Chemical Quantities

Calculating The Number of Atoms in a Specific Mass You have a 1.00 g sample of lead. How many atoms of lead are present? - 1.00 g Pb 1 amu 1.66 x 10 24 g 1 atom Pb 207.2 amu =

Calculating Mass Example Calculate the mass (in amu) of 1.0 х 104 carbon atoms 1) Given: 2) Plan: Convert from atoms to amu 3) CF 4) Set Up Problem

Formula Mass The sum of atomic masses of all atoms in its formula Important role in nearly all chemical calculations Can be calculated for compounds and diatomic elements The atoms present in one formula unit of a substance Can be calculated for both ionic and molecular substances

Calculating Formula Mass Calculate the formula mass of calcium chloride Write the formula from the name given Ca2+ (from group II) and Cl- (from group VII) Formula is CaCl2 due to charge balance Formula mass: Sum of the atomic masses of atoms in the formula (1 Ca atom + 2 Cl atoms) Write the name of the compound by combining Ca2+ and Cl- 1 amu Ca + 2 amu Cl is the formula mass of CaCl2 = 40.08 amu = 70.90 amu Formula mass of CaCl2

Counting Large Quantities Many chemical calculations require counting atoms and molecules 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 Need to use a special counting unit just as used for other items A ream of paper One dozen donuts A pair of shoes Because it requires working with large numbers

The Mole Mole: A unit that contains 6.022 х 1023 objects It is used due to the extremely small size of atoms, molecules, and ions 6.022x1023 particles in 1 mole Called Avogadro’s Number Periodic Table The average atomic mass in amu or g/mol (one atom) The weight of 1 mole of the element in grams Avogadro’s number provides the connecting relationship between molar masses and atomic masses Chemist use a special counting units Objects can be anything “Objects” can be anything Particles in the sense of atoms and molecules

Calculating the Number of Molecules in a Mole How many molecules of bromine are present in 0.045 mole of bromine gas? Avogadro’s number Given: 0.045 mol Br2 Need: molecules of Br2 Equality: Conversion factors: 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 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 (C6H12O6) there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen First case is the microscopic level per molecule Second case is the macroscopic level per mole

Calculating the Moles of an Element in a Compound How many moles of carbon atoms are present in 1.85 moles of glucose? subscript Plan: moles of glucose moles of C atoms Equality: (One) mol C6H12O6 = 6 mols C atoms Conversion Factors: 11.1 mol C atoms Set Up Problem:

Molar Mass 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 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 1023 particles of that element Use the periodic table to obtain the molar mass of any element It was determined experimentally that Avogadro’s number of atoms gives the same numerical value between amu and mol This is connection between the microscopic and macroscopic values

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

Molar Mass of a Compound Calculate the molar mass of iron (II) sulfate Formula is FeSO4 Calculate the molar mass of each element Each element is multiplied by its respective subscript: (number of moles of each element) The molar mass is calculated by the sum of the molar masses of each element Formula Subscript Moles of Compound Moles of Element in Compound

Molar Mass of a Compound 1) Formula is FeSO4: 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 Number of particles Number of moles Number of grams 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 Three most commonly calculated quantities for chemical problems Molar mass can be used to calculate concentrations of solution, to calculate yields of products formed in reactions based on the limiting reagent

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

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? 3 mg NaCl moles of NaCl = 0.003 g NaCl Equality: 1 mol NaCl = 58.44 g

Converting Grams to Particles Ethylene glycol (antifreeze) has the formula C2H6O2. How many molecules are present in a 3.86 × 10-20 g sample? Molar mass Avog Number Plan: convert g moles molecules of ethylene glycol Conversion Factor 1 Equality 1: Equality 2: Conversion Factor 2 375 molecules

Percent Composition

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

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

Percent Composition It is the percent by mass of each element in a compound Can be determined By its chemical formula Molar masses of the elements that compose the compound The percent of each element contributes to the mass of the compound The formula of carbon dioxide indicates it is composed of one atom of carbon and two atoms of oxygen. Now we will express it in terms of mass percent

Calculating Percent Composition Example What is the percent composition of each element in NH4OH? Determine the contribution of each element Molar mass On a per mol basis

Empirical Formulas 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 If the percent composition is known, an empirical formula can be calculated Formulas are determined by calculation of data experimentally obtained Smallest possible set of subscript numbers The subscript numbers in formulas can be read in terms of the number of moles of each element

Empirical Formulas To Determine the empirical formula: Calculate the moles of each element Use molar mass (atomic mass) Calculate the ratios of the elements to each other 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 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 Cannot have 1.5 atoms in a formula

Relating Empirical and Molecular Formulas n represents a whole number multiplier from 1 to as large as necessary Calculate the empirical formula and the mass of the empirical formula Divide the given molecular mass by the calculated empirical mass 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: 40.0% C, 6.71% H, 53.3% O What is the empirical and molecular formula of lactic acid? Assume a 100.0 g sample size Convert percent numbers to grams Lactic acid builds up in muscles after aerobic exercise Since percent represents parts of one element per 100 parts of the total compound

Calculate Empirical Formula from Percent Composition Convert mass of each element to moles Divide each mole quantity by the smallest number of moles Empirical formula is CH2O The ratio of C to H to O is 1 to 2 to 1 Empirical formula mass = 12.01 + 2 (1.008) + 16.00 = 30.03 g/mol

Determination of the Molecular Formula Obtain the value of n (whole number multiplier) Multiply the empirical formula by the multiplier The small interger is the name of the small number multiplier Molecular formula = n х empirical formula Molecular formula = 3 (CH2O) C3H6O3

Formulas for Compounds Empirical Formula Smallest possible set of subscript numbers Smallest whole number ratio All ionic compounds are given as empirical formulas Molecular Formulas The actual formulas of molecules 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 Ionic compounds do not exist as molecules Molecular formulas account for every atom in the structure Molecular formula = n х Empirical formula