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What is the equilibrium constant for the $\ce{Co(H2O)_6^{2+}(aq) + 4 Cl-(aq) <=> CoCl_4^{2-}(aq) + 6H2O(l)}$?

I've looked at various sources but none seem to yield the actual equilibrium constant.

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Thermodynamic Properties and Ionic Equilibria of Cobalt Chloride Solution at $\pu{298 K}$ was estimated by a Korean group in literature (Ref.1). The abstract states that:

We developed a chemical model to analyze ionic equilibria in a cobalt chloride solution at $\pu{298 K}$. The chemical model consisted of chemical equilibria, mass and charge balance equations. The activity coefficients of solutes and water activity were calculated with Bromley equation. Values of the equilibrium constants for the formation of cobalt chloride complexes at zero ionic strength and of the interaction parameters were estimated by applying Bromley equation to the reported equilibrium constants at different ionic strength. The effect of $\ce{CoCl2}$ and $\ce{HCl}$ concentrations on the distribution of cobalt species was obtained. The predicted pH values for $\ce{CoCl2-HCl-NaOH-H2O}$ system agreed well with those measured at $\pu{298 K}$.

Thermodynamic equilibrium constant ($K$) for the formation of $\ce{CoCl4^2-}$ complex for the reaction $\ce{Co^2+ + 4Cl- <=> CoCl4^2-}$ was reported in $\log$ scale where $\log (K)$ is reported as $-9.06$ (or $K = 8.71 \times 10^{-10}$). Although this is not the exact answer for OP's question, I hope OP can find insight into his/her question.

Furthermore, cobalt ion has a strong tendency to form various complexes with chloride ion such as $\ce{CoCl^+}$ and $\ce{CoCl3^-}$. $\log (K)$ for them are also reported as $0.22$ and $-3.02$, respectively (Ref.1). The $\log(K)$ for the equilibrium of neutral species $\ce{CoCl2}$ was reported elsewhere as $-3.95$ (Ref.2).

Reference:

  1. M.-S. Lee, Y.-J. Oh, “Estimation of Thermodynamic Properties and Ionic Equilibria of Cobalt Chloride Solution at $\pu{298 K}$,” Materials Transactions 2004, 45(4), 1317-1321 (https://www.jim.or.jp/journal/e/45/04/1317.html).
  2. J. Bjerrum, G. Schwarzenbach, L.G. Sillén, In Stability Constants of Metal-ion Complexes, Part II: Inorganic ligands; The Chemical Society: London, United Kingdom, 1957, p. 97.
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You can't find the equilibrium constant because that's entirely dependent on the concentration.

To find the equilibrium constant, you take the concentration of the products to the power of their coefficients (so concentration of cobalt (II) chloride to the power 1 multiplied by the concentration of water to the power 6), divided by the concentration of the reactants to the power of their coefficients (same concept for the denominator).

There's no one set equilibrium constant for a reaction.

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    $\begingroup$ Equilibrium constants do not depend on concentration. $\endgroup$ – orthocresol Mar 14 at 20:44

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