Sample Exercise 5.1 Relating Heat and Work to Changes of Internal Energy Gases A(g) and B(g) are confined in a cylinder-and-piston arrangement like that in Figure 5.4 and react to form a solid product C(s): A(g) + B(g) C(s). As the reaction occurs, the system loses 1150 J of heat to the surroundings. The piston moves downward as the gases react to form a solid. As the volume of the gas decreases under the constant pressure of the atmosphere, the surroundings do 480 J of work on the system. What is the change in the internal energy of the system? Solution Analyze The question asks us to determine E, given information about q and w. Plan We first determine the signs of q and w (Table 5.1) and then use Equation 5.4, E = q + w, to calculate E. Solve Heat is transferred from the system to the surroundings, and work is done on the system by the surroundings, so q is negative and w is positive: q = 1150 J and w = 480 J. Thus, E = q + w = (1150 J) + (480 J) = 670 J The negative value of E tells us that a net quantity of 670 J of energy has been transferred from the system to the surroundings. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.1 Relating Heat and Work to Changes of Internal Energy Continued
Comment You can think of this change as a decrease of 670 J in the net value of the systems energy bank account (hence, the negative sign); 1150 J is withdrawn in the form of heat, while 480 J is deposited in the form of work. Notice that as the volume of the gases decreases, work is being done on the system by the surroundings, resulting in a deposit of energy. Practice Exercise 1 A mixture of gases A2 and B2 are introduced to a slender metal cylinder that has one end closed and the other fitted with a piston that makes a gas-tight seal so that the gases are a closed system. The cylinder is submerged in a large beaker of water whose temperature is 25 C, and a spark is used to trigger a reaction in the cylinder. At the completion of the reaction, the piston has moved downward, and the temperature of the water bath has increased to 28 C. If we define the system as the gases inside the cylinder, which of the following best describes the signs of q, w, and E for this reaction? (a) q < 0, w < 0, E < 0 (b) q < 0, w > 0, E < 0 (c) q < 0, w > 0, the sign of E cannot be determined from the information given (d) q > 0, w > 0, E > 0 (e) q > 0, w < 0, the sign of E cannot be determined from the information given Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.1 Relating Heat and Work to Changes of Internal Energy Continued
Practice Exercise 2 Calculate the change in the internal energy for a process in which a system absorbs 140 J of heat from the surroundings and does 85 J of work on the surroundings. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.2 Calculating Pressure-Volume Work A fuel is burned in a cylinder equipped with a piston. The initial volume of the cylinder is 0.250 L, and the final volume is 0.980 L. If the piston expands against a constant pressure of 1.35 atm, how much work (in J) is done? (1 L-atm = 101.3 J) Solution Analyze We are given an initial volume and a final volume from which we can calculate V. We are also given the pressure, P. We are asked to calculate work, w. Plan The equation w = PV allows us to calculate the work done by the system from the given information. Solve The volume change is V = Vfinal Vinitial = 0.980 L 0.250 L = 0.730 L Thus, the quantity of work is w = PV = (1.35 atm)(0.730 L) = 0.9855 L-atm Converting L-atm to J, we have Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus
2018 Pearson Education, Inc. Sample Exercise 5.2 Calculating Pressure-Volume Work Continued Check The significant figures are correct (3), and the units are the requested ones for energy (J). The negative sign is consistent with an expanding gas doing work on its surroundings. Practice Exercise 1 If a balloon is expanded from 0.055 to 1.403 L against an external pressure of 1.02 atm, how many L-atm of work is done? (a) 0.056 L-atm (b) 1.37 L-atm (c) 1.43 L-atm (d) 1.49 L-atm (e) 139 L-atm Practice Exercise 2 Calculate the work, in J, if the volume of a system contracts from 1.55 to 0.85 L at a constant pressure of 0.985 atm. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.3 Determining the Sign of H Indicate the sign of the enthalpy change, H, in the following processes carried out under atmospheric pressure and indicate whether each process is endothermic or exothermic: (a) An ice cube melts; (b) 1 g of butane (C4H10) is combusted in sufficient oxygen to give complete combustion to CO 2 and H2O. Solution Analyze Our goal is to determine whether H is positive or negative for each process. Because each process occurs at constant pressure, the enthalpy change equals the quantity of heat absorbed or released, H = qP.
