something weird in Rxn logK

[tiziano]

Dear GWB users,

I have noticed something weird in the RXN tool. Specifically, writing the reaction:

albite_low + K+ = k-feldspar + Na+

and assigning an activity of 0.891 to k-feldspar, the logK is calculated as:

logK = -0.0501 + logNa - logK

However, in reality, the logarithm of the equilibrium constant should be:

logK = +0.05012 + logNa - logK

because:

logK = log[(Na/(K*0.891)] = logNa - log(K*0.891) = logNa - logK - log(0.891) = logNa - logK + 0.0512

Is that not correct? Or perhaps I am making a mistake somewhere? I would like to specify that I am using version 12.0.9.

[Jia Wang]

Hello,

I think you have albite in the wrong place in your mass action equation. According to your reaction, albite + K+ = k-feldspar + Na+ , the equilibrium constant is calculated as:

K = [activity(K-feldspar) * activity(Na+)] / [activity(albite) * activity(K+)]

Taking log on both sides, we get:

logK = log [activity(K-feldspar) * activity(Na+)] - log[activity(albite) * activity(K+)] 

logK = log activity(K-feldspar) + log activity(Na+) - log activity(albite) - log activity(K+)

substituting the values for feldspar and albite:

logK = log (0.891) + log activity(Na+) - 0 - log activity(K+)

logK = -0.05012 + log activity(Na+) - log activity(K+)

Hope this helps,
Jia Wang
Aqueous Solutions LLC

[tiziano]

Hi Jia, thank you for the quick answer.

I still have a doubt, because taking your formulation:

logK = log activity(K-feldspar) + log activity(Na+) - log activity(albite) - log activity(K+)

then it would be

logK = log activity(1) + log activity(Na+) - log activity(0.891) - log activity(K+)

logK = 0 + log activity (Na+) − (−0.05012) - log activity (K+)

So:

log⁡(K)= log ⁡activity(Na+) + 0.05012 − log ⁡activity(K+))

In other words, there should be +0.05012 because we have -(-0.05012).

Thank you

 

[tiziano]

Let me illustrate it by assigning activity_Na+ = 0.2 and activity_K+ = 0.3. Considering the logarithm of the ratio, we have: log K = log[(0.2*1)/(0.3*0.891)] = -0.126. Considering the relationship log K = log(0.2)+0+0.05012-log(0.3) = -0.126. On the contrary, if we consider the relationship log K = LOG(0.2)+0-0.05012-LOG(0.3) = -0.226; i.e., we get a different number if we have -0.0512.

[tiziano]

Oops, I realized that I was mistaken. I had assigned 1 to the k-feldspar activity instead of albite. Problem solved. I apologize for the false alarm! 🙂

[Jia Wang]

I am glad that you were able to figure it out. I should've have said K-feldspar being in the wrong place in the mass action equation according to your equation and not albite.

Best regards,
Jia