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Composition and formulae. Of moles and men. Learning objectives. Count atoms in formula Define the mole Determine numbers of atoms or molecules in molar quantities Determine molar mass from chemical formula Determine moles from mass of substance Perform calculations of:
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Composition and formulae Of moles and men
Learning objectives • Count atoms in formula • Define the mole • Determine numbers of atoms or molecules in molar quantities • Determine molar mass from chemical formula • Determine moles from mass of substance • Perform calculations of: • Percent composition • Empirical formula • Molecular formula
Molecules or moles • The numbers (coefficients) in chemical equations can refer to molecules • But for practical applications, we need a more useful number: we cannot count molecules
The Mole • The mole is a unit of quantity used in chemistry to measure the number of atoms or molecules • DEFINITION: • The number of atoms in exactly 12 g of 12C • A mole of anything always has the same number of particles: atoms, molecules or potatoes – 6.02 x 1023 – Avogadro’s number
Atomic and molecular mass • Two scales: • Atomic mass unit scale • Mass of individual atom or molecule in atomic mass units (amu) • Molar mass scale • Mass of mole of atoms or molecules in grams • Confusing?...
The Good News • Molar mass in grams of element has same numerical value as mass of atom in amu • Atomic mass of carbon = 12 amu • Molar mass of carbon = 12 g • Formula mass of H2O molecule = 18 amu • Molar mass of H2O = 18 g
Examples • How many moles of Li are in 6.94 g if atomic mass of Li is 6.94 amu? • 1.00 mol • What is the molar mass of NH3 if atomic mass of H = 1 amu and N = 14 amu • 17 g/mol
Significance of formula unit • Ionic compounds do not contain molecules. Simplest formula is the formula unit • Covalent compounds, the molecular formula is the formula unit
Percent composition and empirical formula • Chemical analysis gives the mass % of each element in the compound • Molar masses give the number of moles • Obtain mole ratios • Determine empirical formula
Determining percent composition • Percent composition is obtained from the actual masses. Example: Sample contained 0.4205 g of C and 0.0795 g of H. Total mass = 0.5000 g (0.4205 + 0.0795) Therefore: in 100 g there are: (84.10 %) (15.90 %) Percent composition: 84.10 % C, 15.90 % H
Percent composition from formula • What is percent composition of C5H10O2? • 1 mol C5H10O2 contains 5 mol C, 10 mol H and 2 mol O atoms • Mass of each element • Total mass = 102.13 g
Convert masses into percents • Percent composition: 58.80 % C + 9.870 % H + 31.33 % O = 100.00%
Empirical formula from percent composition: 84.1 % C, 15.9 % H • Convert percents into moles 84.10 g of C ≡ 7.00 mol C 15.9 g of H ≡ 15.8 mol H • Determine mole ratio Mole ratio H:C = • Simplest formula (decimal form): C1H2.26 • Make smallest integers by multiplying C4H9 May require rounding. Errors in real data cause problems • Do percent composition and empirical formula exercises
Empirical formula with more than two elements • Percent composition of vitamin C is: • 40.9 % C, 4.58 % H, 54.5 % O • Convert into moles • Determine mole ratios • Find lowest whole numbers
Inaccuracy can lead to ambiguous or incorrect formulas • What if H:C is 2.20 rather than 2.26? An error of only 3 % • Formula becomes C5H11 rather than C4H9 • What if H:C is 2.30 rather than 2.26? An error of only 2 % • Formula becomes C3H7 • Sometimes chemical intuition is required: we know there is FeO, Fe3O4 and Fe2O3; so a formula FeO3 would indicate an error
Practice empirical formula problem • A compound contains 62.1 % C, 5.21 % H, 12.1 % N and 20.7 % O. What is the empirical formula?
Empirical and molecular formula • Percent composition gives the empirical (simplest) formula. It says nothing about the molecular formula. • Molecular formula describes number of atoms in the molecule • May be much larger than the empirical formula in the case of molecular covalent compounds • For ionic compounds empirical formula = “molecular” formula
Elements and compounds can have molecular formula different from simplest formula
Determination of molecular formula • Require: • Empirical formula from percent composition analysis • Molar mass from some other source • Number of empirical formula units in molecule: • There are n (AaBbCc) in molecule: • Molecular formula is AnaBnbCnc
Molecular formula of vitamin C • Empirical formula of vitamin C is C3H4O3 • Molar mass vitamin C is 176.12 g/mol • Mass of empirical formula = 88.06 g/mol • (3 x 12.01 + 4 x 1.008 + 3 x 16.00) • Number of formula units per molecule = • Molecular formula = 2(C3H4O3) = C6H8O6
Practice molecular formula problem • Ibuprofen contains 75.69 % C, 8.80 % H and 15.51 % O. What is the molecular formula if molar mass is 206 g/mol?
Molarity • Concentration is usually expressed in terms of molarity: • Moles of solute/liters of solution (M) • Moles of solute = molarity x volume of solution
Example • What is molarity of 50 ml solution containing 2.355 g H2SO4? • Molar mass H2SO4 = 98.1 g/mol • Moles H2SO4 = .0240 mol • Volume of solution = 50/1000 = .050 L • Concentration = moles/volume = .0240/.050 = 0.480 M
Dilution • More dilute solutions are prepared from concentrated ones by addition of solvent M1V1 = M2V2 Molarity of new solution M2 = M1V1/V2 To dilute by factor of ten, increase volume by factor of ten