Plan We must predict whether heat is absorbed or released by the system in each process. Processes in which heat is absorbed are endothermic and have a positive sign for H; those in which heat is released are exothermic and have a negative sign for H. Solve In (a) the water that makes up the ice cube is the system. The ice cube absorbs heat from the surroundings as it melts, so H is positive and the process is endothermic. In (b) the system is the 1 g of butane and the oxygen required to combust it. The combustion of butane in oxygen gives off heat, so H is negative and the process is exothermic. Practice Exercise 1 A chemical reaction that gives off heat to its surroundings is said to be _________ and has a _________ value of H. (a) endothermic, positive (b) endothermic, negative (c) exothermic, positive (d) exothermic, negative Practice Exercise 2 Molten gold poured into a mold solidifies at atmospheric pressure. With the gold defined as the system, is the solidification an exothermic or endothermic process? Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.4 Relating H to Quantities of Reactants and Products How much heat is released when 4.50 g of methane gas is burned in a constant-pressure system? (Use the information given in Equation 5.17.) Solution Analyze Our goal is to use a thermochemical equation to calculate the heat produced when a specific amount of methane gas is combusted. According to Equation 5.17, 890 kJ is released by the system when 1 mol CH 4 is burned
at constant pressure. Plan Equation 5.17 provides us with a stoichiometric conversion factor: (1 mol CH 4 890 kJ). Thus, we can convert moles of CH4 to kJ of energy. First, however, we must convert grams of CH4 to moles of CH4. Solve The conversion sequence is: By adding the atomic weights of C and 4 H, we have 1 mol CH4 = 16.0 CH4. We can use the appropriate conversion factors to convert grams of CH4 to moles of CH4 to kilojoules: Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus The negative sign indicates that the system released 250 kJ into the surroundings. 2018 Pearson Education, Inc. Sample Exercise 5.4 Relating H to Quantities of Reactants and Products Continued Practice Exercise 1 The complete combustion of ethanol, C2H5OH (molar mass = 46.0 g/mol), proceeds as follows: C2H5OH(l) + 3 O2(g) 2 CO2(g) + 3 H2O(l)
H = 555 kJ What is the enthalpy change for combustion of 15.0 g of ethanol? (a) 12.1 kJ (b) 181 kJ (c) 422 kJ (d) 555 kJ (e) 1700 kJ Practice Exercise 2 Hydrogen peroxide can decompose to water and oxygen by the reaction 2 H2O2(l) 2 H2O(l) + O2(g) H = 196 kJ Calculate the quantity of heat released when 5.00 g of H2O2(l) decomposes at constant pressure. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.5 Relating Heat, Temperature Change, and Heat Capacity (a) How much heat is needed to warm 250 g of water (about 1 cup) from 22 C (about room temperature) to 98 C (near its boiling point)? (b) What is the molar heat capacity of water? Solution
Analyze In part (a) we must find the quantity of heat (q) needed to warm the water, given the mass of water (m), its temperature change (T ), and its specific heat (Cs). In part (b) we must calculate the molar heat capacity (heat capacity per mole, Cm) of water from its specific heat (heat capacity per gram). Plan (a) Given Cs, m, and T, we can calculate the quantity of heat, q, using Equation 5.21. (b) We can use the molar mass of water and dimensional analysis to convert from heat capacity per gram to heat capacity per mole. Solve (a) The water undergoes a temperature change of: T = 98 C 22 C = 76 C = 76 K Using Equation 5.21, we have: (b) The molar heat capacity is the heat capacity of one mole of substance. Using the atomic weights of hydrogen and oxygen, we have: 1 mol H2O = 18.0 g H2O Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.5 Relating Heat, Temperature Change, and Heat Capacity Continued From the specific heat used in part (a), we have Practice Exercise 1 The coinage metals (Group 1B) copper, silver, and gold have specific heats of 0.385, 0.233, and 0.129 J/g-K,
respectively. Among this group, the specific heat capacity __________ and the molar heat capacity __________ as the atomic weight increases. (a) increases, increases (b) increases, decreases (c) decreases, increases (d) decreases, decreases Practice Exercise 2 (a) Large beds of rocks are used in some solar-heated homes to store heat. Assume that the specific heat of the rocks is 0.82 J/g-K. Calculate the quantity of heat absorbed by 50.0 kg of rocks if their temperature increases by 12.0 C. (b) What temperature change would these rocks undergo if they emitted 450 kJ of heat? Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.6 Measuring H Using a Coffee-Cup Calorimeter When a student mixes 50 mL of 1.0 M HCl and 50 mL of 1.0 M NaOH in a coffee-cup calorimeter, the temperature of the resultant solution increases from 21.0 to 27.5 C. Calculate the enthalpy change for the reaction in kJ/mol HCl, assuming that the calorimeter loses only a negligible quantity of heat, that the total volume of the solution is 100 mL, that its density is 1.0 g/mL, and that its specific heat is 4.18 J/g-K. Solution Analyze Mixing solutions of HCl and NaOH results in an acid-base reaction: HCl(aq) + NaOH(aq) H2O(l) + NaCl(aq) We need to calculate the heat produced per mole of HCl, given the temperature increase of the solution, the number of
