Question

With its components in their standard states, a certain reaction is spontaneous only at high $\mathbf{T}$. What do you know about the signs ofrole="math" localid="1663368103423" ${\mathbf{\Delta H}}^{\mathbf{o}}$and${\mathbf{\Delta S}}^{\mathbf{o}}$? Describe a process for which this is true.

Short answer

Both, ${\mathrm{\Delta H}}_{\mathrm{rxn}}>0$and ${\mathrm{\Delta S}}_{\mathrm{sys}}>0$. The entropy of the surroundings is negative: ${\mathrm{\Delta S}}_{\mathrm{surr}}<0$.

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

Step-by-step solution

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.

Signs of ΔHo and ΔSo.

In this case, ${\mathrm{\Delta H}}_{\mathrm{rxn}}^{\mathrm{o}}>0$- the reaction is endothermic (heat is absorbed from the surroundings). Since we remove the heat from the surroundings, the${\mathrm{\Delta S}}_{\mathrm{surr}}<0$as 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:${\mathrm{\Delta S}}_{\mathrm{sys}}>0$. 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 –

$\mathrm{\Delta G}=\mathrm{\Delta H}-\mathrm{T}·{\mathrm{\Delta S}}_{\mathrm{sys}}<0$

So, to make the $\mathrm{\Delta G}<0$, the $\mathrm{\Delta H}<<\mathrm{T}·{\mathrm{\Delta S}}_{\mathrm{sys}}$.

At high temperatures, this condition is satisfied –

$\mathrm{\Delta G}=\mathrm{\Delta H}(>0)-{\mathrm{T}}_{\mathrm{high}}·{\mathrm{\Delta S}}_{\mathrm{sys}}(>0)\to \mathrm{\Delta G}<<0$

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.