(1): Thermal Decomposition of Potassium Permanganate (KMnO4)
- On heating, potassium permanganate (KMnO4) decomposes to form potassium manganate (K2MnO4), manganese dioxide (MnO2), and oxygen gas (O2).
- This reaction is used in laboratories as a source of oxygen.
The thermal decomposition reaction is:
2KMnO4 heat → K2MnO4 + MnO2 + O2
(2): Redox Reaction of Dichromate and Iodide in Acidic Medium
- Dichromate (Cr2O72−) acts as an oxidizing agent and oxidizes iodide (I−) to iodine (I2) in acidic medium.
- The chromium in dichromate is reduced from Cr6+ to Cr3+.
- The reaction follows the principles of redox balancing, maintaining charge and mass balance.
The balanced redox reaction is:
Cr2O72− + 6I− + 14H+ → 2Cr3+ + 3I2 + 7H2O
Calculate \( \Lambda_m^0 \) for acetic acid and its degree of dissociation (\( \alpha \)) if its molar conductivity is 48.1 \( \Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1} \).
Given that
\( \Lambda_m^0 (\text{HC}) = 426 \, \Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1} \),
\( \Lambda_m^0 (\text{NaCl}) = 126 \, \Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1} \),
\( \Lambda_m^0 (\text{CH}_3\text{COONa}) = 91 \, \Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1} \).
Europium (Eu) resembles Calcium (Ca) in the following ways:
(A). Both are diamagnetic
(B). Insolubility of their sulphates and carbonates in water
(C). Solubility of these metals in liquid NH3
(D). Insolubility of their dichlorides in strong HCI
Choose the correct answer from the options given below:
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 \(P,O,Q\).