Zumdahl • Zumdahl • DeCoste World of CHEMISTRY

Chapter 6 Chemical Composition

Goals of Chapter 6 Average mass/counting by weighing Experimental determination of atomic mass Moles and Avogadro's number Molar Mass Convert between moles and mass Mass percent of elements in compounds Empirical formulas Calculating molecular formulas

One of most important chemical activities: Synthesis of new substances Nylon, aspartame, Kevlar (bulletproof vests), PVC, Teflon All originated in chemist's laboratory Once they make it – they must determine what it is What is it's composition? What is it's chemical formula?

Answer: Counting by weighing Question: How can you determine exactly how many M&M's are in your cup without counting every one? Answer: Counting by weighing

Answer: No, each is slightly different Question: Does every M&M weigh exactly the same as all of the other M&M's? Answer: No, each is slightly different

How can you determine a mass that is typical of each M&M? Weigh several M&M's and determine the average mass

How to determine number of M&M's: Determine average mass of an M&M by weighing several Average mass = sum of the masses divided by the number of M&M's weighed Weigh entire cup of M&M's and divide that weight by the average mass to get the number of M&M's

Mathematical Equations: Av Mass = m1 + m2 + m3 + m4 +m5 5 # M&M's = __total mass (g)__ av mass (g/M&M)

Atomic Masses: Counting Atoms by Weighing Solid carbon reacts with gaseous oxygen to form gaseous carbon dioxide: C(s) + O2(g) → CO2(g) 1 atom C reacts with 1 molecule O2 to yield 1 molecule of CO2

If you have a pile of solid carbon and want to know how much Oxygen you need for the reaction to occur – what do you do? Need to count carbon atoms – but atoms are too small to count Use same principle applied to the M&M's and count by weighing

Atomic Mass Unit (amu) Gram & kilogram too large to use because atoms are so tiny Atomic mass unit is used – much smaller unit than a gram 1 amu = 1.66 x 10-24 grams Atoms exist as isotopes Use average atomic mass (bottom # on periodic table)

To find oxygen needed to react with carbon: Weigh the pile of carbon = 3.00 x 1020 amu From periodic table: 1 C atom weighs 12.01 amu 3.00 x 1020 amu x 1 C atom = 2.50 x 1019 C atoms 12.01 amu

What is another name for 12 donuts? A dozen Other Examples: Ream of paper Gross of pencils

The Mole Definition: the number equal to the number of carbon atoms in 12.01 grams of carbon Used precise counting techniques to determine this number to be 6.02 x 1023 atoms Avogadro's number = 6.02 x 1023 atoms One mole of something consists of 6.02 x 1023 units of that substance

1 dozen eggs = 12 eggs 1 mole eggs = 6.02 x 1023 eggs 1 mole water = 6.02 x 1023 H2O molecules 1 mole Ag = 6.02 x 1023 Ag atoms

What if you were offered $1 million to count from 1 to 6 x 1023 at a rate of one number each second? What would be your hourly wage? Would you do it? Could you do it?

6 x 1023 seconds is about 2 x 1020 hours or 2 x 1016 years Your hourly wage would by $0.000000000000005 per hour If would take hundreds of millions of years to earn a penny In other words – it's impossible

A sample of an element with a mass equal to that element's average atomic mass expressed in grams contains 1 mole of atoms. 1 mole Al = 27 grams = 6.02 x 1023 atoms 1 mole Au = 197 grams = 6.02 x 1023 atoms 1 mole Fe = 55.6 grams = 6.02 x 1023 atoms 1 mole S = 32 grams = 6.02 x 1023 atoms

This is the molar mass of methane Chemical compound is a collection of atoms Methane = CH4 = 1 C atom + 4 H atoms Mass 1 mol of C = 1 x 12.01 g = 12.01 g Mass 4 mol of H = 4 x 1.008 g = _4.032 g Mass of 1 mol of CH4 = 16.04 g This is the molar mass of methane

Figure 6.3: Various numbers of methane molecules. Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Molar Mass Defined as the mass (in grams) of one mole of a substance Obtain molar mass by summing the masses of the component atoms For ionic compounds, sometimes referred to as formula weight Used to be called molecular weight Copyright © Houghton Mifflin Company

