Hess's law illustrates that the enthalpy change of a reaction, denoted as ΔH, is directly proportional to the coefficients in a balanced chemical equation. This means that if the coefficients are multiplied by a factor, ΔH is also multiplied by that same factor. Conversely, if the reaction is reversed, the sign of ΔH changes accordingly.

In contrast, the relationship between the equilibrium constant (K) and the coefficients of a reaction is exponential. For example, consider the balanced chemical equation:

2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g)

With an initial equilibrium constant value of K = 71.3, we can explore how changes to the reaction affect K.

1. **Multiplying the Reaction:** When the reaction is multiplied by a factor, K is raised to that same power. For instance, if we multiply the reaction by 3, the new equation becomes:

6 SO₂(g) + 3 O₂(g) ⇌ 6 SO₃(g)

In this case, the new equilibrium constant is K³ = 71.3³ ≈ 362467.097.

2. **Reversing the Reaction:** If the reaction is reversed, the new equilibrium constant becomes the inverse of the original K. For the reversed reaction:

2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g)

The new equilibrium constant is K^-1 = 71.3^-1 ≈ 0.0140.

3. **Dividing the Reaction:** When the reaction is divided by a factor, K is raised to the reciprocal of that factor. For example, if we divide the reaction by 2, the new equation becomes:

SO₂(g) + 0.5 O₂(g) ⇌ SO₃(g)

Here, the new equilibrium constant is K^1/2 = √71.3 ≈ 8.44.

In summary, the changes made to a chemical reaction—whether multiplying, reversing, or dividing—result in exponential changes to the equilibrium constant K. Understanding these relationships is crucial for predicting how alterations in a reaction will affect its equilibrium state.

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