(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:
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).