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6.5: Dissociative Ligand Substitution

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    300459
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    The second mechanism for ligand substitution is the dissociative mechanism. In the slow step with positive entropy of activation, the departing ligand leaves, generating a coordinatively unsaturated intermediate. The incoming ligand then enters the coordination sphere of the metal to generate the product. The reverse of the first step, re-coordination of the departing ligand (rate constant k–1), is often competitive with dissociation.

    A general scheme for dissociative ligand substitution.

    A general scheme for dissociative ligand substitution. There’s more to the intermediate than meets the eye!

    Let’s begin with the general situation in which \(k_1\) and \(k_{–1}\) are similar in magnitude. Since \(k_1\) is rate limiting, \(k_2\) is assumed to be much larger than \(k_1\) and \(k_{–1}\). Most importantly, we need to assume that variation in the concentration of the unsaturated intermediate is essentially zero. This is called the steady state approximation, and it allows us to set up an equation that relates reaction rate to observable concentrations Hold onto that for a second; first, we can use step 2 to establish a preliminary rate expression.

    \[\text{rate} = k_2[L_nM–◊][Li] \tag{1}\]

    Of course, the unsaturated complex is present in very small concentration and is unmeasurable, so this equation doesn’t help us much. We need to remove the concentration of the unmeasurable intermediate from (1), and the steady state approximation helps us do this. We can express variation in the concentration of the unsaturated intermediate as (processes that make it) minus (processes that destroy it), multiplying by an arbitrary time length to make the units work out. All of that equals zero, according to the steady state approximation. Since Δt must not be zero, the other factor, the collection of terms, must equal zero.

    \[ Δ[LnM–◊] = 0 = (k1[LnM–L^d] – k–1[LnM–◊][L^d] – k_2[LnM–◊][Li])Δt \tag{2}\]

    \[0 = k_1[LnM–Ld] – k_{-1}[LnM–◊][Ld] – k_2[LnM–◊][Li] \tag{3}\]

    Rearranging to solve for [LnM–◊], we arrive at the following.

    \[ [LnM–◊] = k_1 \dfrac{[LnM–L_d]}{(k_{-1}[L_d] + k_2[Li]} \tag{4}\]

    Finally, substituting into equation (1) we reach a verifiable rate equation.

    \[ \text{rate} = k_2k_1 \dfrac{[LnM–Ld][Li]}{(k_{-1}[L_d] + k_2[Li]} \tag{5}\]

    When \(k_{–1}\) is negligibly small, (5) reduces to the familiar equation (6), typical of dissociative reactions like SN1.

    \[\text{rate} = k_1[LnM–L_d] \tag{6}\]

    Unlike the associative rate law, this rate does not depend on the concentration of incoming ligand. For reactions that are better described by (5), we can drown the reaction in incoming ligand to make \(k_2[Li]\) far greater than \(k_{-1}[Ld]\), essentially forcing the reaction to fit equation (6).

    In general, introducing structural features that either stabilize the unsaturated intermediate or destabilize the starting complex can encourage dissociative substitution. Both of these strategies lower the activation barrier for the reaction. Other, quirky ways to encourage dissociation include photochemical methods, oxidation/reduction, and ligand abstraction.

    Contributors and Attributions


    This page titled 6.5: Dissociative Ligand Substitution is shared under a not declared license and was authored, remixed, and/or curated by Michael Evans.