 # Counting Large Quantities Many chemical calculations require counting atoms and molecules Many chemical calculations require counting atoms and molecules.

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Counting Large Quantities Many chemical calculations require counting atoms and molecules Many chemical calculations require counting atoms and molecules It is difficult to do chemical calculations in terms of atoms or formula units It is difficult to do chemical calculations in terms of atoms or formula units Since atoms are so small, extremely large numbers are needed in calculations Since atoms are so small, extremely large numbers are needed in calculations Need to use a special counting unit just as used for other items Need to use a special counting unit just as used for other items A ream of paper A ream of paper One dozen donuts One dozen donuts A pair of shoes A pair of shoes

The Mole It is more convenient to use a special counting unit for such large quantities of particles It is more convenient to use a special counting unit for such large quantities of particles Mole: A unit that contains 6.022 х 10 23 objects Mole: A unit that contains 6.022 х 10 23 objects It is used due to the extremely small size of atoms, molecules, and ions It is used due to the extremely small size of atoms, molecules, and ions 6.022x10 23 particles in 1 mole 6.022x10 23 particles in 1 mole Called Avogadro’s Number Called Avogadro’s Number Periodic Table Periodic Table The average atomic mass in amu (one atom) The average atomic mass in amu (one atom) The weight of 1 mole of the element in grams The weight of 1 mole of the element in grams Avogadro’s number provides the connecting relationship between molar masses and atomic masses Avogadro’s number provides the connecting relationship between molar masses and atomic masses

Calculating the Number of Molecules in a Mole How many molecules of bromine are present in 0.045 mole of bromine gas? How many molecules of bromine are present in 0.045 mole of bromine gas? Given: 0.045 mol Br 2 Need: molecules of Br 2 Avogadro’s number Conversion factors: Equality: Set Up Problem:

Subscripts State Moles of Elements The subscripts in a chemical formula indicate the number of atoms of each element present in a compound The subscripts in a chemical formula indicate the number of atoms of each element present in a compound The subscripts in a chemical formula can also indicate the number of moles of atoms of each element present in one mole of a compound The subscripts in a chemical formula can also indicate the number of moles of atoms of each element present in one mole of a compound i.e. In one molecule of glucose (C 6 H 12 O 6 ) there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen i.e. In one molecule of glucose (C 6 H 12 O 6 ) there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen

Calculating the Moles of an Element in a Compound How many moles of carbon atoms are present in 1.85 moles of glucose? How many moles of carbon atoms are present in 1.85 moles of glucose? Plan: moles of glucose moles of C atoms subscript (One) mol C 6 H 12 O 6 = 6 mols C atoms Equality: Conversion Factors: Set Up Problem: 11.1 mol C atoms

Molar Mass The atomic mass of a carbon-12 atom is 12.00 amu The atomic mass of a carbon-12 atom is 12.00 amu The atomic mass of one mole of carbon-12 atoms 12.00 g The atomic mass of one mole of carbon-12 atoms 12.00 g One mole of any element is the amount of atoms (molecules or ions) that is equal to its atomic mass (in grams) One mole of any element is the amount of atoms (molecules or ions) that is equal to its atomic mass (in grams) This mass contains 6.022 х 10 23 particles of that element This mass contains 6.022 х 10 23 particles of that element Use the periodic table to obtain the molar mass of any element Use the periodic table to obtain the molar mass of any element

Molar Mass When the number of grams (weighed out) of a substance equals the formula mass of that substance, Avogadro’s number of molecules of that substance are present When the number of grams (weighed out) of a substance equals the formula mass of that substance, Avogadro’s number of molecules of that substance are present

Molar Mass of a Compound Calculate the molar mass of iron (II) sulfate Calculate the molar mass of iron (II) sulfate Formula is FeSO 4 Formula is FeSO 4 1) Calculate the molar mass of each element 2) Each element is multiplied by its respective subscript: (number of moles of each element) 3) The molar mass is calculated by the sum of the molar masses of each element Moles of Element in Compound Moles of Compound Formula Subscript

Molar Mass of a Compound Formula is FeSO 4 : 1) Formula is FeSO 4 : The molar masses of iron, sulfur, and oxygen are 2) Multiply each molar mass by its subscript 3) Find the molar mass of the compound by adding the mass of each element

Calculations Using Molar Mass The three quantities most often calculated The three quantities most often calculated Number of particles Number of particles Number of moles Number of moles Number of grams Number of grams Using molar mass as a conversion factor is one of the most useful in chemistry Using molar mass as a conversion factor is one of the most useful in chemistry Can be used for g to mole and mole to g conversions Can be used for g to mole and mole to g conversions

Relationship between Moles, Molar Mass and Avogadro’s number Moles of substance Particles of substance Moles of substance Grams of substance Avogadro’s Number Molar Mass Moles of substance Avogadro’s Number Moles of substance Avogadro’s Number Particles of substance Moles of substance Avogadro’s Number

Converting Mass of a Compound to Moles International Foods Coffee contains 3 mg of sodium chloride per cup of coffee. How many moles of sodium chloride are in each cup of coffee? International Foods Coffee contains 3 mg of sodium chloride per cup of coffee. How many moles of sodium chloride are in each cup of coffee? Equality: 1 mol NaCl = 58.44 g 3 mg NaCl moles of NaCl = 0.003 g NaCl

