Of all of the forms of energy, heat can be considered as the most basic. The other forms of energy, such as chemical, light, radio, and electrical, tend to be transformed into heat by natural processes. When any energy type is converted into heat or when heat is converted into another type of energy, there is no loss in the total amount of energy. Additionally, the amount of heat energy necessary to raise the temperature of a substance is exactly the same as the energy lost when the substance cools to the original temperature. And the amount of energy necessary for a physical state change, such as melting or becoming a gas, is the same as the energy lost in the reverse process (solidification or liquefaction).
The concepts mentioned above all lead to the measurement of energy, energy types, energy conversions, and the effects of the gains and losses of energy. The units most commonly used are listed in Table 6-1. The use of the SI unit, the joule, emphasizes the interconvertibility of the various forms of energy. Chemists have long used the calorie and the kilocalorie (Calorie), but the joule and the kilocalorie have become the preferred units. Engineers are the principal users of the Btu.
The heat capacity of a body is the amount of heat required to raise the temperature of that body 1 K (1°C). For pure substances, it is most convenient to refer to quantities of molar heat capacity (heat capacity per mole) and, as discussed above, the specific heat capacity or, more commonly, the specific heat (heat capacity per unit of mass). As an example, the average specific heat of water is
Using these data for water, the molar heat capacity is 18.02 cal/mol · K (approximately 75.40 J/mol · K). Note that the deviations from this average are all less than 1 percent between the freezing and boiling points. The point being made is that the heat capacity may depend (slightly) on temperature, but is a reasonably stable value making it possible to consider heat capacity as a constant, as it is in this book.
The amount of heat energy entering or leaving a substance undergoing a temperature change can be measured. The relationship for a body under consideration is
The heating or cooling of a body of matter of known heat capacity can be used in calorimetry, the measurement of quantities of heat. Conversely, given all of the information about a substance except the heat capacity (two of the three variables), it can be calculated by the application of the above relationship.
When a system absorbs heat, part of the absorbed energy may be used for doing work. Examples of work in this context are accelerating an automobile, compressing a gas, charging a battery, and changing water from a liquid to a gas. Part of the total amount of energy within a system is associated with rearrangements of the atoms that occur in chemical reactions, the energy of interactions among atoms and molecules, and the energy associated with simply having a temperature (any temperature above absolute zero). This stored portion is known at the internal energy, E. The amount of heat absorbed by any system undergoing a modification, such as an increase in temperature, a change in physical state, or a chemical reaction, depends somewhat on the conditions under which the process occurs. As an example: The amount of heat absorbed is exactly equal to the increase in E if no work is done by the system. This would be the case in an ordinary chemical reaction, not linked to a battery, carried out in a closed reactor vessel so that no expansion against the outside atmosphere occurred. The change in E can be represented by ΔE. (Delta, Δ, is the mathematical symbol representing a change. ΔE is the difference in E accompanying a process, defined as the final value of E minus the initial value.)
Most of the chemical reactions run in laboratory courses are to be performed in open systems. This means that there won’t be a build-up of pressure and some work will be done by the reacting system on the surroundings or, possibly, by the surroundings on the system. In such cases, the principle of conservation of energy requires that the amount of heat shifted must adjust itself to provide for the small, but significant, amount of this work. A new function, the enthalpy, H, can be defined which is related simply to the heat flow in an open or constant-pressure vessel by the definition, H = E + PV. The amount of heat absorbed (or released) in a constant-pressure process is exactly equal to ΔH, the increase (or decrease) in H.
In summary, if q is the amount of heat absorbed by the system from its surroundings,
These equations are exact so long as they are not in use by work-generating devices, such as batteries, motors, and the like. Any of the terms in these equations may have either sign (+ or –). The process can be exothermic, one for which q is negative, where heat is being lost from the system. An endothermic process is one for which q is positive, indicating that heat is being taken up by the system. If the system under investigation is neither exothermic nor endothermic, the system is at equilibrium with the quantitative value zero (0). Most of the thermochemical problems in this book will be looking at H. Even though we may not know the absolute value of ΔE or ΔH, the above equations provide the experimental basis for measuring changes in these functions.
