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Chapter 12: Problem 82

In terms of total energy change, when is entropy an important factor in determining whether or not a solute dissolves in a solvent? When is it not an important factor?

Short Answer

Expert verified
Entropy is an important factor in determining whether a solute dissolves in a solvent when the signs of ΔH and TΔS are opposite, as these two terms are competing in the process. If ΔH > 0 (endothermic) but TΔS > ΔH, then ΔG will be negative and the process will be spontaneous. Entropy is not a significant factor when the signs of ΔH and TΔS are the same, as the change in enthalpy (ΔH) will dominate the process.

Step by step solution

01

Understanding Entropy

Entropy is a measure of randomness or disorder in a system. It is an important concept in thermodynamics, which is the study of heat and its relation to work and energy. When a solute dissolves in a solvent, the total entropy of the system can either increase or decrease. In general, if the process leads to an increase in total entropy, it is more likely to be spontaneous.
02

Gibbs Free Energy

To determine whether a solute will dissolve in a solvent, we can use the Gibbs Free Energy equation: ΔG = ΔH - TΔS where ΔG is the change in Gibbs Free Energy, ΔH is the change in enthalpy (heat energy), T is the temperature in Kelvin, and ΔS is the change in entropy. For a process to be spontaneous, ΔG must be negative. Thus, entropy becomes a significant factor when the enthalpy term (ΔH) and the temperature times entropy term (TΔS) are opposite in sign, meaning one is positive and the other is negative.
03

When Entropy is Important

Entropy is an important factor in determining whether a solute dissolves in a solvent when the signs of ΔH and TΔS are opposite, which means these two terms are competing in the process. For example, if ΔH > 0 (meaning the process is endothermic and requires the input of heat energy) but TΔS > ΔH (meaning that the increase in entropy at a given temperature is enough to make up for the endothermic change in enthalpy), then the overall ΔG will be negative and the process will be spontaneous.
04

When Entropy is Not Important

Entropy is not a significant factor in the dissolution process when the signs of ΔH and TΔS are the same - meaning both the terms are either positive or negative. In such cases, the change in enthalpy (ΔH) will dominate the process. 1. If both ΔH and TΔS are positive and ΔH > TΔS, the overall ΔG will be positive and the process will be nonspontaneous. In this case, the increase in entropy is not enough to overcome the endothermic change in enthalpy. 2. If both ΔH and TΔS are negative and ΔH < TΔS, the overall ΔG will be negative and the process will be spontaneous. In this case, the decrease in entropy has a lesser effect on the exothermic change in enthalpy.

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Most popular questions from this chapter

A 25.00-mL sample of a hydrochloric acid solution of unknown concentration is titrated with \(0.1004 \mathrm{M}\) \(\mathrm{NaOH}\). However, before the acid is titrated, \(27.65\) mL of water is added to it. The phenolphthalein indicator turns red after \(28.70 \mathrm{~mL}\) of \(\mathrm{NaOH}\) has been added. What is the concentration of the \(25.00-\) \(\mathrm{mL}\) sample of hydrochloric acid?

When \(5.00 \mathrm{~g}\) of a solute is dissolved in sufficient solvent to produce \(100.0 \mathrm{~mL}\) of solution, (a) What is the percent by mass/volume concentration of the solute? (b) What additional information do you need to calculate the percent by mass concentration of the solute, and how would you calculate that concentration once you had the missing information?

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