# Notes: Formula Mass and Percent Composition

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1 Notes: Formula Mass and Percent Composition Formula mass - the mass of one mole of a compound, atom or ion. -also called: gram formula mass, molecular mass, gram molecular mass, formula weight, gram formula weight, molecular weight, gram molecular weight, molar mass, and molar weight Find the formula mass of each of the following: sodium chloride arsenic trichloride potassium sulfate ammonium phosphate Analysis of unknown compounds often starts by determining the percent composition by mass or, in other words, the mass of a particular element per 100 g of a compound. Once the percent composition is known, the empirical formula may be calculated. At other times it is helpful to calculate the percent composition from the formula of a compound. These calculations are often useful in other problems. The object of this lessen is to calculate the percent composition of a compound and how to use that data to calculate the mass of a particular element in that compound. Example #1: If there are 95.0 g of barium and 26.3 g of fluorine in a compound, what is the percent composition? Example #2, If 225 g of a compound that is known to contain only phosphorus and oxygen is found to have g of oxygen, what is the percent composition of each element in the compound? Example #3: Calculate the percent composition of ammonium phosphate. Example # 4: Calculate the mass of iron (in g) present in 79.6 g iron (III) phosphate.

2 Notes - Introduction to Moles: One and Two Step Mole Calculations Measuring Matter: There are three ways to measure matter: by counting representative particles (typically molecules or formula units), by mass (in grams), or by volume (in liters for gases). The method used is usually chosen by the ease of each method and the information needed. Once a measurement has been made, it is possible to convert between the units for the other methods. 1 mole of a compound = fm (in g) compound 1 mole of an element = 6.02 x atoms of that element 1 mole of a compound = 6.02 x representative particles (molecules or formula units) The mole is the link between grams and the number of representative particles. Draw the mole map below: For neutral compounds, the representative particle is either the molecule (covalent) or the formula unit (ionic). However, to simplify matters we will just use the term molecule for both. EXAMPLES (One Step Conversions): Remember to show all work using dimensional analysis and to keep significant figures in mind. 1. How many moles are in 18.0 grams of sugar (C 6 H 12 O 6 )? 2. What is the weight of 4.50 moles of barium sulfide? 3. How many molecules are in 28.6 mole of nitrogen gas? 4. How many moles are in 3.90 x molecules of methane (CH 4 )? 5. How many atoms of oxygen are in 2.5 moles of oxygen gas? (Diatomic alarms should be ringing in your head-this one is sneaky)

3 You are now familiar with conversions between grams, moles, and molecules. We can combine these in to two-step or even three-step problems to find more information such as the number of atoms of an individual element in a compound. EXAMPLES: Two-Step and Three-Step Problems 6. How many molecules are in grams of sodium chloride? 7. How many molecules are in 937 g of calcium acetate? 8. How many grams are in 3.21 x molecules of potassium hydroxide? 9. How many atoms of aluminum are in 2.00 moles of aluminum fluoride? 10. How many atoms of chlorine are in grams of calcium chloride? 11. How many moles of carbon are in 1.00 x molecules of propane, C 3 H 8? 12. How many grams of magnesium are in 5.55 x molecules of magnesium sulfide? 13. How many grams of silicon are in 9.76 x molecules of silicon dioxide?

4 Notes: Empirical Formulas, Molecular Formulas and Hydrates Once a scientist has determined the percent composition of the various elements in the sample the empirical formula can then be determined. The empirical formula represents the smallest whole-number ratio of the elements in the compound. When determining the empirical formula always assume that you have a 100-gram sample; therefore the percent composition of each element can be used as the number of grams that you have of each element. There are three steps in determining the empirical formula of a compound: Step 1: Change the number of grams given to moles by using the atomic mass of each element. Use at least 4 significant figures! Step 2: Determine the mole ratio by dividing each number of moles by the smallest number of moles. If this does produce whole number ratios of moles, multiply all mole ratios by a whole number so that you do have whole numbers. Step 3: Use the ratio as subscripts in the formula. The elements usually appear in the problem in the same order that they should appear in the formula. Example Problem: A compound is 12.69% aluminum, 19.73% nitrogen, and 67.57% oxygen. What is the empirical formula of the sample? Example Problem: A g sample of a compound contains grams of chromium and the remainder is oxygen. Calculate the empirical formula of this compound. Since the empirical formula only gives the simplest whole number ratio of atoms, it is sometimes necessary to determine what the molecular formula for the compound would be. For example the empirical formula for hydrogen peroxide is HO, but the correct molecular formula is H 2 O 2. In order to determine the molecular formula both the empirical formula and the molecular (formula) mass must be known. In general: molecular formula = (empirical formula) n To determine n you must first determine the empirical formula s mass. Once this is done a simple calculation will give you the value of n : molecularformulamass n empiricalformulamass Once the value of n is known simple multiply the subscripts in the empirical formula by n to obtain the correct subscripts for the molecular formula.

