4.5 Percentage Composition
Transcription
4.5 Percentage Composition
the amount in moles of silver atoms formed. Describe the procedure, materials, and equipment used, safety procedures, and explain the calculations needed. Making Connections 7. Suppose that there is a prestigious award given by the Academy of Science each year to the most significant scientific concept. Write a paper nominating the mole concept for this award, citing the mole’s role and importance in the application of chemical reactions in society, industry, and the environment. Percentage Composition 4.5 Figure 1 This experimental car burns hydrogen as a fuel, producing water vapour as an exhaust. The dish collects solar energy, which is used to dissociate water into hydrogen and oxygen. Using molar mass values from a periodic table, we can calculate the mass of reactants and products in chemical reactions—if we already know the chemical formulas. However, when a new substance is produced, we first need to determine its chemical formula. To do this, we need to determine the chemical composition of the compound, that is, what elements it is made of and the quantities of each element. In this section, we will experimentally determine the composition by mass of a substance and then convert the mass amounts to percentages, to give us the percentage composition. We can then use atomic mass and molar mass to determine the correct chemical formula. Before we begin, we will practise the mathematical steps in the calculation of percentage composition from mass measurements of reactants and products. Let’s consider 20 g of red jelly beans mixed with 30 g of green jelly beans. What is the percentage composition of the mixture, by mass? The percentage of red jelly beans by mass would be 20 g of the total 50 g, which is 20 g/50 g × 100%, or 40%. Similarly, the percentage of green jelly beans would be 30 g of the total 50 g, which is 60%. Now let’s look at the percentage composition of water. Water is formed when hydrogen is allowed to react with oxygen, a reaction that gives off large amounts of energy (Figure 1). The results of an experiment revealed that 2.5 g of hydrogen, when completely reacted, produced 22.5 g of water. What is the percentage composition of water by mass? Since 2.5 g of hydrogen combined with an amount of oxygen to produce 22.5 g of water, we can calculate the mass of oxygen by subtraction: 2.5 g mH mH O 22.5 g 2 mO (22.5 – 2.5) g 20.0 g mH × 100% %H mH O 2 2.5 g % H × 100% 11.1% 22.5 g Similarly, 20.0 g % O × 100% 22.5 g % O 88.9% 178 Chapter 4 4.5 We will see later how this percentage composition, together with the atomic mass of hydrogen and oxygen, will allow us to determine a possible formula for water. Sample Problem 1 Sodium is a very reactive alkali metal, and chlorine is a poisonous green gas. When they are allowed to react, they combine to form sodium chloride, the stable and usually harmless table salt, an ionic compound. In an experiment, 3.45 g of sodium metal reacted with 5.33 g of chlorine gas to give 8.78 g of sodium chloride. Calculate the percentage composition by mass of sodium chloride. Solution mNa+ 3.45 g mCl 5.33 g mNaCl 8.78 g 3.45 g % Na+ × 100% 8.78 g % Na+ 39.3% 5.33 g % Cl × 100% 8.78 g % Cl 60.7% Therefore, the percentage composition by mass of sodium chloride is 39.3% sodium and 60.7% chlorine. (Note that the two percentages total 100%.) Practice Understanding Concepts 1. A 27.0-g sample of a compound contains 7.20 g of carbon, 2.20 g of hydrogen, and 17.6 g of oxygen. Calculate the percentage composition of the compound. 2. Carbon will burn in sufficient oxygen to produce carbon dioxide. In an experiment, 8.40 g of carbon reacts with oxygen and 30.80 g of carbon dioxide is produced. (a) What mass of oxygen reacted with 8.40 g of carbon? (b) Calculate the percentage composition by mass of carbon dioxide. Answers 1. 26.7%, 8.1%, 65.2% 2. (a) 22.40 g (b) 27.3% C, 72.7% O 3. (a) 80.1% Cu, 19.9% O; 88.9% Cu, 11.1% O 3. In one sample of a compound of copper and oxygen, 3.12 g of the compound contains 2.50 g of copper and the remainder is oxygen. In another sample of a compound of copper and oxygen, 1.62 g of the compound contains 1.44 g of copper and the remainder is oxygen. (a) Calculate the percentage composition of each compound. (b) Are the two samples of the same compound? Give reasons for your answer. Quantities in Chemical Formulas 179 INQUIRY SKILLS Questioning Hypothesizing Predicting Planning Conducting Recording Analyzing Evaluating Communicating Wear eye protection. Use crucible tongs to transfer hot crucible. Care is required in using a laboratory burner and handling hot apparatus. Magnesium ribbon burns with a hot flame and an extremely bright light. If the magnesium ignites, do not look directly at the flame because it may damage your eyes. Investigation 4.5.1 Percentage Composition by Mass of Magnesium Oxide In this investigation, you will test the law of definite proportions. To do this, you will determine the composition by mass of magnesium oxide, calculate the percentage composition, and compare your results and those of other students to the predicted values. Magnesium is a silvery metal that burns with such a bright flame that it was once used in flashbulbs for photography. Magnesium oxide, a white powder, is produced as a result of the synthesis reaction of combusting magnesium. Here, you will conduct a slow combustion of magnesium and then complete the Evidence, Analysis, and Evaluation sections of a lab report. Questions What is the percentage composition by mass of magnesium oxide? Is this percentage constant? Prediction (a) Make a prediction based on the law of definite proportions. What should the percentage composition by mass of magnesium oxide be? Experimental Design DID YOU KNOW ? Magnesium Sparkles Finely ground magnesium powder readily ignites upon heating in air, giving a dazzling white light. This property of magnesium is used in devices such as flares, incendiary bombs, and fireworks. Magnesium dust is a common component of fireworks, including sparklers, a nonexplosive type of fireworks constructed by coating a slurry of chemicals on a wire. The slurry consists of a fuel containing magnesium powder, an oxidizer, iron or steel powder, and a binder, all of which are proportioned to burn slowly, giving off a shower of bright shimmering sparks. 180 Chapter 4 A known mass of magnesium metal is heated in a crucible over a laboratory burner. The mass of the magnesium oxide formed is used to determine the mass of the oxygen that reacted and the percentage composition by mass of the two components. Some of the magnesium also reacts with nitrogen in air to form a nitride. This compound is converted to magnesium oxide by adding water and reheating the solid. Materials lab apron eye protection centigram or analytical balance 7–8 cm magnesium ribbon steel wool porcelain crucible and lid laboratory burner retort stand ring stand and clamp clay triangle crucible tongs glass stirring rod distilled water 4.5 Procedure 1. Using a balance, determine the mass of a clean, dry porcelain crucible and lid. 2. Polish the magnesium ribbon with the steel wool and fold the ribbon to fit into the bottom of the crucible. 3. Determine the mass of the crucible, lid, and magnesium ribbon. 4. Place the crucible securely on the clay triangle. Set the lid slightly off-centre on the crucible to allow air to enter but to prevent the magnesium oxide from escaping. 5. Place the laboratory burner under the crucible, light it, and begin heating with a gentle flame. 6. Gradually increase the flame intensity until all the magnesium turns into a white powder. 7. Cut the flow of gas to the burner and allow the crucible, lid, and contents to cool. 8. Using the stirring rod, crush the contents of the crucible into a fine powder. Carefully add about 10 mL of distilled water to the powder. Use some of the water to rinse any powder on the stirring rod into the crucible. 9. Heat the crucible and contents, with the lid slightly ajar, gently for 3 min and strongly for another 7 min. 10. Allow the crucible and contents to cool. 11. Using the balance, determine the mass of the cooled crucible, lid, and contents. Figure 2 Apparatus for heating in a crucible Analysis (b) What evidence do you have that a chemical reaction took place? (c) Calculate the mass of oxygen that reacted with the magnesium. (d) Use your evidence to calculate the percentage composition by mass of magnesium oxide. (e) Based on the evidence (your results and those of your classmates), what are the answers to the Questions? Evaluation (f) If some of the magnesium oxide had escaped from the crucible, would your percentage composition calculation of magnesium be too high or too low? Explain. (g) If the magnesium had reacted with some other component in the air, would your percentage composition calculation of magnesium be too high or too low? Explain. (h) The magnesium ribbon was polished to remove any white film on its surface before beginning the experiment. Explain why this is necessary. (i) Suggest a modification in the procedure to ensure that all of the magnesium completely reacts with oxygen. (j) Evaluate your prediction. Based on the evidence obtained from several groups, is the law of definite proportions valid? Quantities in Chemical Formulas 181 Practice Making Connections 4. Use the Internet to research information about tires. When you look at the sidewall of a tire, you will see a lot of information, such as the name of the tire, its size, whether it is tubeless or a tube type, the grade, and the speed rating. It also gives important safety information such as the maximum load and maximum inflation for the tire. In addition, the composition of the tire can be obtained from the manufacturer. For example, a Goodyear all-season passenger tire contains approximately Answers 4. (a) 18.6%, 23.7%, 5.2%, 5.2%, 5.2%, 14.4%, 27.8% 1.8 2.3 0.5 0.5 0.5 1.4 2.7 kg kg kg kg kg kg kg of of of of of of of 8 types of natural rubber 8 types of carbon black steel cord for belts polyester and nylon steel bead wire 40 kinds of chemicals, waxes, oils, pigments 5 different types of synthetic rubber (a) Calculate the percentage composition of this tire. (b) Research and compare the percentages of synthetic and natural rubber used in various types of tires, for example, tires for light trucks, racecars, and off-highway vehicles. (c) Relate the characteristics of synthetic and natural rubber mixes to their application in the different types of tires. (d) Research the contributions of Goodyear in the composition of rubber, and assess the impact of the development of rubber tires on society and the environment. Follow the links for Nelson Chemistry 11, 4.5. GO TO www.science.nelson.com Try This Activity What Makes Popcorn Pop? In each kernel of popping corn, there is a small drop of water in a circle of soft starch. When heated, the water expands and builds up pressure against the hard outer surface, eventually exploding and turning the kernel inside out. Materials: popping corn, hot-air popcorn popper, balance • • • • Measure the mass of some unpopped popping corn. Pop the popping corn. Allow the popcorn to cool and measure the mass again. Assume that any difference in masses is caused by loss of water from the kernels. Calculate the percentage of water in the sample of popcorn. • Repeat the activity with kernels of popping corn that have been cut in half either lengthwise or crosswise. • Record the percentage of popped kernels from each cutting method. (a) Do the results confirm the given reason why popcorn pops? Explain. 182 Chapter 4 4.5 Percentage Composition Calculations from a Formula We have seen how to determine the percentage composition of a compound through experimentation. Empirical information is often used to determine the formula of a compound. Sometimes we also need to calculate the percentage composition of a compound whose formula we already know. For example, we may wish to verify the purity of a compound by comparing its percentage composition obtained experimentally to the theoretical value, calculated from the compound’s formula. Percentage composition also has commercial uses, for example, in fertilizers. The chemical formula can be used to determine the percentage by mass that is contributed by each element in the compounds that make up the fertilizer. Nitrogen is one of the key elements delivered to plants by fertilizers; it is important to calculate the percentage of nitrogen in fertilizer compounds to determine the correct quantities of fertilizer to apply. If we know the chemical formula of the compound, calculating percentage composition is straightforward. Essentially, we want to calculate the “contribution” of each element to the total mass of the compound. Thus, we first calculate the mass of all the atoms of each element. Then, we calculate the total mass of all the elements in the compound. To obtain the percentage contribution of each element, we divide the mass of each element by the total mass. Sample Problem 2 Determine the percentage composition of sodium carbonate, Na2CO3, also known as soda ash. Solution mNa 22.99 u × 2 45.98 u mC 12.01 u × 1 12.01 u mO 16.00 u × 3 48.00 u mNa CO 2 3(s) 105.99 u 45.98 u % Na × 100% 105.99 u % Na 43.38% 12.01 u % C × 100% 105.99 u % C 11.33% 48.00 u % O × 100% 105.99 u % O 45.29% The percentage composition of Na2CO3(s) is 43.38% sodium, 11.33% carbon, and 45.29% oxygen. Quantities in Chemical Formulas 183 Practice Understanding Concepts Answers 5. 2.1% H, 32.7% S, 65.2% O 6. 41.6% Mg 7. 77.7% Fe, 22.3% O; 69.9% Fe, 30.1% O 8. 28.2% N 5. Calculate the percentage composition by mass of sulfuric acid, H2SO4(aq), used in car batteries. 6. Calculate the percentage by mass of magnesium in magnesium hydroxide, Mg(OH)2(s), used in some antacids. 7. Iron and oxygen combine to form two different compounds. The formulas of the compounds are FeO(s) and Fe2O3(s). Calculate the percentage composition of each compound. 8. Calculate the percentage of nitrogen in ammonium phosphate, (NH4)3PO4, a compound used in fertilizers. Section 4.5 Questions Understanding Concepts 1. Explain why it is necessary to determine the percentage composition of a new compound by experiment. 2. In a compound consisting of potassium and chlorine, 33.5 g of potassium combined with 30.4 g of chlorine. Calculate the percentage composition of the compound. 3. The following evidence was obtained in an experiment to determine the percentage composition of a compound containing sodium, sulfur, and oxygen: mass of Na atoms 23.0 g mass of S atoms 16.0 g mass of O atoms 32.0 g Calculate the percentage composition of this compound. 4. Ammonium nitrate, NH4NO3(s), and ammonium sulfate, (NH4)2SO4(s), are both compounds used as fertilizers. Determine which compound contains the greater percentage by mass of nitrogen. 5. Calcium sulfate dihydrate, CaSO4•2H2O(s), is commonly called gypsum and is used in building materials such as drywall. It contains water of crystallization, some of which is lost on heating, leaving (CaSO4)2•H2O(s). Compare the percentage by mass of water in each compound. Applying Inquiry Skills 6. In this lab exercise, a synthesis reaction is used to determine the percentage composition of a compound of copper and sulfur. Experimental Design When heated strongly in a crucible, copper wire or turnings react with an excess of sulfur to produce a solid, a sulfide of copper. Procedure (a) Design a Procedure, based on the Experimental Design, to obtain the evidence needed. Analysis (b) Explain how the evidence gathered in your procedure would be used to calculate the percentage composition of the product. 184 Chapter 4 4.6 Evaluation (c) Evaluate the experimental design. Making Connections 7. Name two products that you might find around the house where percentage compositions are given (a) in mass; (b) in measurements other than mass. 4.6 Empirical and Molecular Formulas If we are given an unknown substance and we want to find its chemical formula, how do we begin? We need to identify the elements that are in the compound as well as the number of atoms of each element. To begin with, we can determine its percentage composition by mass. Then, we simply convert the mass values into amounts in moles, which gives us the subscripts in the chemical formula of the substance. A formula derived in this way is called an empirical formula, which means that it is derived from observations in an experiment rather than from theory. An empirical formula tells us the simplest ratio of the combining elements. Currently, many new substances that are synthesized are organic compounds, that is, contain mainly carbon and hydrogen atoms. One of the technologies available to measure the percentage composition of these compounds uses combustion analyzers (Figure 1). In this process, several milligrams of a compound are burned inside a combustion chamber. When the compound is burned, oxygen combines with the carbon atoms to form carbon dioxide and with the hydrogen atoms to form water vapour. Any other elements present are similarly converted to their oxides. The quantities of these combustion products are precisely measured, and computer analysis discloses the percentage by mass of each element detected in the compound. This percentage composition is then used to calculate the empirical formula of the compound. sample H2O absorber O2 furnace empirical formula: simplest wholenumber ratio of atoms or ions in a compound CO2 absorber Figure 1 A substance burned in a combustion analyzer produces oxides that are captured by absorbers in chemical traps. The initial and final masses of each trap indicate the masses of the oxides produced. These masses are then used in the calculation of the percentage composition of the substance burned. An empirical formula does not necessarily provide the correct information about the number of atoms in a molecule. That is, an empirical formula may not Quantities in Chemical Formulas 185