To determine the accuracy of Statements I and II, let's analyze each one:
Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of H₂ gas.
The reaction of propyne (C₃H₄) with sodium (Na) involves the acidic hydrogen present in the terminal alkyne. The reaction is:
C₃H₃ - H + Na → C₃H₃Na + 1/2 H₂
In this reaction, one mole of propyne reacts with sodium to form sodium propyne and release half a mole of hydrogen gas. Therefore, Statement I is correct.
Statement II: Four g of propyne reacts with NaNH₂ to liberate NH₃ gas which occupies 224 mL at STP.
First, calculate the amount of propyne:
When propyne reacts with NaNH₂, the hydrogen atom is replaced, and NH₃ gas is formed. According to stoichiometry, 1 mole of NaNH₂ liberates 1 mole of NH₃:
C₃H₄ + NaNH₂ → C₃H₃Na + NH₃
The molar volume of gas at STP is 22.4 L/mol. Hence, the volume occupied by 0.1 mol NH₃ at STP is:
The calculated volume of NH₃ is 2.24 L, not 224 mL. Hence, Statement II is incorrect.
In conclusion, the correct choice is: Statement I is correct but Statement II is incorrect.
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to: