Molar conductivity

The molar conductivity is the electrical conductivity in electrolytes based on the ion concentration or molarity. Since some ions conduct electricity better than others, depending on their chemical nature , the molar conductivity in aqueous solutions is characteristic of each type of ion and is directly proportional to the migration speed of the ions during electrolysis . ${\displaystyle \Lambda _{\rm {m}}}$

Applications

From knowledge of the molar limit conductivities, one can calculate in advance what electrical conductivity certain salts should have in water.

Conversely, the concentration of a salt or ion type can be determined from a conductivity measurement, as long as it is known which salt or ion is involved. This process is used, for example, in the laboratory or in aquaristics . In agriculture and horticulture , the nutrient and fertilizer concentration in the irrigation water and in the soil is estimated.

The molar limit conductivities of individual ions are also important in electrolysis: knowing this, the migration speeds of the ions can be calculated. In addition, conductivity measurements ( amperometry ) can also be used to track the metabolic rate, the transfer figures or the type of ions formed or converted.

definition

The more salt ions there are in an aqueous solution, the better it conducts the electrical current or the more its electrical resistance decreases. A resistance value for an electrolyte solution that does not depend on the size and spacing of the electrodes is the specific resistance . Its reciprocal value is the electrical conductivity (dimension: ⁻¹ cm ⁻¹ = S / cm), which in not very concentrated solutions (up to approx. 1  mol / liter) is directly proportional to the salt concentration c in distilled water : ${\displaystyle \varkappa }$ ${\displaystyle \Omega }$

${\displaystyle \varkappa =\mathrm {konst.} \cdot c}$

If you now divide the conductivities at the respective concentrations by the respective concentration, you get the molar conductivity as the proportionality factor (dimension (earlier): S cm ² / mol), which, depending on the chemical nature of the salt, still depends slightly on the concentration:

${\displaystyle \Rightarrow \Lambda _{\rm {m}}(c):={\frac {\varkappa }{c}}}$

Molar limit conductivity

If one plots the molar conductivity of different salts as a function of the root of the corresponding concentration in a coordinate system, then straight lines are obtained. This relationship for strong ions (Cl ^- , SO ₄ ²⁻ , Na ⁺ ) is known as Kohlrausch's square root law :

${\displaystyle \Lambda _{\mathrm {m} }(c)=\Lambda _{\mathrm {m} }^{0}-K\cdot {\sqrt {c}}}$

( : Constant). ${\displaystyle K}$

The intersection of one of these straight lines with the ordinate is the molar limit conductivity at infinite dilution . It represents a characteristic constant of the respective type of ion. ${\displaystyle \Lambda _{0}=\Lambda _{\mathrm {m} }^{0}=\Lambda _{\mathrm {m} }(c\to 0)}$

The molar limit conductivity of a salt is made up of the limit conductivities ( equivalent conductivities ) and its individual ions as follows : ${\displaystyle \Lambda _{0}^{+}}$ ${\displaystyle \Lambda _{0}^{-}}$

${\displaystyle \Lambda _{0}=\nu ^{+}\cdot \Lambda _{0}^{+}+\nu ^{-}\cdot \Lambda _{0}^{-}}$

with the stoichiometric factors and the individual ions according to the sum formulas . Even previously unknown limit conductivities can thus be determined by forming the sum or the difference of known limit conductivities. ${\displaystyle \nu ^{+}}$ ${\displaystyle \nu ^{-}}$

To determine the molar limiting conductivity of individual ions, the molar mass of a salt, an acid or a base is divided by the number of charge carriers (charge exchange number) of the ion (previously val ), so that salts with various stoichiometric factors - such as sodium sulfate and sodium chloride - are compared with one another can be.

The Debye-Hückel-Onsager theory represents an improvement to this conductivity theory .

Ostwald's law of dilution applies to weak electrolytes .

