Question

Write the equilibrium expression for ${\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}\mathbf{+}\mathbf{2}{\mathbf{Cl}}^{\mathbf{-}}\mathbf{\to }{\mathbf{Cacl}}_{\mathbf{2}}\left(\mathrm{aq}\right)$with activity coefficients.

Short answer

The equilibrium expression is $K=\frac{A_{CaC}}{{\lambda }_{C{a}^{2+}}{X}_{C^{-}}^2}=\frac{\left[CaC{l}_2\right]}{\left[C{a}^{2+}\right]{\gamma }_{C{a}^2}+{\left[C{l}^{-}\right]}^2{\gamma }_{C{l}^{-}}}$.

Step-by-step solution

Concept used.

Equilibrium expression:

The equilibrium equation determines the ratio of products to reactants.

$$\begin{gathered} \mathbf{aA}\mathbf{+}\mathbf{bB}\mathbf{\to }\mathbf{cC}\mathbf{+}\mathbf{dD} \\ {\mathit{A}}_{\mathbf{A}}^{\mathbf{2}}\mathbf{}{\mathit{A}}_{\mathbf{B}}^{\mathbf{D}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\left|A\right|}^{\mathbf{2}}\mathbf{}\mathbf{}{\mathit{\gamma }}_{\mathbf{A}}^{\mathbf{2}}\mathbf{}{\left|B\right|}^{\mathbf{0}}\mathbf{}{\mathit{\gamma }}_{\mathbf{B}}^{\mathbf{b}} \end{gathered}$$

where,

-activity of species

[] -concentration of species

$\mathit{\gamma }$- activity coefficient of species.

Step 2: Calculate the ionic strength of 1mMCaCl2.

Given reaction,

${\mathrm{Ca}}^{2+}+2{\mathrm{Cl}}^{-}\to {\mathrm{Cacl}}_2\left(\mathrm{aq}\right)$

The equilibrium expression by the activity of all species

$$\begin{gathered} K=\frac{A_{COC}}{A_{C2}2+A_a^2} \\ =\frac{\left|CaC{h}_2\right|{\gamma }_{CaC}}{\left[C{a}^{2+}\right]{\gamma }_{C{a}^{2}2}+Cr|h_C^2} \end{gathered}$$

The equilibrium expression for the given reaction was calculated using the species' activity and concentration.