moles of HCl and NaOH involved, and the density and specific heat of the solution. Plan The total heat produced can be calculated using Equation 5.22. The number of moles of HCl consumed in the reaction must be calculated from the volume and molarity of this substance, and this amount is then used to determine the heat produced per mol HCl. Solve Because the total volume of the solution is 100 mL, its mass is: (100 mL)(1.0 g/mL) = 100 g The temperature change is: T = 27.5 C 21.0 C = 6.5 C = 6.5 K Using Equation 5.22, we have: Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.6 Measuring H Using a Coffee-Cup Calorimeter Continued Because the process occurs at constant pressure, H = qP = 2.7 kJ To express the enthalpy change on a molar basis, we use the fact that the number of moles of HCl is given by the product of the volume (50 mL = 0.050 L) and concentration (1.0 M = 1.0 mol/L) of the HCl solution:
Thus, the enthalpy change per mole of HCl is: H = 2.7 kJ/0.050 mol = 54 kJ/mol Check H is negative (exothermic), as evidenced by the observed increase in the temperature. The magnitude of the molar enthalpy change seems reasonable. Practice Exercise 1 When 0.243 g of Mg metal is combined with enough HCl to make 100 mL of solution in a constant-pressure calorimeter, the following reaction occurs: Mg(s) + 2 HCl(aq) MgCl2(aq) + H2(g) If the temperature of the solution increases from 23.0 to 34.1 C as a result of this reaction, calculate H in kJ/mol Mg. Assume that the solution has a specific heat of 4.18 J/g-C and a density of 1.00 g/mL. (a) 19.1 kJ/mol (b) 111 kJ/mol (c) 191 kJ/mol (d) 464 kJ/mol (e) 961 kJ/mol Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.6 Measuring H Using a Coffee-Cup Calorimeter Continued Practice Exercise 2
When 50.0 mL of 0.100 M AgNO3 and 50.0 mL of 0.100 M HCl are mixed in a constant-pressure calorimeter, the temperature of the mixture increases from 22.30 to 23.11 C. The temperature increase is caused by the following reaction: AgNO3(aq) + HCl(aq) AgCl(s) + HNO3(aq) Calculate H for this reaction in kJ/mol AgNO3, assuming that the combined solution has a mass of 100.0 g and a specific heat of 4.18 J/g-C. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.7 Measuring qrxn Using a Bomb Calorimeter The combustion of methylhydrazine (CH6N2), a liquid rocket fuel, produces N2(g), CO2(g), and H2O(l): 2 CH6N2(l) + 5 O2(g) 2 N2(g) + 2 CO2(g) + 6 H2O(l) When 4.00 g of methylhydrazine is combusted in a bomb calorimeter, the temperature of the calorimeter increases from 25.00 to 39.50 C. In a separate experiment the heat capacity of the calorimeter is measured to be 7.794 kJ/C. Calculate the heat of reaction for the combustion of a mole of CH6N2. Solution Analyze We are given a temperature change and the total heat capacity of the calorimeter. We are also given the
amount of reactant combusted. Our goal is to calculate the enthalpy change per mole for combustion of the reactant. Plan We will first calculate the heat evolved for the combustion of the 4.00-g sample. We will then convert this heat to a molar quantity. Solve For combustion of the 4.00-g sample of methylhydrazine, the temperature change of the calorimeter is: T = (39.50 C 25.00 C) = 14.50 C We can use T and the value for Ccal to calculate the heat of reaction (Equation 5.23): Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.7 Measuring qrxn Using a Bomb Calorimeter Continued We can readily convert this value to the heat of reaction for a mole of CH6N2: Check The units cancel properly, and the sign of the answer is negative as it should be for an exothermic reaction. The magnitude of the answer seems reasonable. Practice Exercise 1 The combustion of exactly 1.000 g of benzoic acid in a bomb calorimeter releases 26.38 kJ of heat. If the combustion of 0.550 g of benzoic acid causes the temperature of the calorimeter to increase from 22.01 to 24.27 C, calculate the heat capacity of the calorimeter. (a) 0.660 kJ/C (b) 6.42 kJ/C (c) 14.5 kJ/C (d) 21.2 kJ/g-C (e) 32.7 kJ/C Practice Exercise 2 A 0.5865-g sample of lactic acid (HC3H5O3) reacts with oxygen in a calorimeter whose heat capacity is 4.812 kJ/C.
