When $Cu ^{2+}$ ion is treated with $KI$, a white precipitate, $X$ appears in solution The solution is titrated with sodium thiosulphate, the compound $Y$ is formed $X$ and $Y$ respectively are
When \( \text{Cu}^{2+} \) reacts with KI, the following reactions occur:
\[ \text{Cu}^{2+} + 2\text{KI} \rightarrow \text{CuI}_2 \downarrow + 2K^+ \]
\[ \text{CuI}_2 \text{(White)} \xrightarrow{\text{Na}_2\text{S}_2\text{O}_3} \text{CuI} + \text{Na}_2\text{S}_4\text{O}_6 \]
Thus, the white precipitate \( X = \text{CuI}_2 \) and the compound formed is \( Y = \text{Na}_2\text{S}_4\text{O}_6 \).
The reaction with sodium thiosulfate (\( \text{Na}_2\text{S}_2\text{O}_3 \)) helps dissolve the precipitate and form a soluble complex, converting copper(I) into copper(I) iodide.
This results in the formation of a colorless solution, making the reaction useful in quantitative analysis and complexation studies.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: