Redox Reactions

Cu is unstable in aqueous solution and undergoes disproportionation: This makes Cu salts unstable due to their tendency to convert into Cu and Cu .

Balancing the redox reaction involves ensuring the number of atoms and the charges are equal on both sides.
The oxidation state of manganese in is +7, and it is reduced to +2 in .
The number of electrons transferred is 5.
Similarly, the oxalate ion is oxidized to , requiring 4 protons ( ) to balance the equation.
Thus, the correct coefficients for and are 5 and 4, respectively.

In this reaction, potassium nitrate reacts with potassium hydroxide, resulting in the formation of manganese dioxide ( ) as the black solid.
Upon heating, this black solid reacts further to form potassium permanganate ( ) and potassium manganate ( ). The correct sequence of compounds is: A: , B: , C: .
Thus, the correct answer is (b).

Positron emission occurs when a proton in the nucleus decays to form a neutron, releasing a positron in the process. Therefore, the correct nuclear reaction is . Thus, the correct answer is (d).

In the reaction, lead in PbS is reduced from +2 to 0, meaning that it gains electrons, which is the characteristic of a reduction process. Similarly, oxygen is reduced as it gains electrons, while sulphur in PbS is oxidized, as it loses electrons (its oxidation state increases from -2 to 0). Therefore, the statement that both lead and sulphur are oxidized is false because, in fact, lead is reduced, not oxidized.

Thus, the correct interpretation is that lead is reduced and sulphur is oxidized in this reaction.

To produce carbon, the combustion of methane should be carried out in excess oxygen. When methane (CH₄) undergoes complete combustion with excess oxygen, it forms carbon dioxide (CO₂) and water (H₂O). However, if there is insufficient oxygen, incomplete combustion may occur, leading to the formation of carbon monoxide (CO) or even elemental carbon (C). To ensure that carbon is produced during combustion, the reaction needs to be controlled, and typically, limiting oxygen in a controlled manner can yield carbon (as soot) rather than CO₂.

Therefore, to avoid the formation of CO₂ and produce carbon (soot), the combustion of methane must be done with limited oxygen, not excess oxygen.

The relationship between the half-life and the rate constant is given by: Substituting , Therefore, the rate constant is , and the correct answer is (b).