The temperature increases from 23.10 to 24.95 C. Calculate the heat of combustion of lactic acid (a) per gram and (b) per mole. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.8 Using Hesss Law to Calculate H The enthalpy of reaction for the combustion of C to CO2 is 393.5 kJ/mol C, and the enthalpy for the combustion of CO to CO2 is 283.0 kJ/mol CO: (1) C(s) + O2(g) (2) CO(g) + O2(g) CO2(g) CO2(g) H = 393.5 kJ H = 283.0 kJ Using these data, calculate the enthalpy for the combustion of C to CO: (3) C(s) + O2(g) CO(g) H = ?
Solution Analyze We are given two thermochemical equations, and our goal is to combine them in such a way as to obtain the third equation and its enthalpy change. Plan We will use Hesss law. In doing so, we first note the number of moles of substances among the reactants and products in the target equation (3). We then manipulate equations (1) and (2) to give the same number of moles of these substances, so that when the resulting equations are added, we obtain the target equation. At the same time, we keep track of the enthalpy changes, which we add. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.8 Using Hesss Law to Calculate H Continued Solve To use equations (1) and (2), we arrange them so that C(s) is on the reactant side and CO(g) is on the product side of the arrow, as in the target reaction, equation (3). Because equation (1) has C(s) as a reactant, we can use that equation just as it is. We need to turn equation (2) around, however, so that CO(g) is a product. Remember that when reactions are turned around, the sign of H is reversed. We arrange the two equations so that they can be added to give the desired equation: When we add the two equations, CO2(g) appears on both sides of the arrow and therefore cancels out. Likewise, O2(g) is eliminated from each side. Practice Exercise 1 Calculate H for 2 NO(g) + O2(g)
N2O4(g), using the following information: N2O4(g) 2 NO(g) + O2(g) 2 NO2(g) 2 NO2(g) H = +57.9 kJ H = 113.1 kJ (a) 2.7 kJ (b) 55.2 kJ (c) 85.5 kJ (d) 171.0 kJ (e) +55.2 kJ Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.8 Using Hesss Law to Calculate H Continued Practice Exercise 2 Carbon occurs in two forms, graphite and diamond. The enthalpy of the combustion of graphite is 393.5 kJ/mol, and that of diamond is 395.4 kJ/mol: C(graphite) + O2(g)
CO2(g) H = 393.5 kJ C(diamond) + O2(g) CO2(g) H = 395.4 kJ Calculate H for the conversion of graphite to diamond: C(graphite) Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus C(diamond) H = ? 2018 Pearson Education, Inc. Sample Exercise 5.9 Using Hesss Law with Three Equations to Calculate H Calculate H for the reaction 2 C(s) + H2(g)
C2H2(g) given the following chemical equations and their respective enthalpy changes: C2H2(g) + O2(g) C(s) + O2(g) H2(g) + O2(g) 2 CO2(g) + H2O(l) H = 1299.6 kJ CO2(g) H2O(l) H = 393.5 kJ H = 285.8 kJ Solution Analyze We are given a chemical equation and asked to calculate its H using three chemical equations and their associated enthalpy changes. Plan We will use Hesss law, summing the three equations or their reverses and multiplying each by an appropriate coefficient so that they add to give the net equation for the reaction of interest. At the same time, we keep track of the H values, reversing their signs if the reactions are reversed and multiplying them by whatever coefficient is employed in the equation. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc.