Example 6.5: Calculate the molar mass of sulfur dioxide – SO2 (exhaust gas that can produce acid rain) 1 mol SO2 molecules = 1 mol S + 2 mol O Mass of 1 mol S = 1 x 32.07 g = 32.07 g Mass of 2 mol O = 2 x 16.00 g = 32.00 g Mass of 1 mol SO2 = 64.07 g The molar mass of sulfur dioxide is 64.07 g Copyright © Houghton Mifflin Company

How many grams of sulfur dioxide do you have if you have 5 moles? 5 mol SO2 x 64.07 grams = 320.4 grams SO2 1mol SO2 Used molar mass from previous slide Copyright © Houghton Mifflin Company

If you have 800 grams of SO2, how many moles is this? 800 g SO2 x 1 mol SO2 = 12.5 mol SO2 64.07 g How many molecules is this? 12.5 mol x 6.02 x 1023 molecules = 7.53 x 1024 1 mole SO2 SO2 molecules Copyright © Houghton Mifflin Company

Percent composition of compounds Mass fraction mass of element in 1 mol of cmpd for a given = element mass of 1 mole of compound To convert mass fraction to mass percent, multiply mass fraction by 100% Copyright © Houghton Mifflin Company

Mass percent: Ethanol (C2H5OH) Mass of C = 2 mol x 12.01 g/mol = 24.02 g Mass of H = 6 mol x 1.008 g/mol = 6.048 g Mass of O = 1 mol x 16.00 g/mol = 16.00 g_ Mass: 1 mol C2H5OH = molar mass = 46.07 g To find mass percent, divide total mass of each element by molar mass of ethanol (x 100%) Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Mass % X = mass of X in 1 mol ethanol x100% mass of 1 mole of ethanol Mass % C = 24.02 g x 100% = 52.14% 46.07 g Mass % H = 6.048 g x 100% = 13.13% 46.07 g Mass % O = 16.00 g x 100% = 34.73% 46.07 g Mass percentages of all of the elements should add up to 100% (52.14% + 13.13% + 34.73% = 100.00%) Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Formulas of Compounds Sometimes a chemical reaction gives a product that has never been formed before: Identify compound by determining which elements are present and how much of each is there Previously, we used formula to determine the mass of each element present in a mole – to obtain the formula of an unknown compound – do the opposite Use measured masses of elements present to determine the formula Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Determining Formula Formula represents relative numbers of the various types of atoms present To determine formula – count the atoms How do we count atoms? - By weighing! Change mass into moles Change moles into atoms Use ratios to determine formula Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company If we have a compound that contains only carbon, hydrogen, and oxygen and we weigh out 0.2015 grams for analysis. The sample is analyzed and found to contain 0.0806 g C, 0.01353 g H, and 0.1074 g O. What is the compound? Step 1: Convert masses of elements to moles Step 2: Convert moles of elements to atoms Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Calculations show the same number of C and O atoms Calculations show twice as many H atoms as C atoms and O atoms Can write formula as CH2O But formula could also be C2H4O2 Must be in 1:2:1 ratio Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Empirical Formula Formula of a compound that expresses the smallest whole number ratio of the atoms present (simplest formula) In a class the girl to boy ratio is 1:8 This could mean the class has 1 girl & 8 boys OR This could mean the class has 2 girls & 16 boys OR This could mean the class has 3 girls & 24 boys etc. Copyright © Houghton Mifflin Company

Steps for Determining Empirical Formula of a Compound Obtain mass of each element present (grams) Determine # moles present for each atom Divide # of moles by smallest # of moles (converts smallest # to 1). If all numbers are integers, these will be the subscripts, if not, go to step 4 Multiply numbers in step 3 by the smallest integer that will convert them to whole numbers. These whole numbers are the subscripts Copyright © Houghton Mifflin Company

Copyright © Houghton Mifflin Company Molecular Formula The actual formula of a compound Gives the composition of the molecules that are present Need molar mass to determine Our mystery compound could be glucose: C6H12O6 (C to H to O ratio is 1:2:1) Copyright © Houghton Mifflin Company

Determining Molecular Formula Always a multiple of empirical formula (Empirical formula)n = molecular formula n = molar mass______ empirical formula mass for glucose n = 6: (CH2O)6 = C6H12O6 Copyright © Houghton Mifflin Company

Figure 6.5: Ball-and-stick model of P4O10. Copyright © Houghton Mifflin Company