## Related questions with answers

(a) Data on a single crystal of $\mathrm{MnF}_{2}$ give $\chi_{m}=0.1463 \mathrm{cm}^{3} \mathrm{mol}^{-1}$ al 294.53 K. Identify the effective number of unpaired electrons in this compound and compare your result with the theoretical value. (b) Data on a single crystal of $\mathrm{NiSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}$ give $\chi_{\mathrm{m}}=6.00 \times 10^{-4} \mathrm{m}^{3} \mathrm{mol}^{-1}$ at 298 K. Identify the effective number of unpaired electrons in this compound and compare your result with the theoretical value.

Solutions

Verified## E15F3

The magnetic susceptibility being proportional to $\dfrac{m^2}{3kT}$ is a result of the contribution of the thermal averaging of the permanent magnetic moments in the presence of an applied magnetic field. Thus, the spin contribution to the molar magnetic susceptibility is

$\chi_m = \dfrac{N_{A}\mathscr{g}_e^2\mu_0\mu_B^2S(S+1)}{3kT}$

where $\mu_0$ is the vacuum permeability.

#### (a)

Here, find the number of unpaired electrons:

We have the formula:

$\chi_{m}=\frac{\mathrm{N}_{A} \mathrm{g}_{e}^{2} \mu_{0} \mu_{B}^{2} \mathrm{S}(\mathrm{S}+1)}{3 \mathrm{kT}}$

The values are:

$\mathrm{n}$ is the number of unpaired electrons

$\chi_{m}=1.463 \cdot 10^{-7} \mathrm{m}^{3} \mathrm{mol}^{-1}$ is the molar susceptibility

$\mathrm{N}_{A}=6.022 \cdot 10^{23} \mathrm{mol}^{-1}$ is the Avogadro's constant

$\mathrm{g}_{e}$=2.0023

$\mu_{0}=4 \pi \cdot 10^{-7} T^{2} J^{-1} m^{3}$

$\mu_{B}=9.274 \cdot 10^{-24} J^{-1}$

$\mathrm{T}=294.53 K$

$\mathrm{k}=1.381 \cdot 10^{-23} J K^{-1}$ is the Boltzmann constant

$S=\frac{n}{2}$ is the spin

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Chemistry: The Molecular Nature of Matter and Change

7th Edition•ISBN: 9780073511177 (2 more)Patricia Amateis, Silberberg#### Chemistry: The Central Science

14th Edition•ISBN: 9780134414232 (5 more)Bruce Edward Bursten, Catherine J. Murphy, H. Eugene Lemay, Matthew E. Stoltzfus, Patrick Woodward, Theodore E. Brown#### Atkins' Physical Chemistry

11th Edition•ISBN: 9780198769866James Keeler, Julio de Paula, Peter Atkins## More related questions

1/4

1/7