Homework #$1$

Use the Davies equation as shown below for calculating mean ionic activity coefficients needed in working the following problems.

Davies equation: $,log{}_{+-}=-0\mathrm{.}51z_{+}|z_{-}|[\frac{(I{)}^{\frac{1}{2}}}{1+(I{)}^{\frac{1}{2}}}-0\mathrm{.}30(I)]$

where $I=\frac{1}{2}{\displaystyle \underset{i}{\overset{?}{}}}{z}_i^2(\frac{b_i}{b^o})$ and $b$ represents molality and $z$ is the charge.

$1.$ What is the ionic strength of a solution prepared by dissolving $1\mathrm{.}00g$ of $KN{O}_3$ and $1\mathrm{.}00gCaC{l}_2$ in $200\mathrm{.}0g$ of water?

$2.$ Estimate the mean ionic activity coefficient for $CaC{l}_2$ in the solution from problem $1.$

$3.$ What is the molality of $H^{+}$in the solution from problem $1$ at $25C?$ Do not neglect ionic activity coefficients.

$4.$ Formic acid, HCOOH, is a weak acid with $K_a=1\mathrm{.}7{10}^{-4}.$ What is the molality of $H^{+}$ions in a $0\mathrm{.}10m$ solution of formic acid in water? Do not neglect ionic activity coefficients.