For borax bead test:
• In the oxidizing flame, metal ions form metaborates, which produce characteristic colours.
• The observed colour is a key indicator of the specific metal ion present.
\(Cu(BO_2)_2\)
\(Cu_3B_2\)
Borax Bead Test:
1. Definition: The borax bead test is a qualitative test used to identify metal ions based on the colour imparted to the bead in the oxidizing or reducing flame.
In this test, borax (\(\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O}\)) decomposes to form sodium metaborate (\(\text{NaBO}_2\)) and boric anhydride (\(\text{B}_2\text{O}_3\)) when heated:
\[\text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3.\]
2. Reaction with \(\text{CuSO}_4\): Copper ions react with boric anhydride (\(\text{B}_2\text{O}_3\)) to form copper metaborate (\(\text{Cu(BO}_2)_2\)) in the oxidizing flame:
\[\text{CuSO}_4 + \text{B}_2\text{O}_3 \rightarrow \text{Cu(BO}_2)_2 + \text{SO}_3.\]
3.Observation: \(\text{Cu(BO}_2)_2\) is responsible for the blue-green colour observed in the oxidizing flame.
Final Answer: \((3)\) \(\mathbf{Cu(BO}_2)_2\).
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32