aqueous neutral
aqueous acidic
both aqueous acidic and neutral
both aqueous acidic and faintly alkaline
The reaction of permanganate \( (\text{MnO}_4^-) \) with thiosulphate \( (\text{S}_2\text{O}_3^{2-}) \) depends on the pH of the medium. Permanganate can be reduced to different manganese species depending on the conditions.
In a neutral or weakly alkaline medium, permanganate is reduced to manganese(IV) oxide \( (\text{MnO}_2) \):
\( \text{MnO}_4^-\text{(aq)} + 2\text{H}_2\text{O(l)} + 3e^- \rightarrow \text{MnO}_2\text{(s)} + 4\text{OH}^-\text{(aq)} \)
In this reaction, the oxidation state of manganese changes from +7 in \( \text{MnO}_4^- \) to +4 in \( \text{MnO}_2 \), a change of 3 units.
In an acidic medium, permanganate is reduced to manganese(II) ions \( (\text{Mn}^{2+}) \):
\( \text{MnO}_4^-\text{(aq)} + 8\text{H}^+\text{(aq)} + 5e^- \rightarrow \text{Mn}^{2+}\text{(aq)} + 4\text{H}_2\text{O(l)} \)
Here, the oxidation state of manganese changes from +7 to +2, a change of 5 units.
Since the question specifies a change in oxidation state of 3, the reaction must be occurring in a neutral or weakly alkaline medium.
The net current flowing in the given circuit is ___ A.
If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to .