If a substance of heat capacity, C, is heated or cooled through a temperature interval ΔT,
q = C ΔT
assuming (as throughout this book) that C is independent of temperature. Subscripts are often used to designate a heat capacity measured at constant pressure, Cp, and at constant volume, Cv. Using Cp,
ΔH = CpΔT
The quantities C and H are extensive, meaning that they are proportional to the amount of material involved in the process or reaction. We choose to let c, cp, and cv represent specific heat capacities with the lower case symbol, w, for the sample’s mass. Then,
C = cw
Where the subscript is omitted in the problems in this book, Cp (constant pressure) is implied. Further, note that, depending on the author, symbols often used for specific heat are c, C, Cs, SH, or s.
The heat that must be absorbed to melt a substance may be called the latent heat of fusion or, in the shortened form, the heat of fusion. For the melting of ice at 0°C, for example, the process may be written as
Just as (gas) or (g) in Chapter 6 referred to the gaseous state, (s) refers to the solid state and (l) to the liquid state.
There is a latent heat of vaporization (shortened to heat of vaporization), ΔH (vaporization), carried out at constant temperature and pressure. The latent heat of vaporization of water at 100°C and 1 atm is 540 cal/g or 9.72 kcal/mol (40.7 kJ/mol).
There is a ΔH for the process of sublimation, called the latent heat of sublimation (heat of sublimation). Sublimation is the conversion from the solid state to the gaseous physical state, skipping the liquid state. Elemental iodine, I2, and CO2 are substances that sublime at 1 atm pressure.
There is a change in enthalpy that accompanies a chemical reaction. The 
is the standard heat of formation, the enthalpy change that occurs when one mole of a substance is formed from its component elements, as shown below.
In the first reaction, 393.51 kJ are liberated (exothermic reaction) when 1 mol of gaseous CO2 is formed from graphite and oxygen. When 2 mol HI are formed from gaseous hydrogen and solid iodine, there are 52.72 kJ absorbed (endothermic reaction). In the case of the second reaction, the standard heat of formation is +26.36 kJ/mol HI formed; the total amount of energy involved in the reaction as written is twice the standard heat of formation because there were two moles of product formed. The reason why ΔH is the symbol instead of is that the reaction does not address the formation of one mole of product; therefore, , which is calculated on a per-mole basis, is not an appropriate symbol for the reaction. Further, notice that the o is used in and with other factors (So, 
, or ΔEo) to indicate the standard condition of pressure, 1 atm (1 bar), usually 25°C and, for dissolved substances, of concentration 1 molal (refer to Chapter 12). For easy reference, selected standard heats of formation for selected substances are located in Table 7-1; however, notice that there are no elements listed in the table.
Table 7-1 Standard Enthalpies of Formation at 25°C
Although there is a standard heat of formation for compounds, the standard heat of formation for elements in their ground state at 25°C and 1 atm is taken to be zero. For example, the standard state of H2, O2, Cl2 or N2 is gaseous; Fe, Na, I2, or Cr is solid; and Br2, Hg, or Cs is liquid—zero (0) is the standard heat of formation for these substances. As a point of interest, the standard state of carbon is graphite, not diamond (heat of formation = +0.45 kcal/mol)!
The standard state had been calculated at 1 atm for many decades before it was changed to 1 bar. Because of this, most available tables are based on 1 atm, which is very close to 1 bar. Fortunately, ΔH is not strongly dependent on pressure, so the numerical values show little or no differences, and any which appear are small enough to be ignored for most purposes.
The internal energy and the enthalpy of a system depend on the state of the system under specific conditions of temperature and pressure. As an example, recall from Chapter 6 that the kinetic energy contribution to E for an ideal gas is uniquely determined by the temperature. Further, when there is a change in a system, ΔE and ΔH depend only on the original and final states, not the path taken between them. This path-independence implies two important rules of thermochemistry.
1. ΔE and ΔH for processes that are the reverse of each other have the same magnitude (number), but have opposite signs.
EXAMPLE 1 For melting ice: ΔH for the fusion of ice is 1440 cal/mol, since it is found experimentally that 1440 cal are absorbed in the melting of 1 mol at constant temperature, 273 K, and at constant pressure, 1 atm. For freezing water: The ΔH for freezing is –1440 cal/mol because this amount of heat must be lost from the water to the surrounding in order to freeze. (Note: Energy in = energy out.)
2. If a process can occur in successive steps, ΔH for the overall process is equal to the sum of the enthalpy changes for the individual steps. This rule is Hess’law or, more formally, Hess’law of constant heat summation.
EXAMPLE 2 We cannot measure accurately the heat given off when C burns to CO because the reaction (combustion) cannot be stopped at CO with no CO2 being produced. However, we can accurately measure the heat given off when C burns to produce CO2 (we use an excess of O2), which is 393.5 kJ/mol CO2. We can also measure the heat given off when CO burns to CO2 (283.0 kJ per mol CO2). Using this information, we can calculate the enthalpy change for the burning of C to CO by recognizing that when we add thermochemical equations, the enthalpies are also additive. The same treatment applies if equations are subtracted. Balanced equations are an absolute necessity.
reversed
We reverse the second equation so that the CO is on the right (crossing out the original equation), but that also cancels the 2CO2 and one of the oxygen molecules (cross them out). Also, when we reverse the chemical equation, we reverse the sign associated with the ΔH of the second equation of +566.0 kJ.
Since there are 2 mol CO produced, then the heat of formation for CO is calculated by
EXAMPLE 3 The heat of sublimation of a substance (gas → solid and vice verse) is the sum of the heats of fusion and vaporization of that substance at the same temperature.
EXAMPLE 4 Hess’ law provides us with the application based on the following:
The enthalpy change of any reaction is equal to the sum of the enthalpies (heats) of formation of all the products minus the sum of the enthalpies of formation of all of the reactants, each being multiplied by the number of moles of substance in the balanced equation.
Let us look at a reaction and perform the calculations on the basis of the heats (enthalpies) of formation.
We are to write the reactions reflecting the formation of the compounds involved from their elements. Further, we must do so conforming with the units from Table 7-1, which are written in a per-mole basis.
Note that two of the reactions (2) and (3) had to be reversed in order to produce the summation reaction. The use of the fractional coefficients is for convenience so that the chlorine and the oxygen will cancel, but also so that we are matching the equation we were given in the problem statement above. The use of fractions in the balancing of equations is common, especially when balancing thermochemical reactions and electrochemical reactions (Chapter 19).
Often times, it looks as though we study concepts, but there are no real-world applications that hit home. Example 4 gives us a piece of information that does have a useful application. Suppose you had to open a container of PCl5 and a room had a high humidity. The water vapor mixing with the PCl5 might just cause the highly exothermic reaction discussed. And if this reaction progresses at a high rate, the results could be very dangerous—a fire or even an explosion; at the very least, there would be hydrogen chloride gas in the air you’d be breathing. Hydrogen chloride gas is very irritating to your lungs and in a high enough concentration (not very high at all), hydrogen chloride will damage your lungs and can kill.
The calculation of the ΔH is important also because it is, along with ΔG (Chapter 16), useful in determining whether or not a reaction is spontaneous and provides information about reactions that are at equilibrium. Further, although ΔH has been calculated in this chapter for standard states and at basically room temperature and 1 atm, it can be calculated under other circumstances, as is done in Physical Chemistry and other upper-level chemistry courses.
7.1. (a) How many joules are required to heat 100 g of copper (c = 0.389 J/g · K) from 10°C to 100°C? (b) The same quantity of heat as in (a) is added to 100 g of aluminum (c = 0.908 j/g · K) at 100°C. Which gets hotter, the copper or aluminum?
(a) 
(b) Since the specific heat of copper is less than that of aluminum, less heat is required to raise the temperature of a mass of copper by 1 K than is required for an equal mass of aluminum; the copper gets hotter.
7.2. One kilogram of anthracite coal when burned evolves about 30,500 kJ. Calculate the amount of coal required to heat 4.0 kg of water from 20°C to the boiling point at 1 atm pressure, assuming no loss of heat in the process.
For the heating of the water:
7.3. A steam boiler is made of steel and weighs 900 kg. The boiler contains 400 kg of water. Assuming that 70% of the heat is delivered to the boiler and water, how much heat is required to raise the temperature of the whole from 10°C to 100°C? The specific heat of steel is 0.11 kcal/kg · K.
7.4. Exactly three grams of carbon were burned to CO2 in a copper calorimeter. The mass of the calorimeter is 1500 g and the mass of the water in the calorimeter is 2000 g. The initial temperature was 20.0°C and the temperature rose to 31.3°C. Calculate the heat of combustion of carbon in joules per gram. The specific heat of copper is 0.389 J/g · K.
7.5. A 1.250-g sample of benzoic acid, C7H6O2, was placed in a combustion bomb. The bomb was filled with an excess of oxygen at high pressure, sealed, and immersed in a pail of water which served as a calorimeter. The heat capacity of the entire apparatus (bomb, pail, thermometer, and water) was found to be 10,134 J/K. The oxidation of the benzoic acid was triggered by passing an electric spark through the sample. After complete combustion, the thermometer immersed in the water registered a temperature 3.256 K greater than before the combustion. What is ΔE per mole of benzoic acid burned?
7.6. A 25.0-g sample of an alloy was heated to 100.0°C and dropped into a beaker containing 90 g of water at 25.32°C. The temperature of the water rose to 27.18°C. Assuming 100% efficiency, what is the specific heat of the alloy?
and, solving for C, C = 0.385 J/g · K.
7.7. Determine the final temperature when 150 g of ice at 0°C is mixed with 300 g of water at 50°C.
Step 1. Consider the heat absorbed by the ice and by the melted water (0°C to Tfinal). Recalling that 1°C is the same size as 1 in the Kelvin scale, we can substitute 1 K for 1°C.
Step 2. Let us consider the change in enthalpy of the hot water.
where, presumably, Tfinal <50°C, consistent with a loss of heat from the hot water.
Step 3. The sum of the ΔH’s must equal zero since heat is assumed not to leak into or out of the system discussed in parts 1 and 2 above.
from which Tfinal = 6.7°C
Note: If the amount of ice were to be 200 g, rather than 150 g, the above procedure would have yielded the result, Tfinal = –2°C. This answer is impossible because the final temperature cannot lie outside the range of the initial temperatures. In this case, the result means that there is insufficient hot water to melt all the ice. The final temperature must be 0°C due to the mixture of ice and water. You can calculate that there is 12.5 g of unmelted ice on completion of the experiment.
7.8. How much heat is given up when 20 g of steam at 100°C is condensed and cooled to 20°C?
The heat of vaporization of water at 100°C is
The amount of heat given up is 51.9 kJ.
7.9. How much heat is required to convert 40 g of ice (C = 0.5 cal/g · K) at –10°C to steam (c = 0.5 cal/g · K) at 120°C? (Refer to 7.7, (1): 1°C can be substituted for 1 K.)
7.10. What is the heat of vaporization of water per gram at 25°C and 1 atm?
We can write the thermochemical equation for the process, which is
H2O(l) → H2O(g)
ΔHo can be evaluated by subtracting of reactants from the of the products (Table 7-1).
The enthalpy of vaporization per gram is
Note that the heat of vaporization at 25°C is greater than the value (2.26 kJ/g) at 100°C.
7.11. The thermochemical equation for the combustion of ethylene gas, C2H4, is
Assuming 70% efficiency, how many kilograms of water at 20°C can be converted into steam at 100°C by burning 1 m3 of C2H4 gas measured at S.T.P.?
The useful heat at 70% efficiency is (0.70)(6.29 × 104 kJ) = 4.40 × 104 kJ.
The next step is to consider the conversion of water from 20°C to 100°C, which occurs in two stages.
The mass of water converted, w, is equal to the amount of heat available divided by the heat required per kilogram of water to be converted.
7.12. Calculate the ΔHo for reduction of ferric oxide by aluminum (thermite reaction) at 25°C.
There is a chemical reaction associated with the problem and that reaction must be written as the starting place for the solution to the problem. We can also place the enthalpy of formation (heat of formation) for the participants in the reaction from Table 7-1, multiplied by the coefficient used in balancing the equation. Recall that for an element in the ground state, the is zero.
We must keep in mind what the units are and what happens to them. As an example, look at the value for Fe2O3, which is 1 mol × (–824.2 kJ/mol) = –824.2 kJ.
The formal statement of the of the reaction is given by
Note that keeping the general formula for ΔHo above in the correct order can be done by noticing that during the reaction the products are gained (positive) and the reactants are lost (negative sign).
7.13. The for N(g) (not the standard state of nitrogen) has been determined as 472.7 kJ/mol, and as 249 kJ/mol for O(g). Calculate the ΔHo in (a) kJ and (b) kcal for a hypothetical reaction in the upper atmosphere,
(a) As with the Problem 7.12, we write the heats of formation (multiplied by 1 mole due to the coefficients in the balanced equation) from Table 7-1. Then, we perform the calculation resulting in the value of ΔHo for the reaction.
(b) The calculation for the conversion from kJ to kcal for this exothermic reaction (–ΔHo) is
7.14. Calculate the enthalpy of decomposition of CaCO3 into CaO and CO2.
The first step is to write the balanced equation for the reaction. The second step is to place all the values for the heats of formation noting that the coefficients are all 1’s. Then, we can calculate ΔHo.
Note that the positive value for the enthalpy of this decomposition tells us that this reaction is endothermic.
7.15. (a) Calculate the enthalpy of neutralization of a strong acid by a strong base in water. (b) The heat liberated on neutralization of HCN, a weak acid, by NaOH is 12.1 kJ/mol. How many kilojoules are absorbed during the ionizing of 1 mol of HCN in water?
(a) The basic equation for the neutralization of an acid by a base is
and
(b) The neutralization of HCN(aq) by NaOH(aq) can be considered as the result of two processes; this means that the ΔHo values of the processes can be added for the summation reaction. The processes are the ionization of HCN(aq) and the neutralization of H+(aq) with OH–(aq). Note that since NaOH is a strong base when dissolved in water, we assume complete ionization and a separate thermochemical equation for the ionization need not be written. We can write the following reactions:
The summation reaction is endothermic; however, the ionization reaction is endothermic because the value of ΔHo for the ionization reaction is
7.16. The heat evolved on combustion of acetylene gas, C2H2, at 25°C is 1299 kJ/mol. Determine the enthalpy of formation of acetylene gas.
Because we are asked for information for 1 mol C2H2, let us balance the chemical reaction using only 1 mol C2H2. We can also place the heats of formation in preparation for the final calculation requested.
and
7.17. How much heat will be required to make 1 kg of CaC2 according to the reaction given below?
As above, the heats of formation are placed and the calculation is performed.
This is the heat required to make 1 mol CaC2 (endothermic reaction). One kilogram of CaC2 requires
7.18. How many kilojoules of heat will be evolved in making one mole of H2S from FeS and dilute hydrochloric acid?
Since HCl and FeCl2 are strong electrolytes (ionize well in water), the chloride ion, which does not participate in the reaction (a spectator ion), can be omitted from the balanced equation.
7.19. How many calories are required to heat each of the following from 15°C to 65°C: (a) 1.0 g water; (b) 5.0 g Pyrex® glass; (c) 20 g platinum? (The specific heat of the glass is 0.20 cal/g · K; of platinum, 0.032 cal/g · K.)
Ans. (a) 50 cal; (b) 50 cal; (c) 32 cal
7.20. The ability to convert between calories and joules is extremely important. Express the answers in Problem 7.19 in joules and in kJ.
Ans. (a and b) 209.2 J and 0.2092 kJ; (c) 133.9 J and 0.1339 kJ
7.21. The combustion of 5.00 g of coke raised the temperature of water of 1.00 kg of water from 10°C to 47°C. Calculate the heating value of coke.
Ans. 7.4 kcal/g or 31 kJ/g
7.22. Assuming that 50% of the heat is useful, how many kilograms of water at 15°C can be heated to 95°C by burning 200 L of methane, CH4, measured at S.T.P.? The heat of combustion for methane is 891 kJ/mol.
Ans. 12 kg water
7.23. The heat of combustion of ethane gas, C2H6, is 1561 kJ/mol. Assuming that 60% of the heat is useful, how many liters of ethane (S.T.P.) must be burned to supply enough heat to convert 50 kg of water at 10°C to steam at 100°C?
Ans. 3150 L
7.24. A substance, metallic in nature, is to be identified, and heat capacity is one of the clues to its identity. A block of the metal weighing 150 g required 38.5 cal to raise its temperature from 22.8°C to 26.4°C. Calculate the specific heat capacity of the metal and determine if it is the correct alloy, which has a specific heat capacity of 0.0713 cal/g · K.
Ans. Yes, it is the same alloy on the basis of heat capacity; it is a match at 0.0713 cal/g · K.
7.25. An ore has been refined and the metal produced is suspected of being gold. A test is to determine the specific heat of the metal and compare against that of gold allowing a 2% tolerance (2% above or below). The amount of heat necessary to raise 25.0 grams of the metal from 10.0°C to 23.6°C was 10.78 cal. The specific heat of gold is 0.0314 cal/g°C.
Ans. The specific heat of the sample is 0.0317 cal/g°C, which is just 1% from the specific heat of gold.
7.26. A 45.0-g sample of an alloy was heated to 90.0°C and then dropped into a beaker containing 82 g of water at 23.50°C. The temperature of the water rose to 26.25°C. What is the specific heat of the alloy?
