[bmu123]

Using the Debye-Hückel Limiting Law, calculate the activity coefficient of H₃O⁺ in a solution of 1 mol kg^–1 HCl. What is the Debye length of the H₃O⁺ ion in this solution and what does this tell us about the ideality of the solution?

OK so logγ+ = A|Z+|²√I
I know we've usually assumed A=0.509, does that apply here too?
Unsure of how to do ionic strength, is it conc x charge?
And unsure of which equation to use for Debye length

[Borek]

Unsure of how to do ionic strength, is it conc x charge?

What is the definition of the ionic strength? I find it hard to believe you were taught DH law without introducing this definition first.

And unsure of which equation to use for Debye length

Whichever contains data that you know and can plug into.

[bmu123]

OK sorry it's concentration x charge so if I assume the concentration is 1 mol kg -1 because the charge is 1.
All I've been taught about Debye length is that it's proportional to 1/√I but obviously I can't use this. Everything I find online is very confusing: Debye length λD =√εT_eff/n₀e²
So ε = ε₀(permittivity of a vacuum) x εr (relative permittivity).
Would I assume room temperature so T = 298K
I've got that n₀ = constant volume density but no idea what that means. and e² - are these both constants?
Thanks for your help

[Borek]

it's concentration x charge

Nope. Please check the definition.

Wikipedia article on Debye length contains several equivalent formulas, have you seen them?