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Chapter 9: Problem 50

Calcium chloride is a salt used in a number of food and medicinal applications and in brine for refrigeration systems. Its most distinctive property is its affinity for water. in its anhydrous form it efficiently absorbs water vapor from gases, and from aqueous liquid solutions it can form (at different conditions) calcium chloride hydrate \(\left(\mathrm{CaCl}_{2} \cdot \mathrm{H}_{2} \mathrm{O}\right)\) dihydrate \(\left(\mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)\) tetrahydrate \(\left(\mathrm{CaCl}_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}\right),\) and hexahydrate \(\left(\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\right)\) You have been given the task of determining the standard heat of the reaction in which calcium chloride hexahydrate is formed from anhydrous calcium chloride: $$\mathrm{CaCl}_{2}(\mathrm{s})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}): \quad \Delta H_{\mathrm{r}}^{\circ}(\mathrm{k} \mathrm{J})=?$$ By definition, the desired quantity is the heat of hydration of calcium chloride hexahydrate. You cannot carry out the hydration reaction directly, so you resort to an indirect method. You first dissolve 1.00 mol of anhydrous \(\mathrm{CaCl}_{2}\) in \(10.0 \mathrm{mol}\) of water in a calorimeter and determine that \(64.85 \mathrm{kJ}\) of heat must be transferred away from the calorimeter to keep the solution temperature at \(25^{\circ} \mathrm{C}\). You next dissolve 1.00 mol of the hexahydrate salt in 4.00 mol of water and find that 32.1 kJ of heat must be transferred to the calorimeter to keep the temperature at \(25^{\circ} \mathrm{C}\). (a) Use these results to calculate the desired heat of reaction. (Suggestion: Begin by writing out the stoichiometric equations for the two dissolution processes.) (b) Calculate the standard heat of reaction in \(\mathrm{kJ}\) for \(\mathrm{Ca}(\mathrm{s}), \mathrm{Cl}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}\) reacting to form \(\mathrm{CaCl}_{2}\) (aq, \(r=10\) ). (c) Speculate about why the standard heat of reaction in forming calcium chloride hexahydrate cannot be measured directly by reacting the anhydrous salt with water in a calorimeter.

Short Answer

Expert verified
The heat of the reaction for the formation of calcium chloride hexahydrate from anhydrous calcium chloride is -96.95 kJ. The heat of reaction can't be measured directly because the reaction is highly exothermic.

Step by step solution

01

Identify the Two Known Heats of Reaction

First, let's identify the known heats of reaction. We know that when dissolving 1.00 mol of anhydrous \(\mathrm{CaCl}_{2}\) in \(10.0 \mathrm{mol}\) of water, \(64.85 \mathrm{kJ}\) of heat is released. When dissolving 1.00 mol of the hexahydrate salt in 4.00 mol of water, \(32.1 \mathrm{kJ}\) of heat is absorbed.
02

Write the Corresponding Chemical Reactions

For the dissolving of anhydrous \(\mathrm{CaCl}_{2}\) in water: \(\mathrm{CaCl}_{2}(\mathrm{s}) + 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaCl}_{2} (aq) + 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}), \Delta H = -64.85 \mathrm{kJ}\). For the dissolving of calcium chloride hexahydrate: \(\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) + 4 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaCl}_{2} (aq) + 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}), \Delta H = 32.1 \mathrm{kJ}\). Note that in both reactions, the products are the same. We've also included the sign legends for the \(\Delta H\) values.
03

Calculate the Desired Heat of Reaction

To calculate the heat of reaction for \(\mathrm{CaCl}_{2}(\mathrm{s})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}\), we use Hess's law which states that the change in enthalpy in going from a set of reactants to a set of products does not depend on the pathway of the reaction. So, \(\Delta H_{\mathrm{r}}^{\circ} = \Delta H_{\mathrm{hydration}} - \Delta H_{\mathrm{dissolution}} = -64.85 \mathrm{kJ} - 32.1 \mathrm{kJ} = -96.95 \mathrm{kJ}\).
04

Speculate on Why the Heat of Reaction Can't be Measured Directly

The heat of reaction for the formation of calcium chloride hexahydrate from the anhydrous salt cannot be measured directly because the reaction is highly exothermic. This means it gives off a large amount of heat that could cause the water to boil, making it difficult to measure the heat accurately in a calorimeter.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hess's Law
Hess's Law is a fundamental concept in chemistry which you can use to calculate the overall enthalpy change for a chemical reaction. It states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction takes. This is because enthalpy is a state function, meaning it only depends on the initial and final states and not on the path taken to get from one to the other.
To apply Hess's Law, you can break complicated reactions into simpler steps whose enthalpy changes are known. Then you add up these enthalpy changes to get the overall reaction enthalpy. This can be incredibly useful when direct measurement is not possible or practical. For example, in calorimetry, if a reaction is too exothermic, making direct measurement difficult, you can instead use known reactions and their enthalpy changes to find the desired value using Hess's Law.
Calorimetry
Calorimetry is the process of measuring the heat of chemical reactions or physical changes. It's a key technique to investigate how energy is exchanged in a chemical process. Calorimetry experiments are typically performed with calorimeters鈥攄evices that isolate the reaction to measure temperature changes accurately.
Using calorimetry, one can deduce the heat involved in dissolving calcium chloride. This heat is crucial for calculating the enthalpy change of reactions, like in this exercise where we couldn't directly measure the hydration of calcium chloride. Calorimeters help by isolating the reaction in a controlled environment, allowing precise measurements of heat release or absorption. However, if a reaction is too vigorous, managing the heat released can become challenging, potentially boiling the water, which is why alternative approaches like Hess's Law are often used alongside calorimetry.
Chemical Reactions
Chemical reactions involve the rearrangement of atoms to transform substances. They play a crucial role in many aspects of life and industrial applications. Each reaction has an enthalpy change, representing the heat absorbed or released.
There are different types of chemical reactions, categorized based on their processes and energy changes. For instance, exothermic reactions release heat, making them tricky to measure under certain conditions, like direct hydration of calcium chloride. Understanding the stoichiometry and thermodynamics of chemical reactions is essential to predict their behavior and impact.
  • Reagents combine or break apart to from products.
  • Each reaction has a unique enthalpy change, \(\Delta H\).
  • Reactions can be direct or require multi-step pathways.
Studying chemical reactions is critical for applications such as energy production, cooking, pharmaceuticals, and environmental science, emphasizing their broad relevance and importance.

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Most popular questions from this chapter

Various uses for nitric acid are given in Problem \(6.43,\) along with information about how this important chemical is synthesized industrially. The key reactions are oxidations of ammonia to nitric oxide and of nitric oxide to nitrogen dioxide, followed by dissolution of \(\mathrm{NO}_{2}\) in water: $$\begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) & \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \\ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \\ 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1) & \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{aligned}$$ Nitric oxide generated on dissolution of \(\mathrm{NO}_{2}\) in water is oxidized to produce additional \(\mathrm{NO}_{2},\) which is then combined with water to form more \(\mathrm{HNO}_{3}\). In this problem we neglect side reactions that would lower the product yield. Ammonia vapor at \(275^{\circ} \mathrm{C}\) and 8 atm is mixed with air, also at \(275^{\circ} \mathrm{C}\) and 8 atm, and the combined stream is fed to a converter. Fresh air entering the system at \(30^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(50 \%\) is compressed to \(100^{\circ} \mathrm{C}\) and 8 atm, and the compressed air then exchanges heat with the product gas leaving the converter. The quantity of oxygen in the feed to the converter is \(20 \%\) in excess of the amount theoretically required to convert all of the ammonia to \(\mathrm{HNO}_{3}\). The entire process after the compressor may be taken to operate at a constant pressure of 8 atm. In the converter, the ammonia is completely oxidized, with a negligible amount of \(\mathrm{NO}_{2}\) formed. The product gas leaves the converter at \(850^{\circ} \mathrm{C}\), and, as described in the preceding paragraph, exchanges heat with the air entering the system. The product gas then is fed to a waste-heat boiler that produces superheated steam at \(200^{\circ} \mathrm{C}\) and 10 bar from liquid water at \(35^{\circ} \mathrm{C}\). The product gas leaving the wasteheat boiler is cooled further to \(35^{\circ} \mathrm{C}\) and fed to an absorption column in which the NO is completely oxidized to \(\mathrm{NO}_{2},\) which in turn combines with water (some of which is present in the product gas). Water is fed to the absorber at \(25^{\circ} \mathrm{C},\) at a rate sufficient to form a 55 wt\% aqueous nitric acid solution. The NO formed in the reaction of \(\mathrm{NO}_{2}\) to produce \(\mathrm{HNO}_{3}\) is oxidized, and the NO \(_{2}\) produced is hydrated to form still more \(\mathrm{HNO}_{3}\). The off-gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (a) Construct a flowchart showing all process streams, including input and output from the process and the following equipment: converter, air compressor, exchanger recovering heat from the converter product, waste-heat boiler producing superheated steam, exchanger cooling the product gas before it is fed to the absorber, and absorber. (b) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, develop spreadsheets (preferably incorporating the use of APEx) to determine the following: (i) Molar amounts (kmol) of oxygen, nitrogen, and water vapor in the air fed to the process, cubic meters of air fed to the process, and kmol of water fed to the absorber. (ii) Molar amounts, molar composition, and volume of the off-gas leaving the absorber. (iii) Mass (kg) of product nitric acid solution. (iv) Molar amounts and composition of the gas leaving the converter. (v) Heat removed from or added to (state which) the converter. (vi) Temperature of the product gas after it has exchanged heat with the air, assuming no heat is transferred between the heat exchanger and the surroundings. (vii) Production rate of superheated steam if the gas temperature leaving the boiler is \(205^{\circ} \mathrm{C}\). Before performing this calculation, determine if condensation of water occurs when the gas is cooled to \(205^{\circ} \mathrm{C}\). Since the superheated steam temperature is \(200^{\circ} \mathrm{C}\), explain why the selected temperature of the product gas is reasonable. (viii) Heat removed from the product gas before it is fed to the absorber (Hint: Check the condition of the gas at \(35^{\circ} \mathrm{C}\) ) and mass of cooling water required to remove that heat if the water temperature can only be increased by \(5^{\circ} \mathrm{C}\). Assume no heat is transferred between the heat exchanger and the surroundings. (ix) Heat removed from or added to the absorber. Assume the heat capacity of the nitric acid solution is approximately the same as that of liquid water and the outlet temperatures of the off-gas and product streams are \(25^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\), respectively. (c) Scale up the results calculated in Part (b) to determine all stream flow rates and heat transfer rates for a production rate of \(5.0 \times 10^{3} \mathrm{kg} / \mathrm{h}\) of the product solution.

A fuel gas containing 85.0 mole\% methane and the balance ethane is burned completely with pure oxygen at \(25^{\circ} \mathrm{C},\) and the products are cooled to \(25^{\circ} \mathrm{C}\). (a) Suppose the reactor is continuous. Take a basis of calculation of \(1 \mathrm{mol} / \mathrm{s}\) of the fuel gas, assume some value for the percent excess oxygen fed to the reactor (the value you choose will not affect the results), and calculate \(-\dot{Q}(\mathrm{k} \mathrm{W}),\) the rate at which heat must be transferred from the reactor. (b) Now suppose the combustion takes place in a constant-volume batch reactor. Take a basis of calculation of 1 mol of the fuel gas charged into the reactor, assume any percent excess oxygen, and calculate \(-Q(\mathrm{kJ}) .\) (Hint: Recall Equation 9.1-5.) (c) Briefly explain why the results in Parts (a) and (b) do not depend on the percent excess \(\mathrm{O}_{2}\) and why they would not change if air rather than pure oxygen were fed to the reactor.

Methane at \(25^{\circ} \mathrm{C}\) is burned in a boiler furnace with \(10.0 \%\) excess air preheated to \(100^{\circ} \mathrm{C}\). Ninety percent of the methane fed is consumed, the product gas contains \(10.0 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO},\) and the combustion products leave the furnace at \(400^{\circ} \mathrm{C}\). (a) Calculate the heat transferred from the furnace, \(-\dot{Q}(\mathrm{kW}),\) for a basis of \(100 \mathrm{mol} \mathrm{CH}_{4}\) fed/s. (The greater the value of \(-\dot{Q}\), the more steam is produced in the boiler.) (b) Would the following changes increase or decrease the rate of steam production? (Assume the fuel feed rate and fractional conversion of methane remain constant.) Briefly explain your answers. (i) Increasing the temperature of the inlet air; (ii) increasing the percent excess air for a given stack gas temperature; (iii) increasing the selcctivity of \(\mathrm{CO}_{2}\) to \(\mathrm{CO}\) formation in the furnace; and (iv) increasing the stack gas temperature.

A gas mixture containing 85 mole\% methane and the balance oxygen is to be charged into an evacuated well-insulated 20-liter reaction vessel at 25^^ C and 200 kPa. An electrical coil in the reactor, which delivers heat at a rate of 100 watts, will be turned on for 85 seconds and then turned off. Formaldehyde will be produced in the reaction $$\mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2} \mathrm{O}$$ The reaction products will be cooled and discharged from the reactor. (a) Calculate the maximum pressure that the reactor is likely to have to withstand, assuming that there are no side reactions. If you were ordering the reactor, why would you specify an even greater pressure in your order? (Give several reasons.) (b) Why would heat be added to the feed mixture rather than running the reactor adiabatically? (c) Suppose the reaction is run as planned, the reaction products are analyzed chromatographically, and some \(\mathrm{CO}_{2}\) is found. Where did it come from? If you had taken it into account, would your calculated pressure in Part (a) have been larger, smaller, or can't you tell without doing the detailed calculations?

An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen, nitrogen, oxygen, and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Dulong formula: $$H H V(\mathrm{k} J / \mathrm{kg})=33,801(\mathrm{C})+144,158[(\mathrm{H})-0.125(\mathrm{O})]+9413(\mathrm{S})$$ where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125(O) term accounts for the hydrogen bound in the water contained in the coal. (a) Derive an expression for the higher heating value ( \(H H V\) ) of a coal in terms of \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{S},\) and compare your result with the Dulong formula. Suggest a reason for the difference. (b) A coal with an ultimate analysis of \(75.8 \mathrm{wt} \% \mathrm{C}, 5.1 \% \mathrm{H}, 8.2 \% \mathrm{O}, 1.5 \% \mathrm{N}, 1.6 \% \mathrm{S},\) and \(7.8 \%\) ash (noncombustible) is burned in a power-plant boiler fumace. All of the sulfur in the coal forms \(\mathrm{SO}_{2}\) The gas leaving the furnace is fed through a tall stack and discharged to the atmosphere. The ratio \(\phi\) (\(\mathrm{kg} \mathrm{SO}_{2}\) in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate \(\phi\), using the Dulong formula for the heating value of the coal. (c) An earlier version of the EPA regulation specified that the mole fraction of \(\mathrm{SO}_{2}\) in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.
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