Sample Exercise 5.9 Using Hesss Law with Three Equations to Calculate H Continued Solve Because the target equation has C2H2 as a product, we turn the first equation around; the sign of H is therefore changed. The desired equation has 2 C(s) as a reactant, so we multiply the second equation and its H by 2. Because the target equation has H2 as a reactant, we keep the third equation as it is. We then add the three equations and their enthalpy changes in accordance with Hesss law: When the equations are added, there are 2 CO2, writing the net equation. O2, and H2O on both sides of the arrow. These are canceled in Check The procedure must be correct because we obtained the correct net equation. In cases like this, you should go back over the numerical manipulations of the H values to ensure that you did not make an inadvertent error with signs. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.9 Using Hesss Law with Three Equations to Calculate H Continued Practice Exercise 1
Calculate H for the reaction C(s) + H2O(g) given the following thermochemical equations: C(s) + O2(g) CO(g) + H2(g) CO2(g) H1 = 393.5 kJ 2 CO(g) + O2(g) 2 CO2(g) H2 = 566.0 kJ 2 H2(g) + O2(g) 2 H2O(g) H3 = 483.6 kJ (a) 1443.1 kJ (b) 918.3 kJ (c) 131.3 kJ (d) 262.6 kJ (e) 656.1 kJ Practice Exercise 2 Calculate H for the reaction
NO(g) + O(g) given the following information: NO(g) + O3(g) O3(g) O2(g) H = 142.3 kJ O2(g) 2 O(g) H = 495.0 kJ Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus NO2(g) NO2(g) + O2(g) H = 198.9 kJ 2018 Pearson Education, Inc. Sample Exercise 5.10 Equations Associated with Enthalpies of
Formation For which of these reactions at 25 C does the enthalpy change represent a standard enthalpy of formation? For each that does not, what changes are needed to make it an equation whose H is an enthalpy of formation? (a) 2 Na(s) + O2(g) Na2O(s) (b) 2 K(l) + Cl2(g) (c) C6H12O6(s) 2 KCl(s) 6 C(diamond) + 6 H2(g) + 3 O2(g) Solution Analyze The standard enthalpy of formation is represented by a reaction in which each reactant is an element in its standard state and the product is one mole of the compound. Plan We need to examine each equation to determine (1) whether the reaction is one in which one mole of substance is formed from the elements, and (2) whether the reactant elements are in their standard states. Solve In (a) 1 mol Na2O is formed from the elements sodium and oxygen in their proper states, solid Na and O 2 gas, respectively. Therefore, the enthalpy change for reaction (a) corresponds to a standard enthalpy of formation. In (b) potassium is given as a liquid. It must be changed to the solid form, its standard state at room temperature. Furthermore, 2 mol KCl are formed, so the enthalpy change for the reaction as written is twice the standard enthalpy of formation of KCl(s). The equation for the formation reaction of 1 mol of KCl(s) is K(s) + Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus Cl2(g)
KCl(s) 2018 Pearson Education, Inc. Sample Exercise 5.10 Equations Associated with Enthalpies of Formation Continued Reaction (c) does not form a substance from its elements. Instead, a substance decomposes to its elements, so this reaction must be reversed. Next, the element carbon is given as diamond, whereas graphite is the standard state of carbon at room temperature and 1 atm pressure. The equation that correctly represents the enthalpy of formation of glucose from its elements is 6 C(graphite) + 6 H2(g) + 3 O2(g) C6H12O6(s) Practice Exercise 1 If the heat of formation of H2O(l) is 286 kJ/mol, which of the following thermochemical equations is correct? (a) 2 H(g) + O(g) H2O(l) H = 286 kJ (b) 2 H2(g) + O2(g) 2 H2O(l) H = 286 kJ (c) H2(g) + O2(g) H2O(l) H = 286 kJ (d) H2(g) + O(g) H2O(g)
H = 286 kJ (e) H2O(l) H2(g) + O2(g) H = 286 kJ Practice Exercise 2 Write the equation corresponding to the standard enthalpy of formation of liquid carbon tetrachloride (CCl 4) and look up for this compound in Appendix C. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.11 Calculating an Enthalpy of Reaction from Enthalpies of Formation (a) Calculate the standard enthalpy change for the combustion of 1 mol of benzene, C 6H6(l), to CO2(g) and H2O(l). (b) Compare the quantity of heat produced by combustion of 1.00 g propane with that produced by 1.00 g benzene. Solution Analyze (a) We are given a reaction [combustion of C6H6(l) to form CO2(g) and H2O(l)] and asked to calculate its standard enthalpy change, H. (b) We then need to compare the quantity of heat produced by combustion of 1.00 g C6H6 with that produced by 1.00 g C3H8, whose combustion was treated previously in the text. (See Equations 5.29 and 5.30.) Plan (a) We first write the balanced equation for the combustion of C 6H6. We then look up values in Appendix C
