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

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02-Jan-2016

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• Counting Large QuantitiesMany chemical calculations require counting atoms and moleculesIt is difficult to do chemical calculations in terms of atoms or formula unitsSince atoms are so small, extremely large numbers are needed in calculationsNeed to use a special counting unit just as used for other itemsA ream of paper One dozen donutsA pair of shoes

• The MoleIt is more convenient to use a special counting unit for such large quantities of particles Mole: A unit that contains 6.022 1023 objectsIt is used due to the extremely small size of atoms, molecules, and ions6.022x1023 particles in 1 moleCalled Avogadros Number

Periodic TableThe average atomic mass in amu (one atom) The weight of 1 mole of the element in gramsAvogadros number provides the connecting relationship between molar masses and atomic masses

• Calculating the Number of Molecules in a MoleHow many molecules of bromine are present in 0.045 mole of bromine gas? Given: 0.045 mol Br2Need: molecules of Br2Avogadros numberConversion factors:Equality:Set Up Problem:

• Subscripts State Moles of ElementsThe subscripts in a chemical formula indicate the number of atoms of each element present in a compoundThe subscripts in a chemical formula can also indicate the number of moles of atoms of each element present in one mole of a compoundi.e. In one molecule of glucose (C6H12O6) there are 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen

• Calculating the Moles of an Element in a CompoundHow many moles of carbon atoms are present in 1.85 moles of glucose?Plan: moles of glucosemoles of C atomssubscript(One) mol C6H12O6 = 6 mols C atomsEquality:Conversion Factors:Set Up Problem:11.1 mol C atoms

• Molar MassThe atomic mass of a carbon-12 atom is 12.00 amuThe atomic mass of one mole of carbon-12 atoms 12.00 gOne 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 1023 particles of that elementUse the periodic table to obtain the molar mass of any element

• Molar MassWhen the number of grams (weighed out) of a substance equals the formula mass of that substance, Avogadros number of molecules of that substance are present

• Molar Mass of a CompoundCalculate the molar mass of iron (II) sulfateFormula is FeSO4Calculate 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 Moles of Element in CompoundMoles of CompoundFormula Subscript

• Molar Mass of a Compound1) Formula is FeSO4: The molar masses of iron, sulfur, and oxygen are2) 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 MassThe three quantities most often calculated Number of particlesNumber of moles Number of gramsUsing molar mass as a conversion factor is one of the most useful in chemistryCan be used for g to mole and mole to g conversions

• Converting Mass of a Compound to MolesInternational 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 g3 mg NaClmoles of NaCl= 0.003 g NaCl

• Converting Grams to ParticlesEthylene glycol (antifreeze) has the formula C2H6O2. How many molecules are present in a 3.86 10-20 g sample?

Plan: convert g moles molecules of ethylene glycolEquality 1:ConversionFactor 1Equality 2:ConversionFactor 2375 moleculesMolarmassAvogNumber

• Percent CompositionSometimes its useful to know the composition of a compound in terms of what percentage of the total is each elementPercentParts per 100The number of specific items per a group of 100 items50% of \$100 is \$50 (50 items/100 total items)

• Percent ExampleYou have 4 oranges and 5 apples. What percent of the total is oranges?

In parts per 100

• Percent CompositionIt is the percent by mass of each element in a compoundCan be determined By its chemical formulaMolar masses of the elements that compose the compound The percent of each element contributes to the mass of the compound

• Calculating Percent Composition ExampleWhat is the percent composition of each element in NH4OH?Determine the contribution of each elementMolar mass

• Empirical FormulasThe simplest ratio of elements in a compoundIt uses the smallest possible whole number ratio of atoms present in a formula unit of a compoundIf the percent composition is known, an empirical formula can be calculated

• Empirical FormulasTo Determine the empirical formula:Calculate the moles of each elementUse molar mass (atomic mass)Calculate the ratios of the elements to each otherFind the lowest whole number ratioDivide each number of moles by the smallest number of moles present

• Empirical Formula: Converting Decimal Numbers to Whole NumbersThe subscripts in a formula are expressed as whole numbers, not as decimalsThe resulting numbers from a calculation represent each elements subscriptIf 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 Formulasn represents a whole number multiplier from 1 to as large as necessary

Calculate the empirical formula and the mass of the empirical formulaDivide the given molecular mass by the calculated empirical massAnswer is a whole number multiplier

• Relating Empirical and Molecular FormulasMultiply each subscript in the empirical formula by the whole number multiplier to get the molecular formula

• Calculate Empirical Formula from Percent CompositionLactic acid has a molar mass of 90.08 g and has this percent composition:40.0% C, 6.71% H, 53.3% OWhat is the empirical and molecular formula of lactic acid?Assume a 100.0 g sample sizeConvert percent numbers to grams

• Calculate Empirical Formula from Percent CompositionConvert mass of each element to molesDivide each mole quantity by the smallest number of moles

The ratio of C to H to O is 1 to 2 to 1Empirical formula isEmpirical formula mass = 12.01 + 2 (1.008) + 16.00 = 30.03 g/mol CH2O

• Determination of the Molecular Formula Obtain the value of n (whole number multiplier)Multiply the empirical formula by the multiplierMolecular formula = n empirical formulaMolecular formula = 3 (CH2O) C3H6O3

• Formulas for CompoundsEmpirical FormulaSmallest possible set of subscript numbers Smallest whole number ratioAll ionic compounds are given as empirical formulasMolecular FormulasThe actual formulas of moleculesIt shows all of the atoms present in a moleculeIt may be the same as the EF or a whole- number multiple of its EF

Molecular formula = n Empirical formula

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*Because it requires working with large numbers *Chemist use a special counting unitsObjects can be anything

Objects can be anythingParticles in the sense of atoms and molecules*First case is the microscopic level per moleculeSecond case is the macroscopic level per mole*It was determined experimentally that Avogadros number of atoms gives the same numerical value between amu and mol This is connection between the microscopic and macroscopic values*Three most commonly calculated quantities for chemical problemsMolar mass can be used to calculate concentrations of solution, to calculate yields of products formed in reactions based on the limiting reagent*The number of items of a specified type in a group of 100 items*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*On a per mol basis*Formulas are determined by calculation of data experimentally obtainedSmallest possible set of subscript numbersThe subscript numbers in formulas can be read in terms of the number of moles of each element*Cannot have 1.5 atoms in a formula*

Lactic acid builds up in muscles after aerobic exerciseSince percent represents parts of one element per 100 parts of the total compound*The small interger is the name of the small number multiplier*Ionic compounds do not exist as moleculesMolecular formulas account for every atom in the structure*Ionic compounds do not exist as moleculesMolecular formulas account for every atom in the structure