Step 1: Reactions of Phosphorus with Alkali - White phosphorus (\(\text{P}_4\)) reacts with \(\text{NaOH}\) and water to give phosphine (\(\text{PH}_3\)) and hypophosphite (\(\text{NaH}_2\text{PO}_2\)).
Step 2: Reaction with Copper and Acid - Phosphine can further react under specific conditions (involving \(\text{Cu}\) and \(\text{H}_2\text{SO}_4\)) to produce copper phosphide, \(\text{Cu}_3\text{P}_2\). Hence, the final product is (copper phosphide), \(\text{Cu}_3\text{P}_2\).
For a reaction, \[ {N}_2{O}_5(g) \rightarrow 2{NO}_2(g) + \frac{1}{2} {O}_2(g) \] in a constant volume container, no products were present initially. The final pressure of the system when 50% of the reaction gets completed is:
In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage composition of chlorine in the compound is ___________%. [Given: Molar mass in g mol\(^{-1}\) of Ag = 108, Cl = 35.5]
In Bohr model of hydrogen atom, if the difference between the radii of \( n^{th} \) and\( (n+1)^{th} \)orbits is equal to the radius of the \( (n-1)^{th} \) orbit, then the value of \( n \) is:
Given the function:
\[ f(x) = \frac{2x - 3}{3x - 2} \]
and if \( f_n(x) = (f \circ f \circ \ldots \circ f)(x) \) is applied \( n \) times, find \( f_{32}(x) \).
For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).
If the real-valued function
\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?