5 Example Problem: In a 50.0 gram sample of hydrazine (a chemical used to treat waste water) there are found to be 43.8 grams of nitrogen and the remainder is hydrogen. The molecular mass of hydrazine is 32.0 grams per mole. What is the molecular formula of hydrazine? Example Problem: A compound is composed of 7.20 grams of carbon, 1.20 grams of hydrogen, and 9.60 grams of oxygen. The molecular mass of the compound is 180 grams. What are the empirical and molecular formulas for this compound? Hydrate - a hydrate is a compound that has a certain number of water molecules chemical bonded to it. Naming a Hydrate - a hydrate is named by first giving the name of the salt followed by the term "hydrate" with a numerical prefix attached. What is the name of Na 2 CO 3 10H 2 O? What is the formula of copper (II) sulfate tetrahydrate? What is the molar mass of copper (II) sulfate tetrahydrate? Determination of a Hydrate Formula: The moles of water molecules that are present must be a whole number multiple of the moles of the salt present, therefore these problems are very similar to working empirical formulas. Example: We have a g sample of hydrated barium iodide. The sample is heated to drive off the water. The dry (anhydrous) sample has a mass of g. What is the formula of the hydrate? What is the name of the hydrate?

6 Notes - Molarity Many chemical compounds are prepared by dissolving the compound into water. These mixtures are called solutions. The component of the solution that is present in the least amount is the solute, and the component that is present in the greatest amount is called the solvent. For example, if sugar is dissolved in water then the sugar is the solute and the water is the solvent. The concentration of the solution is dependent on the amount of solute that is dissolve in a given amount of solvent. For example, weak coffee is a dilute solution of water and coffee; whereas strong coffee is a concentrated solution of water and coffee. Chemists commonly refer to concentration as the molarity of a solution. Molarity is defined as the number of moles of solute per liter of solvent. The symbol for molarity is M; therefore you may see the following notation of a solution: 1M HCl. This would be read as 1 molar hydrochloric acid. It means that there is one mole of hydrochloric acid molecules in one liter of solution. In order to determine molarity a simple equation can be used: Molarity = moles solute/liter solution or M = moles/liter Example: What is the molarity of a solution thant has 25.0 grams of sodium chloride dissolved in enough water to make ml of solution? Example: What is the molarity if 35.0 g of zinc nitrate is dissolved in enough water to make 750. ml of solution? Example: How many grams of sodium chloride are needed to prepare 2.50 liters of a 1.34 M solution? Example: What mass of copper (I) sulfate is present in 1270 ml of a 2.50 M solution? Example: What volume of water (in L) must be added to 65.8 g of potassium silicate to form a 1.25 M solution (assume the volume of the potassium silicate is insignificant)?

7 Name Period Date PreAP Chemistry Homework 9A Copying is not allowed. You must show all work in order to receive credit. 1. What is the percent composition of oxygen in potassium permanganate? 2. What is the percent composition of hydrogen in calcium acetate? 3. An iron ore is known to contain only iron and oxygen. A 45.3 g sample of the ore is analyzed and found to contain 31.7 g of iron and the remainder is oxygen. Find the percent composition. 4. A 138 g sample of a compound is analyzed and found to contain 25.8 g of lithium, g of carbon, and the remainder to be oxygen. Calculate the percent composition. 5. Free hydrogen gas can be obtained from ethyl alcohol, C 2 H 5 OH. How many grams of hydrogen would be obtained from grams of ethyl alcolhol?

