Question

Find$\mathit{\gamma }$for${\mathbf{Cl}}^{\mathbf{-}}$ in 0.33mM${\mathbf{CaCl}}_{\mathbf{2}}$.

Short answer

The activity coefficient value for ${\mathrm{Cl}}^{-}$in 0.33mM${\mathrm{CaCl}}_2$is 0.964.

Step-by-step solution

Concept used.

Extended Debye-Huckel equation:

The extended Debye-Huckel equation describes the link between activity coefficient and ionic strength.

$\mathit{\gamma }$-activity coefficient of ion

$\mathit{\mu }$-ionic strength of solution

$\mathit{\alpha }$-size of ion

Step 2: Calculate the value of γ.

Given information,

$0.33\mathrm{mM}{\mathrm{CaCl}}_2$

Size of ${\mathrm{Cl}}^{-}$ion is 300pm

Ionic strength calculation formula is given by

$\begin{array}{l}\mu =\frac{1}{2}\left(c_1{z}_1^2+c_2{z}_2^2+.............\right)\\ =\frac{1}{2}\sum _i{c}_i{z}_i^2\end{array}$

where,

$c_i$-concentration of the$i^{th}$ species and$z_i$ is its charge.

Calculate the ionic strength of the solution by substituting the numbers into the equation above.

$$\begin{gathered} \mathrm{\mu }=\frac{1}{2}\left[\left[{\mathrm{Ca}}^{2+}\right]{\left(+2\right)}^2+2\left[{\mathrm{Cl}}^{-}\right]{\left(-1\right)}^2\right] \\ =\left(\frac{1}{2}\left[0.33\right]{\left(+2\right)}^2+2\left[0.33\right]{\left(-1\right)}^2\right)\mathrm{mM} \\ =0.99\mathrm{mM} \\ =0.00099\mathrm{M} \end{gathered}$$

Using the extended Debye-Huckel equation, find the value of $\gamma$for ${\mathrm{Cl}}^{-}$.