2mol C8H18) = 54 moles

• Mole O2 consumed = 6.0 mol C8H18 x (25 mol O2/2mol C8H18) = 75 moles

Stoichiometric Calculations

Mass-to-mole-to-mole-to-mass relationship:• Example-1: In the following reaction, if 690 g of octane, C8H18, is

completely combusted in excess of oxygen gas, how many grams of CO2 are formed?

Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g)

Calculation-1:

• Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles

• Moles CO2 formed = 6.0 mol C8H18 x (16 mol CO2/2 mol C8H18)

• = 48 moles CO2

• Mass of CO2 formed = 48 mol CO2 x (44.01 g/mol) = 2.1 x 103 g

Stoichiometric Calculations

Mass-to-mole-to-mole-to-mass relationship:• Example-2: In the following reaction, if 690 g of octane, C8H18, is

completely combusted in excess of oxygen gas, how many grams of H2O are formed?

Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g)

Calculation-2:

• Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles

• Moles H2O formed = 6.0 mol C8H18 x (18 mol H2O/2 mol C8H18)

• = 54 moles CO2

• Mass of H2O formed = 54 mol H2O x (18.02 g/mol) = 970 g

Stoichiometric Calculations

Mass-to-mole-to-mole-to-mass relationship:• Example-3: In the following reaction, if 690 g of octane, C8H18, is

completely combusted in excess of oxygen gas, how many grams of oxygen gas are consumed?

Reaction: 2C8H18(l) + 25 O2(g) 16CO2(g) + 18H2O(g)

Calculation-3:

• Moles C8H18 reacted = 690 g C8H18 x (1 mol/114.2 g) = 6.0 moles

• Moles O2 consumed = 6.0 mol C8H18 x (25 mol O2/2 mol C8H18)

• = 75 moles O2

• Mass of H2O formed = 75 mol O2 x (32.00 g/mol) = 2.4 x 103 g g

Stoichiometry Involving Limiting Reactant

• Limiting reactant

one that got completely consumed in a chemical reaction before the other reactants.

Product yields depend on the amount of limiting reactant

A Reaction Stoichiometry

Example:

In the reaction: 2Cu(s) + S(s) Cu2S(s), 2 moles of copper are required to react completely with 1 mole of sulfur, which will produce 1 mole of copper(I) sulfide.

If a reaction is carried out using 1 mole of copper and 1 mole of sulfur, then copper will be the limiting reactant and sulfur is in excess. Only 0.5 mole of copper(I) sulfide is obtained.

Exercise #4: Stoichiometry Calculations

Ammonia is produced from the reaction with hydrogen according to the following equation:

N2(g) + 3H2(g) 2NH3(g)

If 25 N2 molecules are reacted with 60 H2 molecules in a sealed container, which molecules will be completely consumed? How many NH3 molecules are formed?

(Answer: H2; 40 NH3 molecules)

Exercise #5: Limiting Reactants and Reaction Yields

Ammonia is produced in the following reaction:

N2(g) + 3H2(g) 2NH3(g) (a) If 118 g of nitrogen gas is reacted with 31.5 g of hydrogen gas, which reactant will be completely consumed at the end of the reaction? (b) How many grams of the excess reactant will remain (unreacted)? (c) How many grams ammonia will be produced when the limiting reactant is completely reacted and the yield is 100%?

(Answer: (a) N2; (b) 6.0 g; (c) 143.4 g of NH3)

Theoretical, Actual and Percent Yields

• Theoretical yield:

yield of product calculated based on the stoichiometry of balanced equation and amount of limiting reactant (assuming the reaction goes to completion and the limiting reactant is completely consumed).

• Actual Yield:

Yield of product actually obtained from experiment

• Percent Yield = (Actual yield/Theoretical yield) x 100%

Exercise #6: Limiting Reactant & Yields

In an ammonia production, the reactor is charged with N2 and H2 gases at flow rates of 805 g and 195 g per minute, respectively, at 227oC, and the reaction is as follows:

N2(g) + 3H2(g) 3 NH3(g)

(a) What is the rate (in g/min) that ammonia is produced if the yield is 100%? (b) If the reaction produces 915 g of NH3 per minute, calculate the percentage yield of the reaction.

(Answer: (a) 978.5 g/min; (b) Yield = 93.5%)