# What is the difference between molar conductance and molar conductivity?

I'm learning (or at least trying to learn) about electrochemistry, but a major obstacle to that, is that different books I refer use different terms for the same symbols. So in a last ditch attempt to clear stuff up, I've resorted to Chem.SE.

So here's what I intend to do; I'll list out everything I think I've understood, as well as pose a couple of questions regarding some of them. I'd really appreciate it if someone would take the time to go through what I've listed out, checking them for errors and then clearing those queries which I've got. So here I go

Symbols used:

Resistance ($R$) , Resistivity or specific resistance ($\rho$), Conductance ($C$), Conductivity or specific conductance ($\kappa$), Area of cross-section of the electrode ($A$), distance between the electrodes ($L$),

and the REALLY confusing bit, Molar conductance according to some books and Molar conductivity according to others and one book uses both terms, both represented by $\mathrm{Λ_{m}}$ Now, $$R = \rho \frac{L}{A}\\ R = \frac1C\\$$ Therefore $$\frac1\rho = \frac1R\cdot\frac{L}A = C\cdot\frac{L}A = \kappa$$

Now if I've got this right, then,

1. Conductance is the degree to which the solution conducts electricity.
2. Conductivity is the conductance per unit volume of the solution; it may also be considered as the concentration of ions per unit volume of solution.
3. Molar Conductivity is the conductance of the entire solution having 1 mole of electrolyte dissolved in it.

Q1. So what's Molar Conductance?

Q2. Is there a difference between Molar Conductivity and Molar Conductance?

Also, according to Ostwald's Dilution Law, greater the dilution, greater the dissociation of the electrolyte in solution.

Regarding dilution of an electrolyte solution, this is what I've understood

1. As dilution increases, Conductivity (ion concentration per unit volume) DECREASES.
2. As dilution increases, Molar conductivity (Conductance of 1 mole of electrolyte in the total solution) should INCREASE in accordance with Ostwald's Law

Q3. How does dilution affect Molar Conductance?

Q4. How is Conductance affected upon dilution?

Also if you feel there is are any additional points worth mentioning, by all means go ahead and put it in the answer.

And finally, if anyone could recommend a decent site that deals with the above-mentioned terms and concepts in a fairly lucid manner, it'd be appreciated.

• Yes, terminology is often used inconsistently. Start with the Wikipedia article en.wikipedia.org/wiki/Molar_conductivity which will answer most of your questions. – MaxW Sep 15 '16 at 6:03
• Let me add kudos for both diligence to spot such a difference and curious enough to determine the difference. Using terms inconsistently or unnecessarily using a different form of the term drive me crazy. Another huge annoyance is variables. Very frequently a variable x will be written one way in the text, but another in the equation $y=2x$. So is x=$x$ ?!? – MaxW Sep 15 '16 at 17:24

I can understand your frustration. The use of terminology is often inconsistent and confused (much to my chagrin). I think you've got the general idea, the conductance (G) can be defined as follows:

$$G = \frac{1}{R}$$

i.e the ease with which a current can flow. As you said said, $$R = \rho \frac{l}{A}$$

one can now identify, $$G = \kappa\frac{A}{l}$$ where the conductivity $$\kappa = \frac{1}{\rho}$$

Molar "any quantity" always has the dimensions (it is helpful to think in terms of dimensions)$\text{"quantity"} \mathrm{mol^{-1}}$

so, it follows molar conductivity $$\Lambda_m = \frac{\kappa}{c}$$ where $c$ is the molar concentration. It is useful to define molar conductivity because, as you already know, conductivity changes with concentration.

Now, to address the effect of change of concentration on molar conductivity, we need to consider the case of weak and strong electrolytes separately.

For a strong electrolyte, we can assume ~ 100% disassociation into constituent ions. A typical example is an $\ce{MX}$ salt like $\ce{KCl}$

$$\ce{MX} \rightleftharpoons \ce{M^+} + \ce{X^-}$$ The equilibrium constant for this reaction is $$K = \frac{[\ce{M^+}][\ce{X^-}]}{[\ce{MX}]}$$ and thus, with decreasing molar concentration of the electrolyte, equilibrium shifts towards the disassociated ions.