Example for determination

For a NaCl - solution to a molar boundary conductivity of results based on the table below:

${\displaystyle \Lambda _{0}(\mathrm {NaCl} )=\mathrm {1\cdot 50,1\,{\frac {S\cdot cm^{2}}{mol}}+1\cdot 76,4\,{\frac {S\cdot cm^{2}}{mol}}=126,5\,{\frac {S\cdot cm^{2}}{mol}}} }$

According to the example, a 0.01 molar sodium chloride solution has a specific conductivity of: ${\displaystyle \left(c=\mathrm {0,01\,{\frac {mol}{Liter}}=0,01\,{\frac {mol}{1000\,cm^{3}}}} \right)}$

${\displaystyle \varkappa =126,5\,\mathrm {{\frac {S\cdot cm^{2}}{mol}}\cdot {\frac {0,01}{1000}}\,{\frac {mol}{cm^{3}}}=0,001265\,{\frac {S}{cm}}} }$

With inexpensive conductivity measuring devices, aqueous solutions can be examined quickly and easily.

Numerical values

Molar limit conductivities of ions at 298 K (≈ 25 ° C) in dist. water

cation	Λ 0 + (S cm 2 mol −1 )	Anion	Λ 0 - (S cm 2 mol −1 )
H +	349.8	OH -	198.6
Li +	38.7	F -	55.4
Na +	50.1	Cl -	76.4
K +	73.5	Br -	78.1
Rb +	77.8	I -	76.8
Cs +	77.3	NO 3 -	71.5
Ag +	61.9	ClO 3 -	64.6
NH 4 +	73.4	ClO 4 -	67.4
N (C 2 H 5 ) 4 +	32.4	HCO 3 -	44.5
1/2 mg 2+	53.1	HCOO -	54.6
1/2 Ca 2+	59.5	CH 3 COO -	40.9
1/2 Ba 2+	63.6	1/2 SO 4 2−	80.0
1/2 Cu 2+	53.6	1/2 CO 3 2−	69.3
1/3 La 3+	69.7	1/3 Fe (CN) 6 3−	100.9
1/3 Ce 3+	69.8	1/2 (C 2 O 4 ) 2−	74.2

The limit conductivity values ​​of the ion types can be calculated from their ion mobilities. See ion mobility and the values ​​tabulated there for 25 ° C.

Determination of transfer numbers

During electrolysis, some ions migrate very quickly (e.g. H ⁺ , OH ^- ), while others migrate very slowly (Li ⁺ , CH ₃ COO ^- ). A high migration speed is synonymous with a high transfer rate of the ion, which can be determined from the limit conductivity:

${\displaystyle {\begin{alignedat}{2}\Lambda _{0}&=\nu ^{+}\cdot \Lambda _{0}^{+}&&+\nu ^{-}\cdot \Lambda _{0}^{-}\\\Leftrightarrow 1&=\underbrace {\nu ^{+}\cdot {\frac {\Lambda _{0}^{+}}{\Lambda _{0}}}} _{t_{+}}&&+\underbrace {\nu ^{-}\cdot {\frac {\Lambda _{0}^{-}}{\Lambda _{0}}}} _{t_{-}}\end{alignedat}}}$

With

• the transfer number of cations ${\displaystyle t_{+}}$
• the conversion number of anions . ${\displaystyle t_{-}}$

As a result of different migration speeds, certain ions can accumulate more strongly in one electrode space during electrolysis than in the other electrode space. This can be checked by conductivity measurements.

literature

• Gerd Wedler, Hans-Joachim Freund: Textbook of physical chemistry. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 2012, ISBN 978-3527329090 .

See also

• Electrolytic conductivity
• Conductometry

Individual evidence

1. ↑ EC Meters (English), Gempler's company, accessed 2014.
2. ↑ Conductivity measuring device EC 3000 , company pitchcare, accessed 2014.
3. ^ Sartorius (company): Handbook of Electroanalytics Part 3: The electrical conductivity