Question

Explain why the magnetic susceptibility of a transition metal complex is temperature dependent, whereas the magnetic moment of the complex is not temperature dependent.

Answer 1

First, lets start off with magnetic susceptibility

A metal ion with a single unpaired electron, such as Cu²⁺, in a coordination complex provides the simplest illustration of the mechanism of paramagnetism.

The individual metal ions are kept far apart by the ligands, so that there is no magnetic interaction between them. The system is said to be magnetically dilute.

The magnetic dipoles of the atoms point in random directions.

When a magnetic field is applied, first-order Zeeman splitting occurs.

Atoms with spins aligned to the field slightly outnumber the atoms with non-aligned spins.

In the first-order Zeeman effect the energy difference between the two states is proportional to the applied field strength.

Denoting the energy difference as ΔE, the Boltzmann distribution gives the ratio of the two populations as e − Δ E / k T , where k is the Boltzmann constant and T is the temperature in kelvins.

In most cases ΔE is much smaller than kT and the exponential can be expanded as 1 – ΔE/kT.

It follows from the presence of 1/T in this expression that the susceptibility is inversely proportional to temperature.

This is known as the Curie law and the proportionality constant, C, is known as the Curie constant, whose value, for molar susceptibility, is calculated as

Now, coming to the effective magnetic moment,
When the Curie law is obeyed, the product of molar susceptibility and temperature is a constant. The effective magnetic moment, μ_eff is then defined as

Where C has CGS units cm³ mol⁻¹ K, μ_eff is

The quantity μ_eff is effectively dimensionless,(BECAUSE IT IS DEFINED AS THE PRODUCT OF MAGNETIC SUSCEPTIBILITY AND TEMPERATURE)

It is often stated as in units of Bohr magneton (μ_B).