1 Unit 4 Percent composition, Empirical and Molecular Formulas 1. Write the complete chemical formula from names. 2. Calculate molar mass (molecular mass and gram formula mass) 3. Calculate percent composition 4. Name and calculate percent composition for hydrated compounds 5. Distinguish between empirical and molecular formulas 6. Calculate empirical formulas REVIEW: Polyatomic ions, writing names from formulas, oxidation number rules I. WRITING FORMULAS FROM NAMES: A. Rules: 1. Know the polyatomic ion formulas and their total charge. 2. Write the symbols of elements or polyatomic ions in the name given. Place oxidation numbers above the symbols. 3. If the sum of the charges add up to zero, then the compound is balanced. Do no more. If not, move to step 4. 4. If the sum of the charges do not equal zero, the compound is not balanced. Add subscripts until the sum of the charges equal zero. 5. Polyatomic ions must have parentheses around them if they need a subscript. 6. NOTE: Do NOT use oxidation numbers with two nonmetals. The prefix gives the number of atoms and becomes the subscript to the element to which it is attached. B. In the following examples, first write each ion with charges, then write the balanced formulas with appropriate subscripts. 1. sodium chloride Na + Cl NaCl 2. calcium sulfate 3. iron (III) oxide II. MOLAR MASS (a.k.a. molecular mass or gram formula mass). The molar mass of a compound is simply the sum of the Atomic Weights of the element in the compound. EXAMPLES: What is the molecular weight of H 2 O? - The atomic weight of H is 1.0 - The atomic weight of O is 16.0 1.0 + 1.0 + 16.0 = 18 H 2 O 2 atoms H(1.008 g) + 1 atom O (15.99g) = 18.01 g/mol Note when using atomic weights we usually round off the values to one decimal place
2 What is the molecular weight of Ca(OH) 2 We have: 1 - Ca 2 OH groups so we have two O s and two H s The subscript tells you how many of the group in parentheses you have 40.1 + 16.0 + 16.0 + 1.0 + 1.0 = 74.1 What is the molar mass of Al 2 (SO 4 ) 3 There are 2 atoms of Al 3 atoms of S 12 atoms of O 54 + 96 + 192 = 342 1. What is the mass of one mole of aluminum Chromate? 2. What is the molar mass of (NH 4 ) 2 CO 3 III. PERCENT COMPOSITION: To find the percentage composition of a compound do this 1. Find the molar mass of the compound 2. find the total weight of each element in the compound 3. divide the total weight of each element by the molar mass. Example 1 Find the % Mg in MgF 2 1. The molar mass is 24.3 + 19.0 + 19.0 = 62 grams 2. The percentage Mg is 24.3/62 x 100 = 39.2% Find the % F in MgF 2 38.0/62 x 100 = 60.8% F Note that since there are two F s in MgF 2 we add 19+19 to get the 38 we use in the calculation. Example 2 Find the percentage of each element present in Mg(NO 3 ) 2 1. Find the molar mass Mg = 24.3 2 N s = 14.0 + 14.0 = 28 6 O s = 16 + 16 + 16 + 16 + 16 +16 = 96.0 Molar mass = 24.3 + 28.0 + 96.0 = 148.3
3 2. Find the total weight of each element in the compound and divide by the molar mass. % Mg = 24.3/148.3 = 16.4% % N = 28.0/148.3 = 18.9% % O = 96.0/148.3 = 64.7% Notice that the total or the percentages add up to 100. This will always be the case! Problems: 1. What is the percent of each element in the compound iron (III) oxide? 2. What is the percent of each element in the compound, Ca(OH) 2? 3. What is the percent of water in the hydrate, Na 2 CO 3 10 H 2 O? Hydrates are solid compounds that have water molecules incorporated into their crystalline structure. Even though there is water inside the crystalline structure of hydrates, they do not feel wet to the touch. However if hydrates are heated they will give off this trapped water. III. DETERMINING THE EMPIRICAL FORMULA FROM GRAMS OR PERCENTAGES: Empirical formulas tell us the smallest (simplest) ratio of atoms. A. Procedure: 1. Convert given grams to moles of each element. If value given is in percents, assume percents are equal to grams. 2. Convert moles to simplest whole number by dividing each mole calculated by the smallest number of moles determined from doing step number 1. 3. If the number comes out to be a fraction of ½, multiply everything by 2 to get a whole number. The rule applies to fractions of ¼, multiply by 4. 4. The resulting number for each element is the number of atoms (subscript) of each element in the compound. Example 1 Suppose that you have a compound that is known to be 10.1% Li 20.3% N 69.7% O What is the formula for this compound? 1. Suppose that you had 100 g of this compound than you would have... 10.1g of Li 20.3g of N 69.7g of O
