Section 9.3—Analysis of a Chemical Formula How can we determine a chemical formula?

Percent Composition How is percent composition found?

What is Percent Composition?

Example #1 Example: A 8.5 g sample is composed of carbon and hydrogen. If 5.5 g of the sample is found to be carbon, what is the percent composition by mass of the sample?

Example #1 If total = 8.5 g and C = 5.5 g - then H = 3.0 g Example: A 8.5 g sample is composed of carbon and hydrogen. If 5.5 g of the sample is found to be carbon, what is the percent composition by mass of the sample? If total = 8.5 g and C = 5.5 g - then H = 3.0 g

Let’s Practice #1 A sample is 57.0% by mass chlorine, how many grams of chlorine are present in a 27.5 g sample?

Let’s Practice #1 A sample is 57.0% by mass chlorine, how many grams of chlorine are present in a 27.5 g sample? 27.5 g   27.5 g 100 100

Example #2 Percent composition can also be determined from a chemical formula Example: Find the percent composition, by mass, of CaCl2

Example #2 Percent composition can also be determined from a chemical formula Example: Find the percent composition, by mass, of CaCl2 Ca Cl 1 2 40.08 g/mole 35.45 g/mole  = 70.90 g/mole + 110.98 g/mole So for 1 mole: total = 110.98 g Ca = 40.08 g Cl = 70.90 g

Let’s Practice #2 Find the percent composition, by mass, of NaNO3

Find the percent composition, by mass, of NaNO3 Let’s Practice #2 Find the percent composition, by mass, of NaNO3 Na N 1 22.99 g/mole 14.01 g/mole  = + 85.00 g/mole O 3 16.00 g/mole 48.00 g/mole

Empirical Formulas

What’s an Empirical Formula? Empirical – from data Empirical Formula – Chemical formula determined from lab data. Lowest possible ratio of atoms CH2 is the lowest ratio (and empirical formula) of the molecule C3H6

Ratio of Atoms in a Molecule Subscripts in a chemical formula show the ratio of atoms (or ions) in a molecule a sample of CaCl2 has 1 calcium ion : 2 chlorine ions If the subscripts give the ratio of atoms, then they also give the ratio of moles of atoms a sample of CaCl2 has 1 mole of calcium ions : 2 moles of chlorine ions We can use the unit “mole” to count things Atoms and ions can be counted by “moles”

Using Mole Ratio of Atoms in a Molecule Therefore, if the ratio of moles of each atom is found… then the subscripts of the chemical formula are known 1 mole C 2 mole H CH2

Example #3 If given percents, use those percents as grams (as if you assume you have a 100 g sample)—Remember %’s add up to 100! 1 2 Change grams to moles for each atom Find the lowest possible whole number ratio of the atom (divide all moles by the smallest # of moles) 3 4 Use the ratio as subscripts for writing the chemical formula Example: Find the empirical formula if a sample contains Ca and Cl and is 36.1% Ca

Example #3 If given percents, use those percents as grams (as if you assume you have a 100 g sample)—Remember %’s add up to 100! 1 2 Change grams to moles for each atom Find the lowest possible whole number ratio of the atom (divide all moles by the smallest # of moles) 3 4 Use the ratio as subscripts for writing the chemical formula Example: Find the empirical formula if a sample contains Ca and Cl and is 36.1% Ca 36.1 g Ca 1 mol Ca = _____ mol Ca 0.901 40.08 g Ca CaCl2 63.9 g Cl 1 mol Cl = _____ mol Cl 1.80 35.45 g Cl 0.901 mol Ca = 1 mol Ca 0.901 1.80 mol Cl = 2 mol Cl 0.901

Find the empirical formula if a sample contains Let’s Practice #3 Find the empirical formula if a sample contains 40.92 g C, 4.58 g H and 54.5 g O 40.92 g C = _____ mol C g C mol C 1 12.01 3.41 4.58 g H = _____ mol H g H mol H 1 1.01 4.53 54.5 g O = _____ mol O g O mol O 1 16.00 3.41 C3H4O3 3.41 mol C = 1 mol C 3.41 4.53 mol H = 1.33 mol H 3.41 3.41 mol O = 1 mol O 3.41 Multiply the ratio (1 : 1.33 : 1) by 3 to make a whole number ratio (3 : 4: 3)

