Activity effects for acid solution

What is the pH of a 0.03 M HCl accounting for activity effects? (H+ radius = 900 pm)

What is the % difference if we assumed no activity?

To calculate the pH of the solution accounting for activity, we would use:

pH = -log[H+]*a(H+), where a(H+) is the activity coefficient.

You can find the activity coefficient by the Debye-Huckel equation:

log(a(H+)) = -0.51 * (z)^2 * sqrt(u) / (1 + r(sqrt(u))/305)

Where:
z = charge of all species
u = ionic strength
r = hydrated radius (pm)

You can find u by:

u = 0.5sum(c*z^2)

Where
c = concentration
z = charge

First, we need to find the ionic strength of the acid. It has 2 ions, H+ and Cl-, with +1 and -1 charge, respectively, therefore:

u = 0.5 * [(0.03 * 1^2) + (0.03 * -1^2)] = 0.03 M

This ionic strength is too concentrated for the equation above, so it will give huge percent error. I'm going to use it anyway because I don't remember the extended equation nor do I feel like it.

a(H+) = 10^(-0.51 * (1 * -1)^2 * sqrt(0.03)) / (1 + (900 * sqrt(0.03) / 305)

a(H+) = 0.874

pH = -log(0.874 * 0.03) = 1.58


The pH not accounting activity is pH = -log(0.03) = 1.52

The % difference would be (1.58 - 1.52)/1.58 * 100% = 3.8%