Ans. 0.329 J/g · K or 0.079 cal/g · K
7.27. A fired lead bullet weighed 35.4 g after cleaning; it was heated to 91.50°C, then placed in 50.0 mL of water at 24.73°C. The temperature of the water rose to 26.50°C. A sample bullet was secured from a potential suspect and was found to have a specific heat of 0.03022 cal/g°C. What is the specific heat of the fired bullet and could it be from the same batch of bullets?
Ans. The specific heat of the sample is 0.03946. The specific heats are 0.0.00924 cal/g°C apart. An interpretation is that the collected bullet is 31% higher in specific heat than the sample bullet, which would tend to eliminate the suspected similarity.
7.28. If the specific heat of a substance is h cal/g · K, what is its specific heat in Btu/lb · °F?
Ans. h Btu/lb · °F
7.29. How much water at 20°C would be necessary to cool a 34-g piece of copper, specific heat 0.0924 cal/g · K, from 98°C to 25°C?
Ans. 46 g H2O
7.30. Determine the resulting temperature when 1 kg of ice at 0°C is mixed with 9 kg of water at 50°C. The heat of fusion of ice is 80 cal/g (355 J/g).
Ans. 37°C
7.31. An automatic fire sprinkler depends on a piece of metal with a low melting point to release water when necessary. How much heat would be required to melt a 5 g piece of lead (MP = 327°C, specific heat of 0.03 cal/g · K) used as a plug in a sprinkler normally at room temperature (25°C)? Express in calories and joules.
Ans. 45.3 cal or 189.5 J
7.32. How much heat is required to change 10 g of ice at 0°C to steam at 100°C? The heat of vaporization of water at 100°C is 540 cal/g (2259 J/g).
Ans. 7.2 kcal or 30 kJ
7.33. A boiler that supplies a steam turbine used in an electric power plant must raise the temperature of water from the ambient temperature passing through a physical state change and then to live (very hot) steam. How much energy (kcal and kJ) would be required to raise 15,000 L of water from 25°C to steam at 175°C? (steam requires 0.5 cal/g · K)?
Ans. 9,800 kcal or 41,000 kJ
7.34. A Styrofoam™ coffee cup serves as an inexpensive calorimeter for measurements that do not require high accuracy. One gram of KCl(s) was added to 25.0 ml of water in such a cup at 24.33°C. It dissolved completely and quickly with gentle stirring. The minimum temperature reached was 22.12°C. Estimate the ΔHo of the heat of solution of KCl in kJ/mol. You may assume the solution has the same heat capacity as water and that the heat capacity of the cup and thermometer need not be considered.
Ans. 
7.35. In an ice calorimeter, a chemical reaction is allowed to occur in thermal contact with an ice-water mixture at 0°C. Any heat liberated by the reaction is used to melt ice; the volume change of the ice-water mixture indicates the amount of melting. When solutions containing 1.00 millimole each of AgNO3 and NaCl were mixed in such a calorimeter, both solutions having been precooled to 0°C, 0.20 g of ice melted. Assuming complete reaction, what is ΔH for the reaction Ag+ + Cl– → AgCl?
Ans. –67 kJ or –16 kcal
7.36. A 15.3-g portion of an organic liquid at 26.2°C was poured into the reaction chamber of an ice calorimeter and cooled to 0.0°C. The rise in water level indicated that 3.09 g of ice melted. Calculate the specific heat of this organic liquid.
Ans. 0.616 cal/g · K or 2.58 J/g · K
7.37. What is the heat of sublimation of solid iodine at 25°C?
Ans. 14.92 kcal/mol I2 or 62.4 kJ/mol I2
7.38. Calculate the amount of energy involved in the change of 650 g I2 from a gas to a solid at 25°C.
Ans. 32.67 kcal or 136.7 kJ
7.39. Is the process of dissolving H2S gas in water endothermic or exothermic? To what extent?
Ans. Exothermic, 4.6 kcal/mol (19.1 kJ/mol) (Note: The actual answer is –4.6 cal/mol. Recall that a negative value indicates that the reaction (physical or chemical) is exothermic.)
7.40. How much heat is released on dissolving 1 mol of HCl(g) in a large amount of water? (Hint: HCl is completely ionized in dilute solution.)
