Help with this Debye-Huckle question

Question

using the equation i inputted for Zr+4 and got this answer and it was determined to be wrong don't know where I am misunderstanding. on how to determine the activity coefficient.

Zr charge +4

size 1.100

𝜇=0.0297 M

I got 0.0393 and it was labeled as wrong

Answer 1

To calculate the activity coefficient (γ) using the Debye-Hückel equation, we need to know the ionic strength (μ) of the solution and the size parameter (a) for the Zr4+ ion. The Debye-Hückel equation is given by:

log10(γ±) = -0.51 * z^2 * √(μ) / (1 + a √(μ))

where:

z = charge of the ion (in this case, z = +4 for Zr4+)

μ = ionic strength of the solution

a = size parameter of the ion

You provided the following values:

Zr charge (z) = +4

Size parameter (a) = 1.100

Ionic strength (μ) = 0.0297 M

Now let's calculate the activity coefficient:

log10(γ±) = -0.51 * (4)^2 * √(0.0297) / (1 + 1.100 * √(0.0297))

log10(γ±) = -0.51 * 16 * √(0.0297) / (1 + 1.100 * √(0.0297))

log10(γ±) = -0.51 * 16 * 0.1722 / (1 + 1.100 * 0.1722)

log10(γ±) = -0.51 * 16 * 0.1722 / (1 + 0.1894)

log10(γ±) = -0.51 * 16 * 0.1722 / 1.1894

log10(γ±) = -0.1412

Now, to find γ±, we need to take the antilog (10 raised to the power of -0.1412):

γ± = 10^(-0.1412)

γ± ≈ 0.7978

So, the activity coefficient (γ±) for Zr4+ ion in the given solution is approximately 0.7978.