# Chemical Forums

## Chemistry Forums for Students => Undergraduate General Chemistry Forum => Problem of the Week Archive => Topic started by: Borek on April 22, 2013, 06:30:41 PM

Title: Problem of the week - 22/04/2013
Post by: Borek on April 22, 2013, 06:30:41 PM
Not a difficult one, but definitely based on something else than all the previous ones.

Ultra pure water was put into a cell with electrodes both of exactly 2 cm2 surface and exactly 0.5 cm apart. At 283 K measured resistance was 8.772 MΩ. Estimate value of water ion product at this temperature, knowing that limiting molar conductivities are respectively

$$\Lambda^\infty_{H^+} = 275 \frac {cm^2} {\Omega ~mol}$$

and

$$\Lambda^\infty_{OH^-} = 140 \frac {cm^2} {\Omega ~mol}$$
Title: Re: Problem of the week - 22/04/2013
Post by: Sunil Simha on April 29, 2013, 01:13:48 AM
Given that resistance is 8.772 MΩ,

R = l/(kA) where l is the length and A is the area of the cell. k is the conductivity.

I get k= 2.85 x 10-8 /Ωcm

So molar conductivity is Λ=k/c where c is the concentration. Here assuming 1g/cc as the density of water, I get c = (1/18) mol/cc.

This gives Λ = 51.3 x 10-8 cm2/Ωmol.

knowing that, I can find the degree of dissociation as α= Λ/Λ
Λ = 415 cm2/Ωmol.

So α = 1.23 x 10-9.

Thus the water product is (c*α)2 which is 4.67 x 10-15 mol2/L2.
Title: Re: Problem of the week - 22/04/2013
Post by: Borek on April 29, 2013, 04:42:58 PM
Hard to deny, that's the expected answer.

Actually literature value for the water ion product at 20°C (http://www.chembuddy.com/?left=pH-calculation&right=water-ion-product) is 6.76×10-15. Apparently the measurements were not as accurate as they pretend to be ;)