Ans. 17.9 kcal or 74.8 kJ
7.41. The standard enthalpy of formation of H(g) has been determined to be 218.0 kJ/mol. Calculate the ΔHo in kilojoules for the following two reactions: (a) H(g) + Br(g) → HBr(g); (b) H(g) + Br2(l) → HBr(g) + Br(g)
Ans. (a) –366.2 kJ; (b) –142.6 kJ
7.42. Determine the ΔHo of decomposition of 1 mol of solid KClO3 into solid KCl and oxygen gas.
Ans. –10.9 kcal or –45.5 kJ
7.43. The heat released on neutralization of CsOH with all strong acids is 13.4 kcal/mol. The heat released on neutralization of CsOH with HF (weak acid) is 16.4 kcal/mol. Calculate the ΔHo of the ionization of HF in water.
Ans. –3.0 kcal/mol
7.44. Find the heat evolved in slaking 1 kg of quicklime (CaO) according to the reaction
Ans. 282 kcal or 1180 kJ
7.45. The heat liberated on complete combustion of 1 mol of CH4 gas to CO2(g) and H2O(l) is 890 kJ. Determine the enthalpy of formation of 1 mol of CH4 gas.
Ans. –75 kJ/mol
7.46. The heat evolved on combustion of 1 g of starch, (C6H10O5)n, into CO2(g) and H2O(l) is 17.48 kJ. Compute the standard enthalpy of formation of 1 g starch.
Ans. –5.88 kJ
7.47. The amount of heat evolved on dissolving CuSO4 is 73.1 kJ/mol. What is for 
(aq)?
Ans. –909.3 kJ/mol
7.48. The heat of solution of CuSO4 · 5H2O in a large amount of water is 5.4 kJ/mol (endothermic). Refer to Problem 7.47 and calculate the heat of reaction for
Ans. 78.5 kJ (exothermic and expressed as –78.5 kJ or –18.8 kcal)
7.49. The heat evolved during the combustion of 1 mol C2H6(g) into CO2(g) and H2O(l) is 1559.8 kJ, and for complete combustion of 1 mol C2H4(g) is 1410.8 kJ. Calculate ΔH for the following reaction:
ΔH = –97.0 kJ. What is the heat of solution of CaCl2 (anhydrous) in a large volume of water?
Ans. –136.8 kJ
7.50. The solution of CaCl2 · 6H2O in a large volume of water is endothermic to the extent of 14.6 kJ/mol. For the reaction below, ΔH = –97.0 kJ. What is the heat of solution of CaCl2 (anhydrous) in a large volume of water?
Ans. 82.4 kJ/mol (exothermic)
7.51. Hydrolysis is an important organic reaction in which a large molecule utilizes a water molecule to split into two smaller molecules. Since the same number and kind of chemical bonds are present in both reactants and products, one might expect only a small energy change. Calculate ΔHo for the gas phase hydrolysis of dimethyl ether based on Table 7-1 and the additional heat of formation values following: CH3OCH3(g) = –185.4 kJ/mol and CH3OH(g) = –201.2 kJ/mol. The reaction is
Ans. ΔHo = +24.8kJ
7.52. The commercial production of water gas utilizes the reaction C(s) + H2O(g) → H2(g) + CO(g). The required heat for this endothermic reaction may be supplied by adding a limited amount of oxygen and burning some carbon to CO2. How many grams of carbon must be burned to CO2 to provide enough heat for the water gas conversion of 100 g of carbon? Assume no heat is lost to the environment.
Ans. 33.4 g
7.53. This reaction can be reversed.
The reaction goes completely to the right at temperatures above 32.4°C, and remains completely on the left below this temperature. This system has been used in some solar homes for heating at night with the energy absorbed from the sun’s radiation during the day. How many cubic feet of fuel gas could be saved per night by the reversal of the dehydration of a fixed charge of 100 lb Na2SO4 · 10H2O? Assume that the fuel value of the gas is 2000 Btu/ft 3.
Ans. 5.3 ft3
7.54. A lot of heat is produced when gunpowder burns. A mixture can be produced from charcoal (carbon), KClO4, and sulfur. By the reactions below, calculate the amount of energy given off when a mole of gunpowder burns (assume 1 mole of each substance adds up to 1 mol gunpowder).
Hints: (i) Balance equations—fractions are OK; (ii) O2 can come from the air.
