The elements of the 3d transition series are given as: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn. Answer the following:
Copper has an exceptionally positive \( E^\circ_{\text{M}^{2+}/\text{M}} \) value, why?
Copper exhibits a highly positive standard electrode potential for the half-cell reaction:
\( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \)
This is due to its unique electronic configuration:
\( \text{Cu}: [\text{Ar}]\,3d^{10}\,4s^1 \)
When copper oxidizes from \( \text{Cu} \) to \( \text{Cu}^{2+} \), it loses two electrons. However, this process is less favorable because:
As a result, the half-cell potential:
\( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \)
is highly positive, reflecting copper’s low reactivity and high resistance to oxidation. This stability of the copper ion leads to a greater tendency for the reduction reaction (rather than oxidation), which is why the standard electrode potential is significantly positive.
An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is $ \frac{X}{F} \times 10^3 $ volts, where $ F $ is the Faraday constant. The value of $ X $ is ____.
Use: Standard Gibbs energies of formation at 298 K are:
$ \Delta_f G^\circ_{CO_2} = -394 \, \text{kJ mol}^{-1}; \quad \Delta_f G^\circ_{water} = -237 \, \text{kJ mol}^{-1}; \quad \Delta_f G^\circ_{butane} = -18 \, \text{kJ mol}^{-1} $
Consider the following electrochemical cell at standard condition. $$ \text{Au(s) | QH}_2\text{ | QH}_X(0.01 M) \, \text{| Ag(1M) | Ag(s) } \, E_{\text{cell}} = +0.4V $$ The couple QH/Q represents quinhydrone electrode, the half cell reaction is given below: $$ \text{QH}_2 \rightarrow \text{Q} + 2e^- + 2H^+ \, E^\circ_{\text{QH}/\text{Q}} = +0.7V $$

In the above diagram, the standard electrode potentials are given in volts (over the arrow). The value of \( E^\circ_{\text{FeO}_4^{2-}/\text{Fe}^{2+}} \) is:
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 \(P,O,Q\).