At sufficiently low concentrations, the following relations are obeyed:

$$\Lambda _{m}=\Lambda _{m}^{0}-K{\sqrt {c}}$$

where $\Lambda _{m}^{0}$ is known as the limiting molar conductivity, K is an empirical constant and c is the electrolyte concentration. (Limiting here means "at the limit of the infinite dilution".)

In effect, the observed conductivity of a strong electrolyte becomes directly proportional to concentration, at sufficiently low concentrations

As the concentration is increased however, the conductivity no longer rises in proportion.

Moreover, the conductivity of a solution of a salt is equal to the sum of conductivity contributions from the cation and anion.

$$\Lambda_{m}^{0}= \nu_{+}\lambda_{+}^{0}+\nu _{-}\lambda _{-}^{0}$$ where: $\nu _{+}$ and $\nu _{-}$ are the number of moles of cations and anions, respectively, which are created from the dissociation of 1 mole of the dissolved electrolyte, and $\lambda _{+}^{0}$, $\lambda _{-}^{0}$ are the limiting molar conductivities of the individual ions.

The situation becomes slightly more complex for weak electrolytes, which never fully disassociate into their constituent ions. We no longer have a limit of dilution below which the relationship between conductivity and concentration becomes linear. We always have a mixture of ions and complete molecules in equilibrium Hence, the solution becomes ever more fully dissociated at weaker concentrations.

For low concentrations of "well behaved" weak electrolytes, the degree of dissociation of the weak electrolyte becomes proportional to the inverse square root of the concentration.

A typical example would be a monoprotic weak acid like acetic acid (again, from your graph)

$$\ce{AB} \rightleftharpoons \ce{A^+} + \ce{B^-}$$

Let $\alpha$ be the fraction of dissociated electrolyte, then $\alpha c_0$ is the concentration of each ionic species. And $(1 - \alpha)$, and $(1 - \alpha)c_0$ gives the fraction, and concentration of undissociated electrolyte. The dissociation constant is:

$$K = \frac{\alpha^2 c_0}{1-\alpha}$$

for weak electrolytes, $\alpha$ is tiny, so the denominator is nearly equal to one so, $$K \approxeq \alpha^2 c_0$$ and $$\alpha = \sqrt{\frac{K}{c_0}}$$ (like I said earlier)

for conductivities, one can now write the following relation $$\frac{1}{\Lambda_m} = \frac{1}{\Lambda_m^0} + \frac{\Lambda_mc}{K (\Lambda_m^0)^2}$$ This fits the curve seen in your graph.

Caveat, all these arguments hold for dilute solutions. Things get out of hand at high concentrations, and one has to account for some additional phenomenon (for e.g acetic acid will form hydrogen bonded dimers)

Anyway, long story short conductivity increases with increasing dilution (though differently for strong and weak electrolytes). From the definitions I outlined at the very start, guessing how conductance changes is trivial.

Let's get the terms right, firstly, because that seems to generate some confusion.

Conductance=ability of a component to conduct electric current (it might also refer to heat and others, but we'll stick to the ones in your example for now).

It depends on: the material of your component (that is actually its conductivity), the length of the component (l) and the cross section of the component (A). It's unit measurement is S(from conductivity)*m(from length)/m2 (from area) which yields S/m.

Conductivity is the ability of a material to conduct electric current, regardless of its dimensions. It is also called specific conductance. And it's the reverse of resistivity, measured in S (siemens, mentioned also above).

If I have a cell/component of 1 sqm cross section and 1 m length, conductance and conductivity would be equal in value. If these are different values for the component Im computing, I adjust the conductivity of the material in general with the dimensions, and get the conductance of my particular component (such as a conductor, piece of metal, electrolyte environment etc)

So I would say about a metal that it has high conductivity and about a rod (or other specific piece) of the same metal that is has a (assumably) high conductance.

Now, moving to the questions:

Q1: Molar Conductance = conductance of all the ions produced by ionization of 1 g mole of an electrolyte when present in V mL of solution. Mathematical relation is miu=k * V ; k is the conductivity=specific conductance

Q2: Molar Conductivity=lambda= k/ molecular concentration which makes it equal to molar conductance per mole. So this is pretty much the difference between them, if we could name it as such.

Note that these refer to ionic conductivities, for electrolytes.

