Complete and balance the following chemical equations: (a) \[ 2MnO_4^-(aq) + 10I^-(aq) + 16H^+(aq) \rightarrow \] (b) \[ Cr_2O_7^{2-}(aq) + 6Fe^{2+}(aq) + 14H^+(aq) \rightarrow \]
In an acidic solution, permanganate ions (\( \text{MnO}_4^- \)) act as an oxidizing agent and oxidize iodide ions (\( I^- \)) to iodine (\( I_2 \)). The balanced equation for this reaction is as follows:
\[ 2 \, \text{MnO}_4^-(aq) + 10 \, \text{I}^-(aq) + 16 \, \text{H}^+(aq) \rightarrow 2 \, \text{Mn}^{2+}(aq) + 5 \, \text{I}_2(aq) + 8 \, \text{H}_2\text{O}(l) \]
In this reaction, permanganate ions are reduced to \( \text{Mn}^{2+} \), and iodide ions are oxidized to iodine.
In an acidic solution, dichromate ions (\( \text{Cr}_2\text{O}_7^{2-} \)) are reduced to chromium(III) ions (\( \text{Cr}^{3+} \)), while iron(II) ions (\( \text{Fe}^{2+} \)) are oxidized to iron(III) ions (\( \text{Fe}^{3+} \)). The balanced equation for this reaction is:
\[ \text{Cr}_2\text{O}_7^{2-}(aq) + 6 \, \text{Fe}^{2+}(aq) + 14 \, \text{H}^+(aq) \rightarrow 2 \, \text{Cr}^{3+}(aq) + 6 \, \text{Fe}^{3+}(aq) + 7 \, \text{H}_2\text{O}(l) \]
In this reaction, the dichromate ions are reduced to \( \text{Cr}^{3+} \), and iron(II) is oxidized to iron(III).
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 \(P,O,Q\).