In electrochemistry, what is the SI unit used for equivalent conductance (Λeq) of an electrolyte solution?

Introduction / Context:
This question tests your knowledge of the correct SI unit for equivalent conductance, a quantity commonly used in electrochemistry to describe the conducting power of an electrolyte solution for one gram equivalent of solute. Correct units are important when you interpret experimental data or compare values from different sources.

Given Data / Assumptions:

• We are dealing with equivalent conductance, usually denoted by Λeq or lambda eq.
• Options list different possible units like ohm/cm, S m2 per equivalent and others.
• We assume SI base units and standard definitions are being used.
• Conductance is the reciprocal of resistance and is measured in siemens (S) in SI units.

Concept / Approach:
Equivalent conductance Λeq is defined as the conductance of a solution containing one gram equivalent of electrolyte placed between electrodes that are one metre apart and have a cross sectional area large enough to contain that equivalent. Mathematically, Λeq is related to specific conductance k and equivalent concentration. In SI, specific conductance k has units of S per metre, and equivalent conductance scales this by the volume that contains one equivalent. This leads to units of siemens multiplied by square metre per equivalent, written as S m2 per equivalent.

Step-by-Step Solution:
1) Specific conductance k has SI unit S per metre (S/m).2) Equivalent conductance Λeq is related to k by Λeq = k * V, where V is the volume that contains one gram equivalent of solute.3) If V is expressed in cubic metres per equivalent, then Λeq has units S/m * m3 per equivalent = S m2 per equivalent.4) Therefore, the correct SI unit for equivalent conductance is siemens square metre per equivalent, written as S m2 per equivalent.5) Older units like mho and centimetre based units belong to the CGS system and are not strict SI units.

Verification / Alternative check:
In older literature, equivalent conductance is often given in units of S cm2 per equivalent or previously mho cm2 per equivalent. To convert to SI, note that 1 cm = 0.01 m, so 1 cm2 = 10^-4 m2. Thus multiplying by cm2 per equivalent in CGS naturally corresponds to m2 per equivalent in SI after proper conversion. This is consistent with the expression S m2 per equivalent and confirms the reasoning based on dimensional analysis.

Why Other Options Are Wrong:
ohm/cm: This is a unit of resistivity, not conductance, and it is not in SI form.
siemens per equivalent (S per equivalent): This ignores the squared length dimension that arises from converting specific conductance to equivalent conductance.
mho/cm: This is an older CGS unit for specific conductance, not equivalent conductance and not SI compliant.
ohm square metre per mole: This unit mixes resistance with mole based concentration and does not represent equivalent conductance of electrolyte solutions.

Common Pitfalls:
Students often confuse specific conductance, molar conductance and equivalent conductance, as well as their respective units. Another common error is to memorise CGS units using centimetres and mho and then assume they are SI units. To avoid confusion, always start from the definition of the quantity, express it in terms of basic SI units, and perform dimensional analysis. This approach will lead you reliably to the correct unit even if you forget the exact form from memory.

Final Answer:
The SI unit of equivalent conductance is siemens square metre per equivalent (S m2 per equivalent).