(d) For a reversible isothermal process, write an expression for ΔE in terms of q and w and an expression for ΔS in terms of q and T.

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Identify the first law of thermodynamics, which states that the change in internal energy of a system (\(\Delta E\)) is equal to the heat added to the system (q) minus the work done by the system (w). Mathematically, it is expressed as \(\Delta E = q - w\).

Recognize that for a reversible isothermal process, the temperature (T) remains constant. In such processes, any heat added to the system is used to perform work or increase the internal energy.

Write the expression for \(\Delta E\) in terms of q and w for a reversible isothermal process as \(\Delta E = q - w\).

Understand the definition of entropy change (\(\Delta S\)), which is the heat transferred reversibly divided by the temperature at which the transfer occurs. For a reversible process, this is given by \(\Delta S = \frac{q_{\text{rev}}}{T}\).

Write the expression for \(\Delta S\) in terms of q and T for a reversible isothermal process as \(\Delta S = \frac{q}{T}\), where q is the heat involved in the reversible process.

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Key Concepts

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

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In the context of a reversible isothermal process, the change in internal energy (ΔE) is equal to the heat added to the system (q) minus the work done by the system (w). This relationship is crucial for understanding how energy transfers occur in thermodynamic processes.

Isothermal Process

An isothermal process is one that occurs at a constant temperature. During such a process, the internal energy of an ideal gas remains constant, as it is a function of temperature alone. This characteristic allows for the simplification of the relationship between heat (q), work (w), and internal energy (ΔE) in the context of thermodynamic equations.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. For a reversible isothermal process, the change in entropy can be expressed as ΔS = q/T, where q is the heat exchanged and T is the absolute temperature. This relationship highlights how energy dispersal contributes to the overall disorder of a system, which is a fundamental concept in thermodynamics.

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Textbook Question

The K_b for methylamine (CH₃NH₂) at 25 °C is given in Appendix D. (d) What is the value of ΔG when [H⁺] = 6.7 × 10^-9 M, [CH₃NH₃⁺] = 2.4 × 10^-3 M, and [CH₃NH₂] = 0.098 M?

Textbook Question

(a) Which of the thermodynamic quantities T, E, q, w, and S are state functions? (b) Which depend on the path taken from one state to another?

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Textbook Question

The crystalline hydrate Cd(NO₃)₂⋅4 H₂O(s) loses water when placed in a large, closed, dry vessel at room temperature: Cd(NO₃)₂⋅4 H₂O(s) → Cd(NO₃)₂(s) + 4 H₂O(g) This process is spontaneous and ΔH° is positive at room temperature.

(a) What is the sign of ΔS° at room temperature?

Textbook Question

(b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does ΔS° change for this reaction at room temperature?