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.
Convert Propanoic acid to Ethane
Acidified \(KMnO_4\) oxidizes sulphite to:
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).