The compound(s) having structure similar to that of B\( _2 \)H\( _6 \) is/are
The structure of diborane (B2H6) is characterized by two bridging hydrogen atoms between the two boron atoms. This type of bonding is known as a three-center two-electron bond (3c-2e). The two boron atoms and the two bridging hydrogen atoms lie in one plane, while the four terminal hydrogen atoms are above and below this plane. The boron atoms are sp3 hybridized.
Let's examine the structures of the given compounds:
(A) I2Cl6: Iodine(III) chloride exists as a dimer, I2Cl6, in the solid state and in the gas phase at low temperatures. Its structure consists of two planar ICl3 units linked by two bridging chlorine atoms. The iodine atoms are at the center of a square planar arrangement of chlorine atoms. The bridging involves two I–Cl–I three-center four-electron bonds (3c-4e), which is different from the bonding in diborane.
(B) Si2Cl6: Hexachlorodisilane has a structure analogous to ethane (C2H6), with two SiCl3 tetrahedra linked by a Si–Si single bond. There are no bridging chlorine atoms or 3c-2e bonds.
(C) Al2Cl6: Aluminum(III) chloride exists as a dimer, Al2Cl6, in the vapor phase and in the solid state. Its structure consists of two AlCl3 units linked by two bridging chlorine atoms. The aluminum atoms are four-coordinate, and the bridging involves Al–Cl–Al three-center two-electron bonds (3c-2e), similar to the B–H–B bonds in diborane. The aluminum atoms are sp3 hybridized.
(D) Cl2O6: Chlorine dioxide dimer exists as dichlorohexaneoxide. Its structure is O2Cl–O–ClO3, containing a Cl–O–Cl linkage and a perchlorate-like ClO3 group. It does not have a structure similar to diborane with bridging halogen atoms through 3c-2e bonds.
Conclusion: Based on the structural similarities in bonding (bridging halogen atoms through 3c-2e bonds), Al2Cl6 has a structure most similar to that of B2H6.
The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.
The slope of the line is \(0.36 \times 10^2\) s, and the y-intercept is \(1.20\) mol\(^{-1}\) L s. The value of the Michaelis constant (\(K_M\)) is ________ \( \times 10^{-3} \) mol L\(^{-1}\) (in integer). [Note: \(v\) is the initial rate, and \([S]_0\) is the substrate concentration]
Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is ___________ (rounded off to one decimal place).
For the cell reaction, \[ Hg_2Cl_2 (s) + H_2 (1 \, {atm}) \rightarrow 2Hg (l) + 2H^+ (a=1) + 2Cl^- (a=1) \] The standard cell potential is \( \mathcal{E}^0 = 0.2676 \) V, and \( \left(\frac{\partial \mathcal{E}^0}{\partial T}\right)_P = -3.19 \times 10^{-4} \) V K\(^{-1}\). The standard enthalpy change of the reaction (\( \Delta_r H^0 \)) at 298 K is \( -x \) kJ mol\(^{-1}\). The value of \( x \) is ___________ (rounded off to two decimal places). [Given: Faraday constant \( F = 96500 \) C mol\(^{-1}\)]
The mean energy of a molecule having two available energy states at \( \epsilon = 0 \) J and \( \epsilon = 4.14 \times 10^{-21} \) J at 300 K is ___________ \( \times 10^{-21} \) J (rounded off to two decimal places). [Given: Boltzmann constant \( k_B = 1.38 \times 10^{-23} \) J K\(^{-1}\)]
Wavefunctions and energies for a particle confined in a cubic box are \( \psi_{n_x,n_y,n_z} \) and \( E_{n_x,n_y,n_z} \), respectively. The functions \( \phi_1, \phi_2, \phi_3 \), and \( \phi_4 \) are written as linear combinations of \( \psi_{n_x,n_y,n_z} \). Among these functions, the eigenfunction(s) of the Hamiltonian operator for this particle is/are \[ \phi_1 = \frac{1}{\sqrt{2}} \psi_{1,4,1} - \frac{1}{\sqrt{2}} \psi_{2,2,3} \] \[ \phi_2 = \frac{1}{\sqrt{2}} \psi_{1,5,1} + \frac{1}{\sqrt{2}} \psi_{3,3,3} \] \[ \phi_3 = \frac{1}{\sqrt{2}} \psi_{1,3,8} + \frac{1}{\sqrt{2}} \psi_{3,8,1} \] \[ \phi_4 = \frac{1}{2} \psi_{3,3,1} + \frac{\sqrt{3}}{2} \psi_{2,4,1} \]
The correct option(s) of reagents and reaction sequences suitable for carrying out the following transformation is/are
The UV-visible spectrum of [Ni(en)\(_3\)]\(^{2+}\) (en = ethylenediamine) shows absorbance maxima at 11200 cm\(^{-1}\), 18350 cm\(^{-1}\), and 29000 cm\(^{-1}\).
[Given: Atomic number of Ni = 28] The correct match(es) between absorbance maximum and electronic transition is/are
The correct option with regard to the following statements is
(a) Time-independent Schrödinger equation can be exactly solved for Be\(^{2+}\).
(b) For a particle confined in a one-dimensional box of length \( l \) with infinite potential barriers, the trial variation function \( \phi = \left[ \left( \frac{3}{l^3} \right)^{1/2} x \right] \) is not an acceptable trial wavefunction for \( 0 \le x \le l \).
(c) Wavefunctions for system of Fermions must be anti-symmetric with respect to exchange of any two Fermions in the system.
(d) Born-Oppenheimer approximation can be used to separate the vibrational and rotational motion of a molecule.
Compound K displayed a strong band at 1680 cm−1 in its IR spectrum. Its 1H-NMR spectral data are as follows:
δ (ppm):
7.30 (d, J = 7.2 Hz, 2H)
6.80 (d, J = 7.2 Hz, 2H)
3.80 (septet, J = 7.0 Hz, 1H)
2.20 (s, 3H)
1.90 (d, J = 7.0 Hz, 6H)
The correct structure of compound K is: