To determine which compound is paramagnetic, we need to examine the oxidation state of manganese and the electron configuration of the manganese ion in each compound. - KMnO$_4$ (Potassium permanganate): In KMnO$_4$, the manganese ion exists in the \(+7\) oxidation state (Mn$^{7+}$). The electron configuration of Mn$^{7+}$ is \( 3d^0 4s^0 \), meaning that all d-orbitals are empty. Since there are no unpaired electrons, KMnO$_4$ is diamagnetic.
- K$_2$MnO$_4$ (Potassium manganate): In K$_2$MnO$_4$, the manganese ion exists in the \(+6\) oxidation state (Mn$^{6+}$). The electron configuration of Mn$^{6+}$ is \( 3d^1 4s^0 \), meaning there is one unpaired electron in the d-orbital. Since there is at least one unpaired electron, K$_2$MnO$_4$ is paramagnetic.
Step 1: Examine the oxidation state of manganese in each compound.
Step 2: Check the number of unpaired electrons in the electron configuration of the manganese ion.