Relation between Specific Conductance and Equivalent Conductance

[amk_dbz]

I have a question about the derivation of the formula for relation between Specific Conductance and Equivalent Conductance
i.e. Eq. Conductance = k.V
where, k= Specific Conductance ,V=Volume in ml
Given link explains the derivation http://www.adichemistry.com/physical/electrochemistry/introduction/electrochemistry.html
(Check under "EQUIVALENT CONDUCTANCE & MOLAR CONDUCTANCE" Tab")

Now my question is:
"Also we know that the conductance shown by 1 cm3 solution containing this electrolyte is called specific conductance, κ.

i.e.,

the conductance of V cm3 --------- Λ

the conductance of 1 cm3 --------- κ

Therefore:

Λ = κ.V ---------- equation (3)"

Isn't 'k' defined for a cube of solution i.e. 1 cm^2 area and 1 cm length and not in general any solution of volume 1cm^3?
If we change the area and length keeping the Volume equal to 1 cm^3 doesn't the value of 'k' change?

If that is true then in the derivation above, saying that conductance of 1cm3 is 'k' is incorrect since the area and length have to be 1cm2 and 1cm respectively, which is not specified.
( I mean that the area can be 0.5cm3 and the length be 2cm giving volume still 1cm3 but a different value of 'k')

Thank you in advance.

 

[tiny-tim]

hi amk_dbz!

"Also we know that the conductance shown by 1 cm3 solution containing this electrolyte is called specific conductance, κ.

i.e.,

the conductance of V cm3 --------- Λ

the conductance of 1 cm3 --------- κ

Therefore:

Λ = κ.V ---------- equation (3)"

Isn't 'k' defined for a cube of solution i.e. 1 cm^2 area and 1 cm length and not in general any solution of volume 1cm^3?
If we change the area and length keeping the Volume equal to 1 cm^3 doesn't the value of 'k' change?

If that is true then in the derivation above, saying that conductance of 1cm3 is 'k' is incorrect since the area and length have to be 1cm2 and 1cm respectively, which is not specified.

yes, you are correct … that definition of equivalent conductance appears to be wrong, since, as you say, it omits the shape of the volume

a better definition and explanation (of molar conductance, which i believe has mostly replaced equivalent conductance) is at http://www.emedicalprep.com/study-material/chemistry/electro-chemistry/molar-conductivity.html …

which does specify the shape

 

[amk_dbz]

Thanks tiny-tim for your clarification on the problem...
Almost all the books and websites I have referred to don't consider the shape..Maybe they do so secretly ;-)
Anyways thanks again.The question was bugging me too much.
"a better definition and explanation (of molar conductance, which i believe has mostly replaced equivalent conductance) is at http://www.emedicalprep.com/study-ma...ductivity.html …

which does specify the shape "

But again here,though they specify it for 'k' they don't do the same for the volume 'V'..
Shouldn't in the second case the gap between the plates should be 1 cm so as to make sure that the molar conductivity is a multiple of 'k'(i.e. kV) that the have specified. (So that the volume can be divided into 'V' cubes of 1cm by 1cm^2 length and area respectively, each of conductance 'k')

Thank you in advance.

 

[amk_dbz]

Please anyone can help me?

 

[Borek]

No time to delve deeper, but if memory serves me well - you can define specific conductance using volume, then use a cell constant (which is a function of shape) when calculating the real resistance, this way things take care of themselves automatically. In lab practice cell constant is something that you have to determine experimentally for a real cell before using it for any measurements (which means all measurements are in fact relative, not absolute).

 

[amk_dbz]

Oh yeah...relative measurement does make sense. We do start experiments related to conductance by measuring cell constant specific to the cell and so goes for specific conductance.
Hopefully the books meant the same as well.
Thank you for answering the question sir. :-)