or in Table 5.3 and apply Equation 5.31 to calculate the enthalpy change for the reaction. (b) We use the molar mass of C6H6 to change the enthalpy change per mole to that per gram. We similarly use the molar mass of C 3H8 and the enthalpy change per mole calculated in the text previously to calculate the enthalpy change per gram of that substance. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.11 Calculating an Enthalpy of Reaction from Enthalpies of Formation Continued Solve (a) We know that a combustion reaction involves O2(g) as a reactant. Thus, the balanced equation for the combustion reaction of 1 mol C6H6(l) is: C6H6(l) + O2(g) 6 CO2(g) + 3 H2O(l) We can calculate H for this reaction by using Equation 5.31 and data in Table 5.3. Remember to multiply the value for each substance in the reaction by that substances stoichiometric coefficient. Recall also that = 0 for any element in its most stable form under standard conditions, so [O 2(g)] = 0. (b) From the example worked in the text, H = 2220 kJ for the combustion of 1 mol of propane. In part (a) of this exercise we determined that H = 3267 kJ for the combustion of 1 mol benzene. To determine the heat of combustion per gram of each substance, we use the molar masses to convert moles to grams: Chemistry: The Central Science, 14th Edition
Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.11 Calculating an Enthalpy of Reaction from Enthalpies of Formation Continued Comment Both propane and benzene are hydrocarbons. As a rule, the energy obtained from the combustion of a gram of hydrocarbon is between 40 and 50 kJ. Practice Exercise 1 Calculate the enthalpy change for the reaction 2 H2O2(l) 2 H2O(l) + O2(g) using enthalpies of formation: [H2O2(l)] = 187.8 kJ/mol (a) (b) (c) (d) (e) [H2O(l)] = 285.8 kJ/mol 88.0 kJ
196.0 kJ +88.0 kJ +196.0 kJ more information needed Practice Exercise 2 Use Table 5.3 to calculate the enthalpy change for the combustion of 1 mol of ethanol: C2H5OH(l) + 3 O2(g) Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2 CO2(g) + 3 H2O(l) 2018 Pearson Education, Inc. Sample Exercise 5.12 Calculating an Enthalpy of Formation Using an Enthalpy of Reaction The standard enthalpy change for the reaction CaCO3[s] the standard enthalpy of formation of CaCO3[s]. CaO[s] + CO2[g] is 178.1 kJ. Use Table 5.3 to calculate Solution Analyze Our goal is to obtain [CaCO3]. Plan We begin by writing the expression for the standard enthalpy change for the reaction:
= Solve Inserting the given and the known [CaO] + [CO2] values from Table 5.3 or Appendix C, we have: 178.1 kJ = 635.5 kJ 393.5 kJ Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus [CaCO3] [CaCO3] 2018 Pearson Education, Inc. Sample Exercise 5.12 Calculating an Enthalpy of Formation Using an Enthalpy of Reaction Continued Solving for
[CaCO3] gives: [CaCO3] = 1207.1 kJ/mol Check We expect the enthalpy of formation of a stable solid such as calcium carbonate to be negative, as obtained. Practice Exercise 1 Given 2 SO2(g) + O2(g) (a) (b) (c) 2 (d) 2 (e) 2 [SO3] = [SO3] = [SO3] = [SO3] = [SO3] = 2 2 SO3(g), which of the following equations is correct? [SO2] + [SO2] +2 [SO2]
2 [SO2] [SO2] Practice Exercise 2 Given the following standard enthalpy change, use the standard enthalpies of formation in Table 5.3 to calculate the standard enthalpy of formation of CuO(s): CuO(s) + H2(g) Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus Cu(s) + H2O(l) H = 129.7 kJ 2018 Pearson Education, Inc. Sample Exercise 5.13 Estimating Reaction Enthalpies from Bond Enthalpies Use Table 5.4 to estimate H for the following combustion reaction. Solution Analyze We are asked to use average bond enthalpies to estimate agreement is good. the enthalpy change for a chemical reaction. Plan Energy is required to break twelve CH bonds and two CC bonds in the two molecules of C 2H6, and seven O
O bonds in the seven O2 molecules. Energy is released by forming eight C O bonds, two per molecule of CO2, and twelve OH bonds, two per H2O molecule. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.13 Estimating Reaction Enthalpies from Bond Enthalpies Continued Solve Using Equation 5.32 and data from Table 5.4, we have Check This estimate can be compared with the value of 2856 kJ calculated from more accurate thermochemical data; the agreement is good. Practice Exercise 1 Use the average bond enthalpies in Table 5.4 to estimate H for the water splitting reaction: H2O(g) + O2(g). (a) 242 kJ (b) 417 kJ (c) 5 kJ (d) 5 kJ (e) 468 kJ Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus H2(g) 2018 Pearson Education, Inc.
Sample Exercise 5.13 Estimating Reaction Enthalpies from Bond Enthalpies Continued Practice Exercise 2 Use the average bond enthalpies in Table 5.4 to estimate H for the combustion of ethanol. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.14 Estimating the Fuel Value of a Food from Its Composition (a) A 28-g (1-oz) serving of a popular breakfast cereal served with 120 mL of skim milk provides 8 g protein, 26 g carbohydrates, and 2 g fat. Using the average fuel values of these substances, estimate the fuel value (caloric content) of this serving. (b) A person of average weight uses about 100 Cal/mi when running or jogging. How many servings of this cereal provide the fuel value requirements to run 3 mi? Solution Analyze (a) The fuel value of the serving will be the sum of the fuel values of the protein, carbohydrates, and fat. (b) Here we are faced with the reverse problem, calculating the quantity of food that provides a specific fuel value. Plan (a) We are given the masses of the protein, carbohydrates, and fat contained in a serving. We can use the data in Table 5.4 to convert these masses to their fuel values, which we can sum to get the total fuel value. (b) The problem statement provides a conversion factor between Calories and miles. The answer to part (a) provides us with a conversion factor between servings and Calories. Solve
(a) Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.14 Estimating the Fuel Value of a Food from Its Composition Continued This corresponds to 160 kcal: Recall that the dietary Calorie is equivalent to 1 kcal. Thus, the serving provides 160 Cal. (b) We can use these factors in a straightforward dimensional analysis to determine the number of servings needed, rounded to the nearest whole number: Practice Exercise 1 A stalk of celery has a caloric content (fuel value) of 9.0 kcal. If 1.0 kcal is provided by fat and there is very little protein, estimate the number of grams of carbohydrate and fat in the celery. (a) 2 g carbohydrate and 0.1 g fat (b) 2 g carbohydrate and 1 g fat (c) 1 g carbohydrate and 2 g fat (d) 32 g carbohydrate and 10 g fat Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Exercise 5.14 Estimating the Fuel Value of a Food from Its
Composition Continued Practice Exercise 2 (a) Dry red beans contain 62% carbohydrate, 22% protein, and 1.5% fat. Estimate the fuel value of these beans. (b) During a very light activity, such as reading or watching television, the average adult expends about 7 kJ/min. How many minutes of such activity can be sustained by the energy provided by a serving of chicken noodle soup containing 13 g protein, 15 g carbohydrate, and 5 g fat? Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Integrative Exercise Putting Concepts Together Trinitroglycerin, C3H5N3O9 (usually referred to simply as nitroglycerin), has been widely used as an explosive. Alfred Nobel used it to make dynamite in 1866. Rather surprisingly, it also is used as a medication, to relieve angina (chest pains resulting from partially blocked arteries to the heart) by dilating the blood vessels. At 1 atm pressure and 25 C, the enthalpy of decomposition of trinitroglycerin to form nitrogen gas, carbon dioxide gas, liquid water, and oxygen gas is 1541.4 kJ/mol. (a) Write a balanced chemical equation for the decomposition of trinitroglycerin. (b) Calculate the standard heat of formation of trinitroglycerin. (c) A standard dose of trinitroglycerin for relief of angina is 0.60 mg. If the sample is eventually oxidized in the body (not explosively, though!) to nitrogen gas, carbon dioxide gas, and liquid water, what number of calories is released? (d) One common form of trinitroglycerin melts at about 3 C. From this information and the formula for the substance, would you expect it to be a molecular or ionic compound? Explain.
