Question

What is the activity coefficient of H in a solution containing 0.073 M HCl and 0.0090 M Ca(ClO4)2? A table of activity coefficients at various ionic strengths can be found here.
What is the pH of the solution?

Answer 1

Answer:

The value is $pH = 1.22$

Explanation:

From the question we are told that

The concentration of $H^{+}$ is $[H^{+}] = 0.073 \ M$

The concentration of $Cl^{-}$ is $[Cl{+}] = 0.073 \ M$

The concentration of $Ca^{+}$ is $[Ca{2+}] = 0.0090 \ M$

The concentration of $ClO^{-}$ is $[ClO^{-}] = 2 *0.0090 = 0.018$

Generally the log of the activity coefficient is mathematically represented as

$log \ \gamma__{H^+}} = \frac{-0.5z^2 * \sqrt{\mu} }{1 + (\alpha * \frac{\sqrt{\mu}}{305} )}$

Here z is the charge which for $H^{+}$ is +1

$\alpha$ is the size which for $H^{+}$ is $900pm = 900*10^{-12} \ m$

$\mu$ is the ionic strength which is mathematically represented as

$\mu = \frac{1}{2} * \{ 0.073* (+1)^2 +0.073 * (-1)^2+0.0090 * (+2)^2+ 0.018* (-1)^2 \}$

=> $\mu = 0.1$

So

$log \ \gamma__{H^+}} = \frac{-0.5(+1)^2 * \sqrt{0.1} }{1 + (900*10^{-12} * \frac{\sqrt{0.1}}{305} )}$

=> $log \ \gamma_{H^+} = -0.083$

=> $\gamma__{H^+}} = antilog(-0.083)$

=> $\gamma__{H^+}} =0.82$

Generally the pH is mathematically represented as

$pH = -log [H^{+}] * \gamma__{H^{+}}$

$pH = -log 0.073 * 0.82$

=> $pH = 1.22$