The reaction of K3[Fe(CN)6] with freshly prepared FeSO4 solution produces a dark blue precipitate called Turnbull’s blue. The reaction of K4[Fe(CN)6] with the FeSO4 solution in the complete absence of air produces a white precipitate X, which turns blue in the air. Mixing the FeSO4 solution with NaNO3, followed by slow addition of concentrated H2SO4 through the side of the test tube produces a brown ring.
Precipitate X is
Fe4[Fe(CN)6]3
Fe4[Fe(CN)6]
K2Fe[Fe(CN)6]
KFe[Fe(CN)6]
Step 1: Reaction of K3[Fe(CN)6] with FeSO4:
When K3[Fe(CN)6] reacts with freshly prepared FeSO4 solution, a dark blue precipitate is formed. This precipitate is called Turnbull’s blue. This reaction occurs when Fe2+ ions from FeSO4 interact with [Fe(CN)6]3- ions, resulting in the formation of Turnbull's blue.
The reaction is as follows:
\( K_3[Fe(CN)_6] + FeSO_4 \rightarrow \text{Turnbull’s blue (dark blue precipitate)} \).
Step 2: Reaction of K4[Fe(CN)6] with FeSO4 in the absence of air:
When K4[Fe(CN)6] reacts with FeSO4 solution in the complete absence of air, a white precipitate is initially formed. This precipitate is denoted as X. However, when exposed to air, this white precipitate turns blue, indicating the formation of a complex that contains iron in both +2 and +3 oxidation states. This suggests that X is a compound formed by the interaction of Fe2+ and [Fe(CN)6]4-.
The precipitate X formed is \( K_2Fe[Fe(CN)_6] \), a white precipitate that turns blue upon exposure to air due to the oxidation of Fe2+ to Fe3+.
Step 3: Reaction of FeSO4 with NaNO3 and H2SO4:
When FeSO4 solution is mixed with NaNO3, followed by slow addition of concentrated H2SO4 through the side of the test tube, a brown ring forms at the junction of the two liquids. This brown ring is due to the formation of the complex ion [Fe(H2O)5NO]2+, which is a characteristic test for the presence of Fe2+ ions in solution.
The reaction is as follows:
\( FeSO_4 + NaNO_3 + H_2SO_4 \rightarrow \text{brown ring} \) (due to the formation of [Fe(H2O)5NO]2+).
Conclusion:
The precipitate X formed in the absence of air is identified as \( K_2Fe[Fe(CN)_6] \), which is a white precipitate that turns blue upon exposure to air due to the oxidation of Fe2+ to Fe3+.
Final Answer:
Precipitate X is \( K_2Fe[Fe(CN)_6] \).
Among the following, the brown ring is due to the formation of
\([Fe(NO)_2(SO_4)_2]^{2-}\)
\([Fe(NO)_2(H_2O)_4]^{3+}\)
\([Fe(NO)_4(SO_4)_2]\)
\([Fe(NO)(H_2O)_5]^{2+}\)
Step 1: Reaction of K3[Fe(CN)6] with FeSO4:
When K3[Fe(CN)6] reacts with freshly prepared FeSO4 solution, a dark blue precipitate called Turnbull’s blue is formed. This reaction occurs when Fe2+ ions from FeSO4 react with [Fe(CN)6]3- ions. The resulting precipitate is Turnbull’s blue.
The reaction can be represented as:
\( K_3[Fe(CN)_6] + FeSO_4 \rightarrow \text{Turnbull's blue (dark blue precipitate)} \).
Step 2: Reaction of K4[Fe(CN)6] with FeSO4 in the absence of air:
When K4[Fe(CN)6] reacts with FeSO4 solution in the absence of air, a white precipitate X is formed. This precipitate is identified as \( K_2Fe[Fe(CN)_6] \), which remains white in the absence of air but turns blue when exposed to air due to oxidation of Fe2+ to Fe3+.
The reaction can be written as:
\( K_4[Fe(CN)_6] + FeSO_4 \rightarrow K_2Fe[Fe(CN)_6] \text{ (white precipitate)} \),
which turns blue upon exposure to air.
Step 3: Brown ring test:
When FeSO4 solution is mixed with NaNO3, followed by the slow addition of concentrated H2SO4 through the side of the test tube, a brown ring forms at the interface of the two liquids.
This brown ring is due to the formation of the complex ion \([Fe(NO)(H_2O)_5]^{2+}\), which is characteristic of Fe2+ ions in the presence of nitric acid and sulfuric acid.
The reaction responsible for the brown ring formation is as follows:
\( FeSO_4 + NaNO_3 + H_2SO_4 \rightarrow [Fe(NO)(H_2O)_5]^{2+} \) (brown ring at the interface).
Final Answer:
The brown ring is due to the formation of \([Fe(NO)(H_2O)_5]^{2+}\), which is the characteristic complex ion formed in the brown ring test.

Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 