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With its components in their standard states, a certain reaction is spontaneous only at high T. What do you know about the signs ofrole="math" localid="1663368103423" Δ±áoandΔ³§o? Describe a process for which this is true.

Short Answer

Expert verified

Both, Δ±árxn>0and Δ³§sys>0. The entropy of the surroundings is negative: Δ³§surr<0.

An example of such a process – is the evaporation of water or melting of metal.

Step by step solution

01

Concept Introduction.

Entropy is a measure of a system's unpredictability or disorder in general.

Entropy is a thermodynamic property that describes how a system behaves in terms of temperature, pressure, entropy, and heat capacity.

02

Signs of ΔHo and ΔSo.

In this case, Δ±árxno>0- the reaction is endothermic (heat is absorbed from the surroundings). Since we remove the heat from the surroundings, theΔ³§surr<0as the particles have less energy and move less freely, decreasing the surroundings disorder (entropy).

As the heat is consumed, the entropy of the system increases:Δ³§sys>0. The entropy of the system is positive and Temperature too (in Kelvin, the temperature scale is positive).

The negative Gibb's free energy change corresponds to the spontaneous reaction –

Δ³Ò=Δ±á-T·Δ³§sys<0

So, to make the Δ³Ò<0, the Δ±á<<T·Δ³§sys.

At high temperatures, this condition is satisfied –

Δ³Ò=Δ±á(>0)-Thigh·Δ³§sys(>0)→Δ³Ò<<0

03

Example of the process.

An example of such a process can be the evaporation of water and the melting of metal. The evaporation occurs only when the temperature is high enough to allow the water molecules to break out from the bulk and surface, connected via an intermolecularbond. Similarly, the metallic lattice corresponds to metal atoms tightly attached to each other - so only at a really high temperature, the metal lattice can be broken (for example, gold melting).

Therefore, both entropy and heat are zero. An example of the process is the evaporation of water.

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Most popular questions from this chapter

(a) Is an endothermic reaction more likely to be spontaneous at higher temperatures or lower temperatures? Explain.

(b) The change depicted below occurs at constant pressure. Explain your answers to each of the following:

(1) What is the sign of Δ±á?

(2) What is the sign of Δ³§?

(3) What is the sign of Δ³§surr?

(4) How does the sign ofΔ³Òvary with temperature?

Is each statement true or false? If false, correct it.

(a) All spontaneous reactions occur quickly.

(b) The reverse of a spontaneous reaction is nonspontaneous.

(c) All spontaneous processes release heat.

(d) The boiling of water at 100°Cand 1 atm is spontaneous.

(e) If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases.

(f) The energy of the universe is constant; the entropy of the universe decreases toward a minimum.

(g) All systems disperse their energy spontaneously.

(h) BothΔSsysandrole="math" localid="1663321957929" ΔSsurrequal zero at equilibrium.

Use Δ±á°and Δ³§Â°values to find the temperature at which these sulfur allotropes reach equilibrium at 1atm:

S(rhombic)⇌S(monoclinic)

When heated, the DNA double helix separates into two random-coil single strands. When cooled, the random coils reform the double helix: double helix 2 random coils.

(a) What is the sign of∆sfor the forward process? Why?

(b) Energy must be added to overcome H bonds and dispersion forces between the strands. What is the sign of∆Gfor the forward process whenTΔ³§is smaller thanrole="math" localid="1663303287852" ∆H?

(c) Write an expression that shows T in terms of∆Hand∆swhen the reaction is at equilibrium. (This temperature is called the melting temperature of the nucleic acid.)

To prepare nuclear fuel, U3O8 ("yellow cake") is converted to UO2(NO3)2, which is then converted to UO3 and finally UO2.The fuel is enriched (the proportion of the 235U is increased) by a two-step conversion of UO2 into UF6, a volatile solid, followed by a gaseous-diffusion separation of the 235Uand238Uisotopes:

UO2(s)+4HF(g)→UF4(s)+2H2O(g)UF4(s)+F2(g)→UF6(s)

Calculate Δ³Ò° for the overall process at 85°C.

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