Which of the following statement is true with respect to H\(_2\)O, NH\(_3\) and CH\(_4\)?
(A) The central atoms of all the molecules are sp\(^3\) hybridized.
(B) The H–O–H, H–N–H and H–C–H angles in the above molecules are 104.5°, 107.5° and 109.5° respectively.
(C) The increasing order of dipole moment is CH\(_4\)<NH\(_3\)<H\(_2\)O.
(D) Both H\(_2\)O and NH\(_3\) are Lewis acids and CH\(_4\) is a Lewis base.
(E) A solution of NH\(_3\) in H\(_2\)O is basic. In this solution NH\(_3\) and H\(_2\)O act as Lowry-Bronsted acid and base respectively.
Let's analyze the given options:
The central atoms in all three molecules (H\(_2\)O, NH\(_3\), CH\(_4\)) are sp\(^3\) hybridized. This is true because the oxygen, nitrogen, and carbon atoms form single bonds with surrounding atoms, which requires sp\(^3\) hybridization in each case.
The bond angles in H\(_2\)O, NH\(_3\), and CH\(_4\) are 104.5°, 107.5°, and 109.5°, respectively. This is correct: - H\(_2\)O has an angle of 104.5° due to lone pair repulsion. - NH\(_3\) has 107.5°, with one lone pair on nitrogen. - CH\(_4\) has 109.5°, as it is tetrahedral with no lone pairs.
The increasing order of dipole moment is CH\(_4\) < NH\(_3\) < H\(_2\)O. This is true because: - CH\(_4\) has no dipole moment due to its symmetrical tetrahedral shape. - NH\(_3\) has a dipole moment due to the lone pair on nitrogen. - H\(_2\)O has the highest dipole moment because of its bent shape and the high electronegativity of oxygen.
Both H\(_2\)O and NH\(_3\) are Lewis acids and CH\(_4\) is a Lewis base. This statement is incorrect. H\(_2\)O and NH\(_3\) act as Lewis bases (donors), not acids. CH\(_4\) is a Lewis base, as it has a pair of electrons on the carbon atom that can donate. Therefore, this statement is false.
A solution of NH\(_3\) in H\(_2\)O is basic, and in this solution, NH\(_3\) acts as a base and H\(_2\)O acts as an acid. This is true because NH\(_3\) accepts a proton from water to form NH\(_4^+\) and OH\(^-\), making the solution basic.
The correct answer is \( \boxed{(1)} \), which corresponds to **A, B, and C only** being true.
Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is (are):
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to:
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).