The values of ΔGf^∘ for the hydrogen halides become less...

The values of $\Delta G_{f}^{\circ}$ for the hydrogen halides become less negative with increasing atomic number. The $\Delta G_{\mathrm{f}}^{\circ}$ of HI is slightly positive. On the other hand, the trend in $\Delta S_{\mathrm{f}}^{\circ}$ is to become more positive with increasing atomic number. Explain.

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic function defined by the equation ?G = ?H - T?S, where ?H is the enthalpy change and ?S is the entropy change. It determines whether a reaction is thermodynamically favorable: negative values indicate spontaneous processes. The balance between bond energies (enthalpy) and disorder (entropy) determines the overall free energy change in the formation of compounds.

Enthalpy Contribution

The enthalpy of formation (?H) largely depends on the strengths of the chemical bonds being formed. Stronger bonds lead to more exothermic (more negative) enthalpy changes, while weaker bonds result in less exothermic changes. In trends where atomic size increases, bond strengths typically decrease, leading to less negative ?H values, which in turn affects the computed ?G.

Entropy Contribution

Entropy of formation (?S) reflects the change in disorder or randomness when reactants form products. In forming compounds, increased atomic or molecular freedom—such as additional vibrational, rotational, or translational modes—can contribute to higher (more positive) entropy values. This increased disorder can help drive the formation reaction even when the enthalpic contribution is less favorable.

Atomic Size Effects

As atomic size increases, several interrelated factors come into play. Larger atoms are generally less effective in orbital overlap, which leads to weaker bonds and a less exothermic (less negative) enthalpy of formation. At the same time, these larger atoms exhibit more vibrational and rotational modes, resulting in a higher (more positive) entropy contribution. The interplay of these factors explains the observed trends in both ?H and ?S, ultimately influencing the Gibbs free energy of formation.

Transcript

00:01 In this question, we've been given some trends and we've been asked to explain them.

00:05 And when we look at this in terms of, we've been given the standard gibbs energy of formation and we've been told that it becomes less negative, less negative with increasing atomic number.

00:22 In other words, less negative as we go down the crop.

00:25 And when we are looking at this, the give standard the enthalpy of formation, it becomes less negative because the bond length gets stronger.

00:34 This is one property that occurs when we are going down the group for the hydration halides.

00:40 Say this is hydration highlights.

00:42 When we go down the group, the bond length between the hydrogen and the halide is increasing.

00:51 As a result, it becomes less stronger.

00:57 As a result, we are reducing the stability of that compound.

01:02 So there is less chemical energy that is stored within that the hydrogen bonds.

01:08 So as a result, this gives energy of formation, the standard gives formation becomes less negative as we go down the group or as we increase the atomic number.

01:20 Then in terms of the standard entropy, the standard entropy of formation, what is important to note about the entropy is this is the measure of the disorderness, of a system.

01:34 And when we are talking about entropy in terms of thermal energy or thermodynamics, we are saying this is the amount of energy or thermal energy that is actually available to do useful work.

01:46 So in general terms, this is just a measure of the discordance of a system.

01:52 So this becomes more positive as the atomic number increases, that is, becomes more positive as we increase the atomic number increases.

02:02 Make number.

02:03 In other ways it becomes more positive as we go down the group.

02:08 Go down the group...

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