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Chapter 18: Problem 51

Under what conditions does a substance have a standard entropy of zero? Can a substance ever have a negative standard entropy?

Short Answer

Expert verified
A substance has a standard entropy of zero at absolute zero temperature (0 Kelvin). As for the possibility of a negative standard entropy, it is not possible because entropy measures the disorder within a system and cannot drop below the most ordered state, which is represented by zero.

Step by step solution

01

Zero Entropy Condition

Standard entropy of a substance is zero at absolute zero temperature (0 Kelvin). This is a consequence of the Third Law of Thermodynamics, which states that the entropy of a perfectly organized crystalline substance is zero at absolute zero temperature. This is because, at 0 Kelvin, a perfect crystal has only one possible microstate and its energy is well defined, so it is completely ordered.
02

Possibility of Negative Standard Entropy

A substance cannot have a negative standard entropy. The second law of thermodynamics states that in an isolated system, entropy can only increase over time. In addition, entropy measures the number of specific ways in which a system may be arranged, often taken to be a measure of 'disorder'. The most orderly situation can be represented with a 0 value (all particles in one state), so you cannot have 'less than the most orderly state', hence negative entropy doesn't make physical sense.

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Most popular questions from this chapter

In the Mond process for the purification of nickel, carbon monoxide is reacted with heated nickel to produce \(\mathrm{Ni}(\mathrm{CO})_{4},\) which is a gas and can therefore be separated from solid impurities: $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ Given that the standard free energies of formation of \(\mathrm{CO}(g)\) and \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) are \(-137.3 \mathrm{~kJ} / \mathrm{mol}\) and \(-587.4 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the equilibrium constant of the reaction at \(80^{\circ} \mathrm{C}\). Assume that \(\Delta G_{f}^{\circ}\) is temperature independent.

Arrange the following substances ( 1 mole each) in order of increasing entropy at \(25^{\circ} \mathrm{C}:\) (a) \(\mathrm{Ne}(g)\), (b) \(\mathrm{SO}_{2}(g),\) (c) \(\mathrm{Na}(s)\) (d) \(\mathrm{NaCl}(s)\) (e) \(\mathrm{H}_{2}(g)\). Give the reasons for your arrangement.

Describe two ways that you could measure \(\Delta G^{\circ}\) of a reaction.

Large quantities of hydrogen are needed for the synthesis of ammonia. One preparation of hydrogen involves the reaction between carbon monoxide and steam at \(300^{\circ} \mathrm{C}\) in the presence of a copper-zinc catalyst: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$.

Consider the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ Given that \(\Delta G^{\circ}\) for the reaction at \(25^{\circ} \mathrm{C}\) is 173.4 \(\mathrm{kJ} / \mathrm{mol}\), (a) calculate the standard free energy of formation of \(\mathrm{NO},\) and (b) calculate \(K_{P}\) of the reaction. (c) One of the starting substances in smog formation is NO. Assuming that the temperature in a running automobile engine is \(1100^{\circ} \mathrm{C},\) estimate \(K_{P}\) for the above reaction. (d) As farmers know, lightning helps to produce a better crop. Why?
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