Molar magnetic susceptibility units

The molar magnetic susceptibility, xm> is related to a quantity of more interest to the chemist, the Bohr magneton number (or magnetic dipole moment in Bohr magneton units), designated p. The relationship is ... 

The effective magnetic moment, can be obtained from the experimentally measured molar magnetic susceptibility, Xm, and is expressed in Bohr magnetons p ) where l B = eh/Attm = 9.27 x 10 JT . Equation 20.12 gives the relationship between and Xml using SI units for the constants, this expression reduces to equation 20.13 in which Xm is in cm moU. In the laboratory, the continued use of Gaussian units in magnetochemistry means that irrational susceptibility is the measured quantity and equation 20.14 is therefore usually applied. ... 

On proceeding to the molar magnetic susceptibility the necessary transformation to SI units is... 

Most experimental results in the literature are expressed in terms of the quantities Xg or Xm- The system of units employed almost exclusively in the field of magnetism is therefore the electromagnetic cgs system. Thus the unit of Xg is 10 emu/g (10" cm /g) and that of Xm is 10" emu/mol (10 cm /mol). Similarly, the unit usually employed for M, and M is 10 Gau.ss-emu/g and 10 Gauss emu/mol, respectively. If a rationalized system of units would be chosen by defining B = H + M, the experimental results would have to be multiplied by 4tt. This is the case for SI units which are consequently little used in magnetic studies [98,99, 100], For the molar magnetic susceptibility, the conversion from SI to cgs units is determined by... 

Alongside with magnetic susceptibility x of the unit volume a specific magnetic susceptibility Xsp is often used in practice Xsp=(3sp/ ) the relation being exist Xsp ( /p)X- The same is for molar magnetic susceptibility Xm which is equal to... 

Thereby, the held dependence of M dehnes the magnetic susceptibility y (which can be referred to volume, mass, or molar units) in the following way ... 

Magnetic susceptibilities are usually given in the literature on a mass or molar basis. Thus, while the volume susceptibility x is induced moment per unit volume per unit applied field and is dimensionless, the mass susceptibility... 

The magnetization per unit volume has the same units as the H-field for both cgs and SI units so the volume susceptibility is dimensionless. In practice, it is much more common to work with the molar magnetization Mmoi = My x (MW/p) where MW is the molecular weight and p is the density of the material. 

The magnetic susceptibility C, and the molar diamagnetic susceptibility m (see Equation 10.2) are nearly independent of the temperature. They are usually expressed in units of 1Q 6 cc/g and 10 6 cc/mole, respectively, and C,m is predicted by using group contributions. 

Fig. 11.17. Modelling of the molar differential magnetic susceptibility (in units of 10-6m3mol ) for a tetrahedral 5, = 52 = S3 = S4 = 1/2 system, xmol = f(B, T).

Figure 3. Molar susceptibility of the elements at room temperature (cgs units of 10 cmVmol). Values are not available for Z=9, 61, and 84-89 Fe, Co, and Ni (Z = 26-28) are ferromagnetic. Data taken from the table Magnetic Susceptibility of the Elements and Inorganic Compounds in Section 4.

TABLE 2.4 The Magnetic Susceptibility,[6], the Molar Refraction at the Sodium D Line, (normalized to the Value for Na ) [6], and the Softness Parameter [6], Modified by 0.3 Units, of Isolated Ions ... 

The molar susceptibility thus has units of volume per mole for all unit systems. In practice, the molar susceptibihty is frequently reported in cgs units as emu Oe mol (Scientists studying magnetism continue to utilize an eccentric mix of mostly cgs units in which the unit of magnetic moment, properly ergOe is given the name of emu . The volume susceptibihty remains dimensionless but is said to have units of emu cm Oe and the molar susceptibihty can be expressed as emuOe mol which is equivalent to cm mol" . See Reference 31 for a lucid discussion of SI units.) ... 

In keeping with customary practice, the molar susceptibility is given here in units appropriate to the cgs system. These values should be multiplied by 4n to obtain values for use in SI equations (where the magnetic field strength H has units of A m ). 

When a material is placed in a magnetic field H, a magnetization (magnetic moment per unit volume) M is induced in the material which is related toHhyM = kH, where k is called the volume susceptibility. Since H and M have the same dimensions, k is dimensionless. A more useful parameter is the molar susceptibility defined by... 

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