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Chapter 19: Problem 38

Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in \(H,\) we can know absolute values of $S .(\mathbf{b})\( If you heat a gas such as \)\mathrm{CO}_{2}$, you will increase its degrees of translational, rotational and vibrational motions. (c) \(\mathrm{CO}_{2}(g)\) and \(\mathrm{Ar}(g)\) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

Short Answer

Expert verified
(a) True - We can know the absolute values of entropy due to the reference point provided by the third law of thermodynamics. (b) True - Heating a gas like CO2 increases its degrees of translational, rotational, and vibrational motions. (c) False - CO2(g) and Ar(g) have different numbers of microstates at a given temperature due to their differing molecular complexities.

Step by step solution

01

Statement (a) Evaluation

In this statement, the claim is that unlike enthalpy, we can know the absolute values of entropy. Enthalpy (H) is a state function, and we can only measure the change in enthalpy between two states (∆H). On the other hand, entropy (S) is also a state function, but we can determine its absolute value because we have a reference point, the entropy of a perfect crystal at 0 K, which is defined as zero according to the third law of thermodynamics. Therefore, this statement is \(True\).
02

Statement (b) Evaluation

This statement asserts that heating a gas like CO2 will increase its degrees of translational, rotational, and vibrational motions. As a gas molecule is heated, its energy increases leading to an increase in its different types of motion, which include translational, rotational, and vibrational motions. Therefore, this statement is \(True\).
03

Statement (c) Evaluation

The claim in this statement is that CO2(g) and Ar(g) have nearly the same molar mass, and at a given temperature, they will have the same number of microstates. While it may be true that CO2(g) and Ar(g) have nearly the same molar mass, the number of microstates depends not only on the molar mass but also on the molecule's complexity. Since CO2 is a more complex molecule compared to the noble gas Ar due to its additional vibrational and rotational modes, the number of microstates at a given temperature will be different between them. Therefore, this statement is \(False\).

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Most popular questions from this chapter

(a) Which of the thermodynamic quantities \(p, H, q, w,\) and \(G\) are state functions? (b) Consider a system going from state 1 to state 2 in a reversible and an irreversible way. Compare \(q_{\text {rev }}\) and \(q_{\text {irtev }}\) (c) Consider a system going from state 1 to state 2 in a reversible and an irreversible way. Compare \(w_{\text {rev }}\) and \(w_{\text {trev }}\). (d) For a reversible isothermal process, write an expression for \(\Delta H\) and an expression for \(\Delta G\) in terms of \(q, w\) and \(T, p\) and \(\Delta V\).

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

(a) For each of the following reactions, predict the sign of \(\Delta H^{*}\) and \(\Delta S^{\circ}\) without doing any calculations. (b) Based on your general chemical knowledge, predict which of these reactions will have \(K>1\) at \(25^{\circ} \mathrm{C} .(\mathbf{c})\) In each case, indicate whether \(K\) should increase or decrease with increasing temperature. (i) \(2 \mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{FeO}(s)\) (ii) \(\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}(g)\) (iii) $\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$ (iv) $\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{CaO}(s) \rightleftharpoons \mathrm{CaCO}_{3}(s)$

Trouton's rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about $88 \mathrm{~J} / \mathrm{mol}-\mathrm{K} .($ a) Estimate the normal boiling point of bromine, \(\mathrm{Br}_{2}\), by determining \(\Delta H_{\text {vap }}^{\circ}\) for \(\mathrm{Br}_{2}\) using data from Appendix \(C\). Assume that $\Delta H_{\text {vap }}^{\circ}$ remains constant with temperature and that Trouton's rule holds. (b) Look up the normal boiling point of \(\mathrm{Br}_{2}\) in a chemistry handbook or at the WebElements website (www.webelements.com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to $25^{\circ} \mathrm{C} .$ (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).
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