What amount of electric charge is required for the reduction of 1 mole of MnO$_4^{2-}$ into Mn$^{2+}$?
To reduce MnO$_4^{2-}$ to Mn$^{2+}$, we need to consider the change in oxidation state of Mn. In MnO$_4^{2-}$, Mn is in the +2 oxidation state, and in Mn$^{2+}$, Mn is also in the +2 state. Thus, no change in oxidation state occurs. However, the reduction process involves the addition of 2 electrons per ion, and for 1 mole of MnO$_4^{2-}$, 4 moles of electrons are required.
This corresponds to a charge of 4 Faradays.
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 \(P,O,Q\).