Ch.19 - Chemical Thermodynamics

Problem 104

Chapter 19, Problem 104

In chemical kinetics, the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. Predict whether the entropy of activation for a bimolecular process is usually positive or negative.

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Understand the concept of the activated complex: In a chemical reaction, the activated complex (or transition state) is a high-energy, unstable arrangement of atoms that forms momentarily as reactants are converting into products.

Consider the nature of a bimolecular reaction: A bimolecular reaction involves two reactant molecules colliding to form the activated complex. This implies an increase in molecular order as two separate entities form a single complex.

Analyze the effect on entropy: Entropy, a measure of disorder or randomness in a system, tends to decrease when the system becomes more ordered. Since the bimolecular process involves the coming together of two molecules to form one complex, the system becomes more ordered.

Predict the sign of the entropy of activation: Given that the system's disorder decreases as the reactants form a more ordered activated complex, the entropy change (entropy of activation) for this process is expected to be negative.

Generalize the concept: For most bimolecular reactions, where two reactant molecules combine to form a single activated complex, the entropy of activation is typically negative, reflecting the decrease in system disorder.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy of Activation

The entropy of activation refers to the change in entropy that occurs when reactants transition to an activated complex during a chemical reaction. It reflects the degree of disorder or randomness in the system as the reactants approach the transition state. A positive entropy of activation indicates an increase in disorder, while a negative value suggests a decrease in disorder.

Bimolecular Reactions

Bimolecular reactions involve two reactant molecules colliding to form products. These reactions are characterized by their dependence on the concentration of both reactants, which influences the rate of reaction. The nature of the collision and the arrangement of molecules during the transition state play a crucial role in determining the entropy of activation.

Transition State Theory

Transition state theory posits that during a chemical reaction, reactants must pass through a high-energy transition state before forming products. This theory helps explain the energy barrier that must be overcome for a reaction to proceed. The characteristics of the transition state, including its entropy, are essential for understanding the kinetics of bimolecular processes.

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Textbook Question

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane (C₂H₆), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH₄(g) → C₂H₆(g) + H₂(g) In practice, this reaction is carried out in the presence of oxygen: 2 CH₄(g) + 1/2 O₂(g) → C₂H₆(g) + H₂O(g) (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the 'Chemistry and Life' box in Section 19.7.

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Textbook Question

The potassium-ion concentration in blood plasma is about 5.0⨉10^-3 M, whereas the concentration in muscle-cell fluid is much greater (0.15 M ). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to K⁺. (a) What is ΔG for the transfer of 1 mol of K⁺ from blood plasma to the cellular fluid at body temperature 37 °C? (b) What is the minimum amount of work that must be used to transfer this K⁺?

Most liquids follow Trouton’s rule (see Exercise 19.93), which states that the molar entropy of vaporization is approximately 88 J/mol⋅K. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton’s rule? By using data in Appendix B, check the accuracy of your conclusion.

Textbook Question

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Textbook Question

An ice cube with a mass of 20 g at -20 °C (typical freezer temperature) is dropped into a cup that holds 500 mL of hot water, initially at 83 °C. What is the final temperature in the cup? The density of liquid water is 1.00 g>mL; the specific heat capacity of ice is 2.03 J>g@C; the specific heat capacity of liquid water is 4.184 J>g@C; the enthalpy of fusion of water is 6.01 kJ>mol.

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