To solve the problem, we need to identify compounds (A), (B), (C), and (D) in the given reaction sequence starting from the fusion of \( \text{FeCr}_2\text{O}_4 \) with \( \text{Na}_2\text{CO}_3 \).
1. Reaction of \( \text{FeCr}_2\text{O}_4 \) with \( \text{Na}_2\text{CO}_3 \) in Air:
\( \text{FeCr}_2\text{O}_4 \) contains Cr in the +3 state. When fused with \( \text{Na}_2\text{CO}_3 \) in the presence of air (oxygen), Cr³⁺ is oxidized to Cr⁶⁺, forming sodium chromate (\( \text{Na}_2\text{CrO}_4 \)), a yellow solution. The reaction is:
\( 2\text{FeCr}_2\text{O}_4 + 4\text{Na}_2\text{CO}_3 + 7/2\text{O}_2 \rightarrow 2\text{Na}_2\text{CrO}_4 + 2\text{NaCrO}_2 + \text{Fe}_2\text{O}_3 + 4\text{CO}_2 \).
Compound (A) is \( \text{Na}_2\text{CrO}_4 \).
2. Acidification of Compound (A):
Acidifying \( \text{Na}_2\text{CrO}_4 \) converts chromate (\( \text{CrO}_4^{2-} \)) to dichromate (\( \text{Cr}_2\text{O}_7^{2-} \)) via:
\( 2\text{Na}_2\text{CrO}_4 + 2\text{H}^+ \rightarrow \text{Na}_2\text{Cr}_2\text{O}_7 + 2\text{Na}^+ + \text{H}_2\text{O} \).
Compound (B) is \( \text{Na}_2\text{Cr}_2\text{O}_7 \).
3. Reaction of Compound (B) with KCl:
\( \text{Na}_2\text{Cr}_2\text{O}_7 \) reacts with KCl to form potassium dichromate (\( \text{K}_2\text{Cr}_2\text{O}_7 \)), an orange-colored compound:
\( \text{Na}_2\text{Cr}_2\text{O}_7 + 2\text{KCl} \rightarrow \text{K}_2\text{Cr}_2\text{O}_7 + 2\text{NaCl} \).
Compound (C) is \( \text{K}_2\text{Cr}_2\text{O}_7 \).
4. Oxidation of \( \text{Na}_2\text{SO}_3 \) by Acidified Compound (C):
Acidified \( \text{K}_2\text{Cr}_2\text{O}_7 \) acts as an oxidizing agent, converting \( \text{Na}_2\text{SO}_3 \) (where S is +4) to \( \text{Na}_2\text{SO}_4 \) (where S is +6):
\( \text{K}_2\text{Cr}_2\text{O}_7 + 4\text{H}_2\text{SO}_4 + 3\text{Na}_2\text{SO}_3 \rightarrow \text{Cr}_2(\text{SO}_4)_3 + \text{K}_2\text{SO}_4 + 3\text{Na}_2\text{SO}_4 + 4\text{H}_2\text{O} \).
Compound (D) is \( \text{Na}_2\text{SO}_4 \).
Final Answer:
(A) is \( \text{Na}_2\text{CrO}_4 \), (B) is \( \text{Na}_2\text{Cr}_2\text{O}_7 \), (C) is \( \text{K}_2\text{Cr}_2\text{O}_7 \), and (D) is \( \text{Na}_2\text{SO}_4 \).
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 \(P,O,Q\).