Converting Grams to Particles Ethylene glycol (antifreeze) has the formula C 2 H 6 O 2. How many molecules are present in a 3.86 × 10 -20 g sample? Ethylene glycol (antifreeze) has the formula C 2 H 6 O 2. How many molecules are present in a 3.86 × 10 -20 g sample? Plan: convert g moles molecules of ethylene glycol Equality 1: Conversion Factor 1 Equality 2: Conversion Factor 2 375 molecules Molar mass Avog Number

Percent Composition Sometimes it’s useful to know the composition of a compound in terms of what percentage of the total is each element Sometimes it’s useful to know the composition of a compound in terms of what percentage of the total is each element Percent Percent “Parts per 100” “Parts per 100” The number of specific items per a group of 100 items The number of specific items per a group of 100 items 50% of \$100 is \$50 (50 items/100 total items) 50% of \$100 is \$50 (50 items/100 total items)

Percent Example You have 4 oranges and 5 apples. What percent of the total is oranges? You have 4 oranges and 5 apples. What percent of the total is oranges? In “parts per 100” In “parts per 100”

Percent Composition It is the percent by mass of each element in a compound It is the percent by mass of each element in a compound Can be determined Can be determined By its chemical formula By its chemical formula Molar masses of the elements that compose the compound Molar masses of the elements that compose the compound The percent of each element contributes to the mass of the compound The percent of each element contributes to the mass of the compound

Calculating Percent Composition Example What is the percent composition of each element in NH 4 OH? What is the percent composition of each element in NH 4 OH? Determine the contribution of each element Molar mass

Empirical Formulas The simplest ratio of elements in a compound The simplest ratio of elements in a compound It uses the smallest possible whole number ratio of atoms present in a formula unit of a compound It uses the smallest possible whole number ratio of atoms present in a formula unit of a compound If the percent composition is known, an empirical formula can be calculated If the percent composition is known, an empirical formula can be calculated

Empirical Formulas To Determine the empirical formula: To Determine the empirical formula: 1) Calculate the moles of each element  Use molar mass (atomic mass) 2) Calculate the ratios of the elements to each other 3) Find the lowest whole number ratio  Divide each number of moles by the smallest number of moles present

Empirical Formula: Converting Decimal Numbers to Whole Numbers The subscripts in a formula are expressed as whole numbers, not as decimals The subscripts in a formula are expressed as whole numbers, not as decimals The resulting numbers from a calculation represent each element’s subscript The resulting numbers from a calculation represent each element’s subscript If the number(s) are NOT whole numbers, multiply each number by the same small integer (2, 3, 4, 5, or 6) until a whole number is obtained If the number(s) are NOT whole numbers, multiply each number by the same small integer (2, 3, 4, 5, or 6) until a whole number is obtained

Relating Empirical and Molecular Formulas n represents a whole number multiplier from 1 to as large as necessary n represents a whole number multiplier from 1 to as large as necessary Calculate the empirical formula and the mass of the empirical formula Calculate the empirical formula and the mass of the empirical formula Divide the given molecular mass by the calculated empirical mass Divide the given molecular mass by the calculated empirical mass Answer is a whole number multiplier Answer is a whole number multiplier

Relating Empirical and Molecular Formulas  Multiply each subscript in the empirical formula by the whole number multiplier to get the molecular formula

Calculate Empirical Formula from Percent Composition Lactic acid has a molar mass of 90.08 g and has this percent composition: Lactic acid has a molar mass of 90.08 g and has this percent composition: 40.0% C, 6.71% H, 53.3% O 40.0% C, 6.71% H, 53.3% O What is the empirical and molecular formula of lactic acid? What is the empirical and molecular formula of lactic acid? Assume a 100.0 g sample size Assume a 100.0 g sample size Convert percent numbers to grams Convert percent numbers to grams

Calculate Empirical Formula from Percent Composition Convert mass of each element to moles Convert mass of each element to moles Divide each mole quantity by the smallest number of moles Divide each mole quantity by the smallest number of moles The ratio of C to H to O is 1 to 2 to 1 Empirical formula is Empirical formula mass = 12.01 + 2 (1.008) + 16.00 = 30.03 g/mol CH 2 O

Determination of the Molecular Formula Obtain the value of n (whole number multiplier) Obtain the value of n (whole number multiplier) Multiply the empirical formula by the multiplier Multiply the empirical formula by the multiplier Molecular formula = n х empirical formula Molecular formula = 3 (CH 2 O) C3H6O3C3H6O3

Formulas for Compounds Empirical Formula Empirical Formula Smallest possible set of subscript numbers Smallest possible set of subscript numbers Smallest whole number ratio Smallest whole number ratio All ionic compounds are given as empirical formulas All ionic compounds are given as empirical formulas Molecular Formulas Molecular Formulas The actual formulas of molecules The actual formulas of molecules It shows all of the atoms present in a molecule It shows all of the atoms present in a molecule It may be the same as the EF or a whole- number multiple of its EF It may be the same as the EF or a whole- number multiple of its EF Molecular formula = n х Empirical formula

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