Question

Show by calculation whether the reaction \(2 \mathrm{HOCl}(\mathrm{aq}) \longrightarrow \mathrm{HClO}_{2}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\) will go essentially to completion as written for standardstate conditions.

Short answer

No, the reaction \(2 HOCl(aq) \rightarrow HClO_{2}(aq) + H^{+}(aq) + Cl^{-}(aq)\) does not go essentially to completion as written for standard state conditions.

Step-by-step solution

Calculate the standard Gibb's free energy

First, we can use the standard free energy of formation of all species involved in the reaction. We can look up these values in a standard table. The standard Gibbs free energy for a reaction can be calculated with the formula: \(\Delta G° = \Delta G_{products}° - \Delta G_{reactants}°\). From a standard table we obtain that the formation of \(HOCl(aq)\), \(HClO_{2}(aq)\), \(H^{+}(aq)\) and \(Cl^{-}(aq)\) is respectively: -137.3 kJ/mol, -121.9 kJ/mol, 0 kJ/mol and -131.2 kJ/mol. Applying these values into the formula, we get \(\Delta G° = [(-121.9) + 0 + (-131.2)] - [2*(-137.3)] = 58.8 kJ/mol\)

Interpretation of the result

Since the Gibbs free energy change \(\Delta G°\) is greater than 0, it means the reaction is not spontaneous. For a reaction to go to completion, it must be spontaneous, which implies \(\Delta G°\) should be negative under standard state conditions.

Conclusion

The reaction \(2 HOCl(aq) \rightarrow HClO_{2}(aq) + H^{+}(aq) + Cl^{-}(aq)\) does not go to completion under standard state conditions because it has a nonspontaneous Gibbs free energy change of +58.8 kJ/mol. A negative Gibbs free energy change would suggest otherwise.

Key concepts

Spontaneous Reaction

A spontaneous reaction is a chemical reaction that occurs naturally without needing any external energy input. It happens when the system's Gibbs free energy decreases as the reaction proceeds. In simple terms, the system moves toward a more stable, lower-energy state on its own.
For a reaction to be spontaneous under given conditions, the change in Gibbs free energy, denoted as \( \Delta G \), must be negative:\[ \Delta G < 0 \]
When \( \Delta G \) is negative, it indicates that the products of the reaction have lower energy compared to the reactants, making the process favorable. It's like a ball rolling downhill, naturally moving in the direction of least resistance.
Spontaneous reactions are more likely to occur:

• When heat is released (exothermic reaction).
• When the disorder or randomness of the system increases (positive entropy change).

Understanding if a reaction is spontaneous or not is crucial in predicting whether it will occur in the direction written under standard state conditions.

Standard State Conditions

Standard state conditions are reference points used for calculating enthalpies, entropies, and free energies. They simplify analyzing reactions because they provide a common baseline. Here’s what they typically entail:

• For gases, a partial pressure of 1 atm.
• For pure substances in liquid or solid form, the substance itself under its stable form at 1 atm and a specified temperature (commonly 298 K or 25°C).
• For solutions, a concentration of 1 M.

Reactions, like the conversion of \(2 \mathrm{HOCl}(\mathrm{aq}) \rightarrow \mathrm{HClO}_{2}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\), can be analyzed under these conditions using standard Gibbs free energies. Comparing \( \Delta G° \) under standard state conditions helps us understand whether a reaction tends to proceed spontaneously when all species have their standard concentrations and ambient conditions. However, changes in concentration, pressure, or temperature can shift the reaction towards spontaneity or away from it.

Nonspontaneous Reaction

A nonspontaneous reaction is one that does not occur on its own under given conditions. It requires outside intervention to proceed, often in the form of energy input or catalysts.
In terms of Gibbs free energy, a nonspontaneous reaction is indicated when:\[ \Delta G > 0 \]
This means the energy of the products is higher than that of the reactants, akin to trying to push a ball uphill against gravity.
In the given reaction \(2 \mathrm{HOCl}(\mathrm{aq}) \rightarrow \mathrm{HClO}_{2}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\), the calculated \( \Delta G° \) is +58.8 kJ/mol under standard conditions, signifying that the reaction does not naturally proceed to completion by itself. Instead, external energy would be needed to drive this process.
Understanding nonspontaneous reactions is crucial for figuring out when to apply an external energy source or identify a suitable catalyst to make the reaction viable in practical applications.