Question

By interpolation, find $\mathit{\gamma }$for${\mathbf{H}}^{\mathbf{+}}$ when $\mathbf{\mu }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{06}\mathbf{M}$.

Short answer

The activity coefficient value for ${\mathrm{H}}^{+}$ion is 0.854.

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

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

Step 2: Calculate the value of γ.

The activity coefficient and ionic strength values for ion:

The linear interpolation:

$$\begin{gathered} \frac{Unknowninterval}{∆\gamma }=\frac{knowninterval}{∆\gamma } \\ \frac{0.83-1}{0.83-0.86}=\frac{0.1-0.06}{0.1-0.05} \\ 0.83-\gamma =\frac{0.04}{0.05}\left(-0.03\right) \\ -\gamma =-0.024-0.83 \\ =-0.854 \\ \gamma =0.854 \end{gathered}$$

The activity coefficient value for ${\mathrm{H}}^{+}$ion is 0.854.