Q3: The variation of molar conductance with concentration can be explained on the basis of conducting ability of ions for weak and strong electrolytes. A strong electrolyte is a compound that is totally dissociated in water in its component ions while a weak one is an electrolyte where we have present the compound in itself, as well as component ions separately. I remind you that ionic conductivity/conductance both rely on the presence of ions in solution.

For weak electrolytes: as we increase the volume (thus the dilution), we encourage the equilibrium to shift towards dissociation. Therefore, we will have more ions in solution and a implicit increase in molar conductance. It basically means that 1 mole dissolved into 10 mL of water gives out less ions than 1 mole of the same, in the same conditions, in 100 mL of water.

For strong electrolytes, the observed effect is the same (molar cond. increases with V increasing), but the reasons are different. In concentrated solutions (less solvent) the strong opposingly charged ions tend to attract each other. Give them enough space (i.e increase V) to move freely of these attractions and you get an increased molar conductance.

Q4: Conductance, we said is conductivity* cross area/ length of component, and the reverse of resistance. So conductance=current intensity/tension; The intensity of the current in turn, is directly proportional with ion concentration (no of ions/volume) and ionic mobility (nevermind this for a bit). Therefore, if we have lower ions concentration (same ions/bigger volume), we will have a smaller current and hence, a decrease in conductance.

Hope these help with sth. If you have some follow-up questions, please feel free. In the meanwhile, I will think of some resources to send you as trustworthy source.

Cheers.

In my Opinion, 1) Conductance= It is reciprocal of the electrical resistance. Or you can say it is the ease with which a conductor or an electrolyte allows the flow of electrons through it. It does not take dimensions into account. It's SI unit is Siemens.

2) Conductivity = It is the Conductance of a solution of 1cm length and having 1 Sq. cm as the area of cross section. Or it can alternatively defined as the Conductance of 1cm^3 solution of an electrolyte. It does take dimensions into account. Hence it's SI unit is Siemens/meter.

3)Molar Conductance = It is the Conductance of 1mole of an electrolyte in V cm^3 of the solution.

4)Molar Conductivity= It is the Conductivity of 1 mole of the electrolyte. Or you can say, Molar conductivity of a solution at a dilution V is the Conductance of all the ions produced from 1 mole of the electrolyte dissolved in V cm^3 of the solution when the electrodes are 1 cm apart (note : here dimension is mentioned) and the area of the electrodes is so large that the whole of the solution is contained between them. Molar Conductivity= (specific conductivity × 1000) / Molarity It's SI unit is S m^2 mol^-1.

So in simple term, Conductivity always takes dimensions into account( i.e.,electrode area) but Conductance never does so.

Q. What happens to Conductance , Molar Conductance equivalent Conductance , conductivity, Molar Conductivity, equivalent conductivity on dilution?

Ans- Now, let us understand this by taking an example.

Case 1- Consider 1cc of the solution containing 1 g eq. of the electrolyte taken in a vessel. Now, Conductance of this solution will be then specific conductivity or simply conductivity. Also as per definition equivalent Conductivity is the Conductance of 1g eq. of electrolyte dissolved in V cc of the solution when the distance between the electrodes is 1cm and area of the electrodes are so large that the whole of the solution is contained in between them (NOTE - area may or may not be1cm2 and if so then eq. Conductivity will be same as specific conductivity). Thus, when 1cc of the solution containing 1 gram equivalent of the electrolyte is considered, the equivalent conductivity is equal to it's specific conductivity.

Case 2 - Now, Suppose 4cc of the solution containing 1 gram equivalent of the electrolyte is taken. The Conductance of the solution will still be equal to it's equivalent conductivity at this dilution ( i.e., 4 times) but now there will be four cubes each of volume 1cc. The Conductance of each 1 cc of the solution is equal to it's specific conductivity so that the total Conductance of the solution i.e., equivalent conductivity is four times the specific conductivity. So eq conductivity = specific conductivity × V cc of solution Similar is the case with Molar conductivity.

So, Conductance , Molar Conductance , equivalent Conductance , Molar conductivity , Equivalent conductivity increases with dilution as on dilution more no. Of ions are produced , also they are much free to move or to conduct.

wheareas the specific Conductance of an electrolytic solution decreases with dilution as the no. Of ions contained in between electrodes which are 1cm apart and have area of 1cm^2 decreases.

I have tried my level best to clear the concept.Hope this will help you.... Any further questions and suggestions are most welcome.