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Chapter 12: Problem 68

Gas streams containing \(\mathrm{CO}_{2}\) are frequently passed through absorption tubes filled with \(\mathrm{CaO}(s),\) where the following reaction takes place to remove the \(\mathrm{CO}_{2}\) from the stream:$$\mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)$$. a. Use the data in Appendix 4 to calculate \(\Delta G^{\circ}\) at \(298 \mathrm{K}\) for this reaction. b. Is the reaction spontaneous at \(298 \mathrm{K} ?\) c. Calculate \(\Delta G\) for this reaction at \(1500 \mathrm{K},\) a typical temperature for a lime kiln. (Assume \(\Delta H\) and \(\Delta S\) do not change with temperature.) d. Is the reaction as written spontaneous at \(1500 \mathrm{K}\) ? e. In a lime kiln, calcium carbonate (in the form of oyster shells) is roasted to produce \(\mathrm{CaO}\) and \(\mathrm{CO}_{2} .\) Is this process spontaneous at the temperature of a kiln?

Short Answer

Expert verified
Answer: The reaction is spontaneous at 298 K but not at 1500 K.

Step by step solution

01

Calculate 螖G掳 using standard Gibbs Free Energy of formation values

To calculate the Gibbs Free Energy change at 298 K, we can use the equation: $$螖G掳rxn = 危 螖Gf掳(products) - 危 螖Gf掳(reactants)$$ From Appendix 4, we have the following 螖Gf掳 values: 螖Gf掳 (CaO) = -604.1 kJ/mol 螖Gf掳 (CO2) = -394.4 kJ/mol 螖Gf掳 (CaCO3) = -1128.8 kJ/mol So, we can calculate: 螖G掳rxn = (-1128.8) - ((-604.1) + (-394.4)) 螖G掳rxn = -130.3 kJ/mol b. Is the reaction spontaneous at 298 K? Since 螖G掳rxn is negative, the reaction is spontaneous at 298 K. c. Calculate 螖G for this reaction at 1500 K.
02

Calculate 螖G at 1500 K using 螖H掳, 螖S掳, and T

We use the following equation to find 螖G at 1500 K: $$螖G = 螖H - T螖S$$ First, we need to calculate 螖H掳 and 螖S掳 for this reaction. We can do this by using the equation: $$螖H掳rxn = 危 螖Hf掳(products) - 危 螖Hf掳(reactants)$$ $$螖S掳rxn = 危 S掳(products) - 危 S掳(reactants)$$ From Appendix 4, we find the following values: 螖Hf掳 (CaO) = -635.1 kJ/mol 螖Hf掳 (CO2) = -393.5 kJ/mol 螖Hf掳 (CaCO3) = -1206.9 kJ/mol S掳 (CaO) = 39.8 J/mol路K S掳 (CO2) = 213.7 J/mol路K S掳 (CaCO3) = 92.9 J/mol路K Now, we can calculate: 螖H掳rxn = (-1206.9) - ((-635.1) + (-393.5)) 螖H掳rxn = -178.3 kJ/mol 螖S掳rxn = (92.9) - (39.8 + 213.7) 螖S掳rxn = -160.6 J/mol路K Now we can calculate 螖G at 1500 K: 螖G = 螖H - T螖S = -178.3 kJ/mol - (1500 K 脳 (-160.6 J/mol路K)) 螖G = 59.6 kJ/mol d. Is the reaction as written spontaneous at 1500 K? Since 螖G is positive, the reaction is not spontaneous at 1500 K. e. In a lime kiln, calcium carbonate (in the form of oyster shells) is roasted to produce CaO and CO2. Is this process spontaneous at the temperature of a kiln? The reverse reaction is given by: $$CaCO_{3}(s) \rightarrow CaO(s) + CO_{2}(g)$$ A positive 螖G for the original reaction indicates that the reverse reaction is spontaneous at the temperature of a kiln (1500 K). Therefore, the process of producing CaO and CO2 in a lime kiln is spontaneous at 1500 K.

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Key Concepts

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

Spontaneity of Reactions
Understanding whether a reaction is spontaneous depends on the Gibbs Free Energy change (\( \Delta G \)). A reaction is spontaneous if \( \Delta G \) is negative. This means the reaction can occur without the need for additional energy, moving naturally from reactants to products.
The sign of \( \Delta G \) is crucial:
  • Negative \( \Delta G \): Reaction is spontaneous
  • Positive \( \Delta G \): Reaction is non-spontaneous
  • Zero \( \Delta G \): Reaction is at equilibrium
Spontaneity is temperature-dependent because both enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) play vital roles. For example, at 298 K, the reaction involving \( \text{CaO} \) and \( \text{CO}_{2} \) is spontaneous. However, at 1500 K, the same reaction's \( \Delta G \) becomes positive, making it non-spontaneous.
This showcases how the same reaction can behave differently at various temperatures, emphasizing the importance of conditions in determining reaction spontaneity.
Thermodynamics
Thermodynamics is the study of energy transfer, particularly in chemical reactions. It helps us understand how and why reactions occur by examining changes in enthalpy (\( \Delta H \)), entropy (\( \Delta S \)), and Gibbs Free Energy (\( \Delta G \)).
Key thermodynamic terms:
  • Enthalpy (\( \Delta H \)): Heat absorbed or released during a reaction. Negative \( \Delta H \) indicates exothermic reactions, while positive \( \Delta H \) indicates endothermic.
  • Entropy (\( \Delta S \)): Measure of disorder or randomness. High entropy corresponds to more disorder.
To determine \( \Delta G \), we use:\[\Delta G = \Delta H - T\Delta S\]where \( T \) is the temperature in Kelvin. Lowerings of \( \Delta G \) often occur due to negative \( \Delta H \) and positive \( \Delta S \), emptying the system鈥檚 potential energy. Changes in temperature can significantly alter reactions, as seen in the shift of spontaneity at different temperatures in the given reaction.
Chemical Reactions
In chemical reactions, substances convert into other substances, involving transformation at the atomic level. Understanding the thermodynamic aspects of chemical reactions, like enthalpy, entropy, and Gibbs Free Energy changes, helps predict how and why these transformations occur.
The specific reaction of \( \text{CaO}(s) + \text{CO}_{2}(g) \rightarrow \text{CaCO}_{3}(s) \) involves combining a solid and a gas into another solid. This is a type of chemical reaction known as a synthesis reaction, where multiple reactants combine to form a single product.
Factors dictating reactions:
  • Nature of reactants and products
  • Change in energy (enthalpy and entropy)
  • Temperature and pressure conditions
In industrial contexts, like in lime kilns, the reaction conditions are adjusted to favor desired products. For instance, the production of \( \text{CaO} \) and \( \text{CO}_{2} \) from \( \text{CaCO}_{3} \) at high temperatures (1500 K) is favored due to its spontaneity, in the reverse reaction of the original synthesis.
This highlights the chemical industry's reliance on understanding and manipulating these processes for optimal efficiency and product output.

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Most popular questions from this chapter

Two allotropes ( \(A\) and \(B\) ) of sulfur interconvert at \(369 \mathrm{K}\) and 1 atm pressure:$$\mathrm{S}_{\mathrm{s}}(s, \mathrm{A}) \rightarrow \mathrm{S}_{\mathrm{g}}(s, \mathrm{B})$$.The enthalpy change in this transition is \(297 \mathrm{J} / \mathrm{mol}\). What is the entropy change?

Copper forms two oxides, \(\mathrm{Cu}_{2} \mathrm{O}\) and \(\mathrm{CuO}\). a. Name these oxides. b. Predict over what temperature range this reaction is spontaneous using the following thermodynamic data:$$\mathrm{Cu}_{2} \mathrm{O}(s) \rightarrow \mathrm{CuO}(s)+\mathrm{Cu}(s)$$ $$\begin{aligned}&]\\\&\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{kJ} / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\C u_{2} \mathrm{O}(s) & -170.7 & 92.4 \\\\\hline \mathrm{CuO}(s) & -156.1 & 42.6 \\\\\hline\end{array}\end{aligned}$$.c. Why is the standard molar entropy of \(\mathrm{Cu}_{2} \mathrm{O}(s)\) larger than that of \(\mathrm{CuO}(s) ?\)

The value of \(\Delta S_{\mathrm{rxn}}\) of the spontaneous reaction \(\mathrm{D}+\mathrm{E} \rightarrow \mathrm{F}\) is \(72.0 \mathrm{J} / \mathrm{K} .\) What is the minimum value of the entropy change in the reaction's surroundings?

Imagine you have four identical chairs to arrange on four steps leading up to a stage, one chair on each step. The chairs have numbers on their backs: \(1,2,3,\) and \(4 .\) How many different micro states for the chairs are possible? (When viewed from the front, all the micro states look the same. When viewed from the back, you can identify the different micro states because you can distinguish the chairs by their numbers.)

Which of the following combinations of entropy changes for a process are mathematically possible? a. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}>0\) b. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}<0, \Delta S_{\text {univ }}>0\) c. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0\)
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