1. Predicting the Best Metal for Coating Iron:
Given Data:
- \( E^\circ_{X^{2+}/X} = -2.36 \, \text{V} \)
- \( E^\circ_{Y^{2+}/Y} = -0.14 \, \text{V} \)
- \( E^\circ_{Fe^{2+}/Fe} = -0.44 \, \text{V} \)
Explanation:
The \( E^\circ \) values represent the standard electrode potentials of the half-reactions. The more negative the \( E^\circ \) value, the more easily the substance will undergo oxidation. In the case of corrosion protection, a metal that is more easily oxidized (has a more negative \( E^\circ \)) can protect iron by sacrificing itself and forming a protective coating.
Step 1: Analyzing the Electrode Potentials:
- The more negative the \( E^\circ \) value, the more readily the substance will lose electrons and undergo oxidation. Therefore, the metal with the most negative \( E^\circ \) will be more easily oxidized and form a sacrificial layer to protect iron from corrosion.
- Iron (\( Fe^{2+}/Fe \)) has a standard electrode potential of \( -0.44 \, \text{V} \), which means iron can be oxidized in the presence of a more easily oxidized metal.
Step 2: Comparing X and Y for Coating:
- \( E^\circ_{X^{2+}/X} = -2.36 \, \text{V} \): Metal X has a very negative electrode potential, meaning it is highly prone to oxidation. This makes it a good candidate for sacrificial protection.
- \( E^\circ_{Y^{2+}/Y} = -0.14 \, \text{V} \): Metal Y has a less negative \( E^\circ \), meaning it is less prone to oxidation compared to metal X.
Conclusion:
Since metal X has a more negative \( E^\circ \) value, it is more likely to undergo oxidation and form a protective sacrificial coating on iron. Thus, metal X is a better choice for coating the surface of iron to prevent corrosion.
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 \(P,O,Q\).