(e) Describe the various conversions of forms of energy when trinitroglycerin is used as an explosive to break rockfaces in highway construction. Solution (a) The general form of the equation we must balance is C3H5N3O9(l) Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus N2(g) + CO2(g) + H2O(l) + O2(g) 2018 Pearson Education, Inc. Sample Integrative Exercise Putting Concepts Together Continued We go about balancing in the usual way. To obtain an even number of nitrogen atoms on the left, we multiply the formula for C3H5N3O9 by 2, which gives us 3 mol of N2, 6 mol of CO2 and 5 mol of H2O. Everything is then balanced except for oxygen. We have an odd number of oxygen atoms on the right. We can balance the oxygen by using the coefficient for O2 on the right: 2 C3H5N3O9(l) 3 N2(g) + 6 CO2(g) + 5 H2O(l) + O2(g) We multiply through by 2 to convert all coefficients to whole numbers: 4 C3H5N3O9(l)
6 N2(g) + 12 CO2(g) + 10 H2O(l) + O2(g) (At the temperature of the explosion, water is a gas rather than a liquid as shown in the equation above. The rapid expansion of the gaseous products creates the force of an explosion.) (b) We can obtain the standard enthalpy of formation of nitroglycerin by using the heat of decomposition of trinitroglycerin together with the standard enthalpies of formation of the other substances in the decomposition equation: 4 C3H5N3O9(l) 6 N2(g) + 12 CO2(g) + 10 H2O(l) + O2(g) The enthalpy change for this decomposition is 4(1541.4 kJ) = 6165.6 kJ. [We need to multiply by 4 because there are 4 mol of C3H5N3O9(l) in the balanced equation.] Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Integrative Exercise Putting Concepts Together Continued This enthalpy change equals the sum of the heats of formation of the products minus the heats of formation of the reactants, each multiplied by its coefficient in the balanced equation: 6165.6 kJ = 6 [N2(g)] + 12 [CO2(g)] + 10
[H2O(l)] + [O2(g)] 4 [C3H5N3O9(l)] The values for N2(g) and O2(g) are zero, by definition. Using the values for H2O(l) and CO2(g) from Table 5.3 or Appendix C, we have 6165.6 kJ = 12(393.5 kJ) + 10(285.8 kJ) 4 [C3H5N3O9(l)] [C3H5N3O9(l)] = 353.6 kJ/mol Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc. Sample Integrative Exercise Putting Concepts Together Continued (c) Converting 0.60 mg C3H5N3O9(l) to moles and using the fact that the decomposition of 1 mol of C 3H5N3O9(l) yields 1541.4 kJ we have: (d) Because trinitroglycerin melts below room temperature, we expect that it is a molecular compound. With few
exceptions, ionic substances are generally hard, crystalline materials that melt at high temperatures. (Section 2.6 and 2.7) Also, the molecular formula suggests that it is a molecular substance because all of its constituent elements are nonmetals. (e) The energy stored in trinitroglycerin is chemical potential energy. When the substance reacts explosively, it forms carbon dioxide, water, and nitrogen gas, which are of lower potential energy. In the course of the chemical transformation, energy is released in the form of heat; the gaseous reaction products are very hot. This high heat energy is transferred to the surroundings. Work is done as the gases expand against the surroundings, moving the solid materials and imparting kinetic energy to them. For example, a chunk of rock might be impelled upward. It has been given kinetic energy by transfer of energy from the hot, expanding gases. As the rock rises, its kinetic energy is transformed into potential energy. Eventually, it again acquires kinetic energy as it falls to Earth. When it strikes Earth, its kinetic energy is converted largely to thermal energy, though some work may be done on the surroundings as well. Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus 2018 Pearson Education, Inc.
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