2. Now convert each into moles 4 10.1g Li 20.3g N 69.7g O 6.94 g/mol 14.0g/mol 16.0g/mol 1.45 moles Li 1.45 moles N 4.35 moles O Li 1.45 N 1.45 O 4.35 Atoms combine in whole number ratios, we need to change the subscripts to whole numbers. Divide each mole amount by the smallest mole amount 1.45 moles Li = 1 mole of Li 1.45 moles on N = 1 mole of N 4.35 mole of O = 3 mole of O 1.45 1.45 1.45 So the Ratio between Li:N:O is 1:1:3 (4.35 is 3 times as big as 1.45) Since the ratio of Li : N : O is 1:1:3, the formula must be LiNO 3 This is the simple formula for a compound it may or may not be the actual formula Example 2 Pretend that there are two elements in a compound. Lets call them element A and Element B. Suppose that you calculate the moles of each element just like you did in before and you got 1.4 moles of A and 2.8 moles of B The formula must be AB 2 Because there are twice as many moles of B as A Suppose you got 1.4 moles of A and 2.1 moles of B If you divide by the smallest number, the 1.4 you will see that 2.1 is 1.5 times as big as 1.4. You might think the formula is AB 1.5 but we can t have fractions of atoms so we double both subscripts to get A 2 B 3 Problems: I. A compound is found to contain 75.0 grams of carbon and 25.0 grams of hydrogen. What is the empirical formula? 2. A typical charcoal briquette that is used in making a barbeque fire is composed of 43.2 grams of carbon. When the charcoal lump is burned, it combines with oxygen and the resulting compound has a mass of 159.0 grams. What is the formula of the compound?
5 3. What is the empirical formula of a compound that contains 70.0% iron and 30.0% oxygen? IV. Molecular Formulas (Actual Formulas): 1. Determine the empirical formula. 2. Determine the molar mass of the empirical formula. 3. Divide the molecular mass given by the problem by the calculated molar mass of the empirical formula. 4. Multiply the subscripts of the empirical formula by the number resulting from # 3 above. Suppose a compound has an empirical formula of CH 3 and it has a molar mass of 30. If you find the empirical formula mass you get: C = 12.0g/mol +H = 3 x 1.0 g/mol = 15 g/mol But CH 3 s molecular weight is only 15 not 30 To make it have a molecular weight of 30 the formula must be twice as big as it is. Divide the molar mass by the empirical formula mass 30g = 2 15g So multiply all subscripts in the empirical formula by 2 (CH 3 ) So the actual formula must be C 2 H 6 Problems: 1. What is the molecular formula of a compound that contains 40.0% carbon, 6.7% hydrogen, 53.3% oxygen. The molar mass of the compound is 180.0 grams/mole. 2. The sweetener, Saccharin, is 45.90% carbon, 2.75% hydrogen, 26.2% oxygen, 17.5% sulfur and 7.65% nitrogen. The molecular weight of Saccharin equals 183.18 grams/mole. What is the molecular formula of Saccharin? 3. Cholesterol is composed of 83.9% carbon, 12.0% hydrogen and 4.1% oxygen. The molecular mass of the cholesterol is 386 grams/mole. What is the molecular formula of cholesterol?
Hydrated Compounds 1. Contain water loosely bonded as part of its structure, Na 2 CO 3 10 H 2 O. 6 2. The means to add the mass of all the waters to the mass of the anhydrous salt, Na 2 CO 3, [the part of the compound or residue without the water]. 3. When trying to solve for amount of water, use empirical formula method. EXAMPLES: Find the percent water without masses given: 1. What percent of water is found in BaCl 2 2 H 2 O? 2. Find the percent of anhydrous salt in Sr(NO 3 ) 2 4 H 2 O.