Ans. –189.5 kcal or –792.6 kJ
7.55. An important criterion for the desirability of fuel reactions for rockets is the fuel value in kilojoules, either per gram of reactant, or per cubic centimeter of reactant. Compute both of these quantities for each of the following reactions:
(a) N2H4(l) + 2H2O2(l) → N2(g) + 4H2O(g)
(b) 2LiBH4(s) + KClO4(s) → Li2O(s) + B2O3(s) + KCl(s) + 4H2(g)
(c) 6LiAlH4(s) + 2C(NO2)4(l) → 3Al2O3(s) + 3Li2O(s) + 2CO2(g) + 4N2(g) + 12H2(g)
(d) 4HNO3(l) + 5N2H4(l) → 7N2(g) + 12H2O(g)
(e) 7N2O4(l) + C9H20(l) → 9CO2(g) + 10H2O(g) + 7N2(g)
(f) 4ClF3(l) + (CH3)2N2H2(l) → 2CF4(g) + N2(g) + 4HCl(g) + 4HF(g)
Use the following density values: N2H4(l), 1.01 g/cm3; H2O2(l), 1.46 g/cm3; LiBH4(s), 0.66 g/cm3; KClO4(s), 2.52 g/cm3; LiAlH4(s), 0.92 g/cm3; C(NO2)4(l), 1.65 g/cm3; HNO3(l), 1.50 g/cm3; N2O4(l), 1.45 g/cm3; C9H20(l), 0.72 g/cm3; ClF3(l), 1.77 g/cm3; (CH3)2N2H2(l), 0.78 g/cm3. When computing the volume of each reaction mixture, assume that the reactants are present in stoichiometric proportions.
Ans. (a) 6.4 kJ/g, 8.2 kJ/cm3; (b) 8.3 kJ/g, 12.4 kJ/cm3; (c) 11.4 kJ/g, 14.6 kJ/cm3; (d) 6.0 kJ/g, 7.5 kJ/cm3; (e) 7.2 kJ/g, 8.9 kJ/cm3; (f) 6.0 kJ/g, 9.1 kJ/cm3
7.56. Fires often times are hotter than normal due to the use of an accelerant; nonane, C9H20, is an example. How much additional heat would there be in a fire contributed to by the complete combustion of 500 g nonane (gases for products)?
Ans. 1358.6 kcal or 5684.2 kJ
7.57. An early-model Concorde supersonic airplane consumed 4700 gallons of aviation fuel per hour at cruising speed. The density of the fuel was 6.65 pounds per gallon and the ΔH of combustion was –10,500 kcal/kg. Express the power consumption in megawatts (1 MW = 106 W = 106 J/s) during cruise.
Ans. 173 MW
7.58. Two solutions, initially at 25.08°C, were mixed in an insulated bottle. One consisted of 400 mL of a weak monoprotic acid solution of concentration 0.200 mL. The other consisted of 100 mL of a 0.800 mol of NaOH per liter of solution. The temperature rose to 26.25°C. How much heat is evolved in the neutralization of one mole of the acid? Assume that the densities of all solutions are 1.00 g/cm3 and that their specific heat capacities are all 4.2 J/g · K. Actually, these assumptions are in error by several percent, but they nearly cancel each other.
Ans. 31 kJ/mol
7.59. An old type of miner’s lamp burns acetylene, C2H2, which is made as needed by dropping water onto calcium carbide, CaC2. The lamp designer needs to be concerned about how hot the calcium carbide chamber will get because the lamp is worn on the miner’s hat and an explosion is not a good idea. Calculate the heat produced per liter (kJ/L at S.T.P.) of C2H2 generated. (Refer to Problem 7.16.)
Ans. 5.77 kJ/L (ΔHo = –129.3 kJ/mol)
7.60. The miner’s lamp discussed in Problem 7.59 is the basis for this problem. (a) How does the heat of combustion of the C2H2 compare to the heat generated in making it from calcium carbide? (b) If we add the generating reaction to the combustion reaction, the overall reaction of the lamp becomes
Calculate the ΔHo for the above reaction and compare it to the results of the separate calculations made in Problems 7.59 and 7.60(a).
Ans. (a) Heat of combustion = 58.0 kJ/L (ΔH = –1299 kJ/mol). This is about ten times the result of Problem 7.59. (b) The result is exactly the sum of the previous calculations (–129.3 – 1299.1); ΔHo = –1428 kJ/mol.
7.61. Calcium carbonate reacts with HCl gas, and the reaction can neutralize a release of the corrosive gas. Calculate and interpret the thermodynamic value for the neutralization of 200 kg HCl gas by the reaction: 2HCl(g) + CaCO3(s) → CaCl2(s) + CO2(g) + H2O(g). (The heat of formation for CaCl2 is –190.0 kcal/mol.)
Ans. –25.3 kcal (–106 kJ). The negative value tells us it is an exothermic reaction.