Molecular Formulas

What’s a Molecular Formula? Empirical Formula – Chemical formula determined from lab data. Lowest possible ratio of atoms Molecular Formula – Actual ratio of atoms in a molecule

Empirical versus Molecular Formula The empirical formula is the lowest possible ratio. The molecular formula is the actual ratio A molecule with the empirical formula: Could have one of the following molecular formulas: NO2 NO2, N2O4, N4O8… CH2 CH2, C2H4, C4H8…

Find the molecular formula. Example #4 1 Find the empirical formula, if not given 2 Find the molar mass of the empirical formula Find the ratio of the molecular formula’s molar mass (must be given to you) to the empirical formula’s molar mass 3 Multiply the empirical formula’s subscripts by the ratio found in step 3. 4 Example: Empirical formula = C3H4O3. The molecular formula’s molar mass = 176.14 g/mole. Find the molecular formula.

Find the molecular formula. Example #4 1 Find the empirical formula, if not given 2 Find the molar mass of the empirical formula Find the ratio of the molecular formula’s molar mass (must be given to you) to the empirical formula’s molar mass 3 Multiply the empirical formula’s subscripts by the ratio found in step 3. 4 Example: Empirical formula = C3H4O3. The molecular formula’s molar mass = 176.14 g/mole. Find the molecular formula. 176.14 g/mole = 2 88.07 g/mole C 3  12.01 g/mole = 36.03 g/mole H 4  1.01 g/mole = 4.04 g/mole C3H4O3  2 O 3  16.00 g/mole = + 48.00 g/mole C6H8O6 88.07 g/mole

Hydrate Formulas

What’s a Hydrate? Hydrate – Molecule that has water physically attached to it It’s not dissolved in water…hydrates can be solid, liquid or gas!

Hydrates are inorganic salts "containing water molecules combined in a definite ratio as an integral part of the crystal“ either bound to a metal center or have crystallized with the metal When writing a hydrate, a dot is used to separate the formula compound from the number of water molecules Examples) magnesium sulfate heptahydrate cobalt (II) chloride hexahydrate tin (II) chloride dihydrate

Hydrate & anhydride Hydrate = molecule with water molecules physically attached anhydride = molecule with water removed The water can be removed by heating the hydrate Hydrate anhydride + water heat Finding the ratio of anhydride molecules to water molecules gives you the hydrate formula

Example #5 1 Find the mass of anhydride & water if not given 2 Change mass of anhydride & water to moles 3 Find the ratio of the moles water to moles anhydride 4 Write the hydrate formula Example: 2.46 g MgSO4 hydrate is heated and 1.20 g MgSO4 anhydride is left. Find the hydrate formula.

Hydrate = anhydride + water Example #5 1 Find the mass of anhydride & water if not given 2 Change mass of anhydride & water to moles 3 Find the ratio of the moles water to moles anhydride 4 Write the hydrate formula Example: 2.46 g MgSO4 hydrate is heated and 1.20 g MgSO4 anhydride is left. Find the hydrate formula. Hydrate = anhydride + water 2.46 g = 1.20 g + water Water = 1.26 g 1.20 g MgSO4 1 mol MgSO4 0.0699 mol H2O = 7.01 0.00997 mole MgSO4 = _______ mol MgSO4 0.00997 120.38 g MgSO4 1.26 g H2O 1 mol H2O = _______ mol H2O 0.0699 MgSO4  7 H2O 18.02 g H2O

Calculating % of Water Determine the mass of the hydrated compound Determine the mass of JUST the water Then divide % H2O = Mass of water x 100 Mass of hydrate Example) CuSO4 ⋅ 5H2O CuSO4 + 5H2O Blue white