8 Name Period Date PreAP Chemistry Homework 9B Copying is not allowed. You must show all work in order to receive credit. 1. How many moles are in 4177 g of aluminum chloride? 2. How many grams are in 4.1 moles of zinc oxide? 3. How many moles are in 5.00 x molecules of fluorine? 4. How many molecules are in 16.2 moles of carbon monoxide? 5. How many grams are in 5.00 x molecules of lithium hydroxide? 6. How many molecules are in 67.0 grams of potassium chloride? 7. How many grams of oxygen are in 4.50 x molecules of potassium sulfate? 8. How many hydrogen atoms are in 78.4 grams of hydrochloric acid? 9. How many chlorine atoms are in grams of chlorine gas? moles of an unknown element have a mass of grams. What is this element?

9 Name Period Date PreAP Chemistry Homework 9C Copying is not allowed. You must show all work in dimensional analysis in order to receive credit. 1. A compound is composed of 4.80 grams of carbon and 0.40 grams of hydrogen. The molecular mass of the compound is 78.0 g/mole. What is the molecular formula of the compound? 2. Oxalic acid is compound used in cosmetics and paints. A gram sample of oxalic acid was found to contain grams of carbon, grams of hydrogen, and grams of oxygen. If the molecular mass of oxalic acid is g/mole, what is the molecular formula? 3. A compound is analyzed and found to have the following percent composition: 54.52% carbon, 9.17% hydrogen, and % nitrogen. Further testing revealed the molecular mass to be g/mole. Calculate the molecular formula 4. Calculate the molecular formula of a compound that is 56.27% phosphorus and the remainder is oxygen. The molecular mass is g/mole. 5. Calculate the molecular formula of a compound that is 93.70% carbon and the remainder is hydrogen. The molecular mass is g/mole. Turn This Page Over There is a Back!!!!!

10 6. What is the formula for cobalt (II) chloride hexahydrate? What is the name of NaC 2 H 3 O 2 3H 2 O? 7. A hydrate is found to have the following percent composition: 48.8% magnesium sulfate and 51.2% water. What is the formula and name for this hydrate? 8. Gypsum is hydrated calcium sulfate. A 4.89 g sample of this hydrate was heated, and after the water was driven off, 3.87 g of anhydrous calcium sulfate remained. Determine the formula of this hydrate and name the compound. 9. A g sample of a hydrate of magnesium iodide is heated until is mass is reduced to g and all water has been removed. What is the formula of the hydrate? What is the name of the hydrate? 10. Hydrated sodium tetraborate (Na 2 B 4 O 7 xh 2 O)is commonly called borax. Chemical analysis indicates that this hydrate is 52.8% sodium tetraborate and 47.2% water. Determine the formula and name of this compound.

11 Name Period Date PreAP Chemistry Homework 9D Copying is not allowed. You must show all work in dimensional analysis in order to receive credit. 1. How many moles of sulfuric acid are in 1.25 liters of a 1.55 M sulfuric acid solution? 2. How many grams of sulfuric acid are in 1.50 liters of a 1.55 M sulfuric acid solution? 3. If 5.00 grams of potassium bromide are dissolved in 2.50 liters of water what is the concentration of the solution? 4. If 3.4 x 10-3 moles of nickel (II) sulfate are dissolved in 1.90 liters of water what is the concentration of the solution? 5. If 8.40 grams of sodium hydroxide are dissolved in ml of water what is the concentration of the solution? 6. How many grams of sodium sulfate are needed to prepare 1500 ml of a 0.25 M solution of sodium sulfate? 7. How many liters of water are needed to prepare a 1.67 M solution of ammonium phosphate if you need to dissolve 235 gram of ammonium phosphate? 8. What is the molarity of a solution that 49.0 grams of calcium bromide in 2.0 liters of solution? 9. What mass of aluminum phosphate is needed to prepare 145 ml of a 0.23 M solution? 10. What volume of water must 500 grams of sodium fluoride should be dissolved in to make a M solution?

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