Phthalimide undergoes the following transformations:
In the presence of KOH, the acidic hydrogen of phthalimide is removed, forming the phthalimide anion.
The phthalimide anion then reacts with benzyl chloride via an S\(_N2\) reaction, leading to the formation of product 'P'.
In product 'P':
The benzene ring contributes \(3 \, \pi\)-bonds.
Each carbonyl group (C=O) provides \(2 \, \pi\)-bonds, giving a total of \(4 \, \pi\)-bonds for both groups.
The benzyl group attached to nitrogen contributes \(1\) additional \(\pi\)-bond.
Thus, the total number of \(\pi\)-bonds in product 'P' is:
\[3 + 2 + 2 + 1 = 8\]
Consider the gas phase reaction: \[ CO + \frac{1}{2} O_2 \rightleftharpoons CO_2 \] At equilibrium for a particular temperature, the partial pressures of \( CO \), \( O_2 \), and \( CO_2 \) are found to be \( 10^{-6} \, {atm} \), \( 10^{-6} \, {atm} \), and \( 16 \, {atm} \), respectively. The equilibrium constant for the reaction is ......... \( \times 10^{10} \) (rounded off to one decimal place).
Molten steel at 1900 K having dissolved hydrogen needs to be vacuum degassed. The equilibrium partial pressure of hydrogen to be maintained to achieve 1 ppm (mass basis) of dissolved hydrogen is ......... Torr (rounded off to two decimal places). Given: For the hydrogen dissolution reaction in molten steel \( \left( \frac{1}{2} {H}_2(g) = [{H}] \right) \), the equilibrium constant (expressed in terms of ppm of dissolved H) is: \[ \log_{10} K_{eq} = \frac{1900}{T} + 2.4 \] 1 atm = 760 Torr.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: