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Chapter 12: Problem 48

What are the signs of \(\Delta S, \Delta H,\) and \(\Delta G\) for the formation of dew on a cool night?

Short Answer

Expert verified
Answer: The signs of the changes are as follows: 鈭哠 is negative, 鈭咹 is negative, and 鈭咷 is negative.

Step by step solution

01

Determine the change in entropy (鈭哠) for the formation of dew

Entropy is a measure of the disorder in a system. When water vapor molecules in the air condense to form dew on a surface, the disorder of the system decreases. The molecules go from the vapor phase, which has higher entropy, to the liquid phase, which has lower entropy. Therefore, the change in entropy (鈭哠) for the formation of dew is negative.
02

Determine the change in enthalpy (鈭咹) for the formation of dew

Enthalpy is a measure of the total energy in a system. When water vapor condenses to form dew, it releases heat energy into the environment. This is because the vapor phase has higher energy content than the liquid phase. Hence, the change in enthalpy (鈭咹) for the formation of dew is negative since heat is released.
03

Determine the change in Gibbs free energy (鈭咷) for the formation of dew

Gibbs free energy is a measure of the maximum amount of work that can be extracted from a thermodynamic system. The relationship between Gibbs free energy (鈭咷), enthalpy (鈭咹), and entropy (鈭哠) is given by the equation: 鈭咷 = 鈭咹 - T鈭哠 where T is the temperature in Kelvin. Since we previously determined that both 鈭咹 and 鈭哠 are negative for the formation of dew, the term T鈭哠 is positive. For a process to be spontaneous, 鈭咷 must be negative. In this case, the negative 鈭咹 outweighs the positive T鈭哠 term, so the overall 鈭咷 is also negative. In conclusion, the signs of 鈭哠, 鈭咹, and 鈭咷 for the formation of dew on a cool night are: 鈭哠: negative 鈭咹: negative 鈭咷: negative

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Most popular questions from this chapter

Chlorofluorocarbons (CFCs) are no longer used as refrigerants because they catalyze the decomposition of stratospheric ozone. Trichlorofluoromethane (CC1 \(_{3} \mathrm{F}\) ) boils at \(23.8^{\circ} \mathrm{C}\) and its molar heat of vaporization is \(24.8 \mathrm{kJ} / \mathrm{mol}\) What is the molar entropy of vaporization of \(\mathrm{CCl}_{3} \mathrm{F}(\ell) ?\)

Above what temperature does nitrogen monoxide form from nitrogen and oxygen? $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)$$ Assume that the values of \(\Delta H_{\mathrm{rxn}}^{\circ}\) and \(\Delta S_{\mathrm{rxn}}^{\circ}\) do not change appreciably with temperature.

Lime Enormous amounts of lime (CaO) are used in steel industry blast furnaces to remove impurities from iron. Lime is made by heating limestone and other solid forms of \(\mathrm{CaCO}_{3}(s) .\) Why is the standard molar entropy of \(\mathrm{CaCO}_{3}(s)\) higher than that of \(\mathrm{CaO}(s)\) ? At what temperature is the pressure of \(\mathrm{CO}_{2}(g)\) over \(\mathrm{CaCO}_{3}(s)\) equal to 1.0 atm?$$\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{k} J / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\C a C O_{3}(s) & -1207 & 93 \\\\\hline \mathrm{CaO}(s) & -636 & 40 \\\\\hline \mathrm{CO}_{2}(g) & -394 & 214 \\\\\hline\end{array}$$

Adding sidewalk deicer (calcium chloride) to water causes the temperature of the water to increase. If solid \(\mathrm{CaCl}_{2}\) is the system, what are the signs of \(\Delta S_{\mathrm{sys}}\) and \(\Delta S_{\mathrm{surr}} ?\)

Predict whether the entropy of the system increases or decreases for the following reaction, which describes the process used to remove hydrogen sulfide from natural gas: $$8 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow 3 \mathrm{S}_{8}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$$
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