Solid State And Instrumental Analysis Mock Tests

X-ray diffraction analysis of a cubic crystal using Cu Kα radiation (λ = 154 pm) reveals a diffraction peak at 2θ = 43.3° for the (111) reflection. Assuming first-order diffraction (n = 1) and θ is the Bragg angle, what is the lattice parameter a of the cubic unit cell? (Use Bragg's law: nλ = 2d sin θ, and for a cubic lattice: d_hkl = a/√(h² + k² + l²).)

Titanium dioxide (TiO₂) crystallizes in the rutile structure, which can be described as a body-centred tetragonal lattice. In this structure, each Ti⁴⁺ ion is surrounded by 6 O²⁻ ions, and each O²⁻ ion is bonded to 3 Ti⁴⁺ ions. What are the coordination numbers of Ti and O in the rutile structure, and how many formula units of TiO₂ are present per unit cell? (The unit cell contains Ti atoms at the corners and body centre, and O atoms at specific positions within the cell.)

In the mass spectrum of 2-pentanone (CH₃COCH₂CH₂CH₃), the McLafferty rearrangement produces a characteristic fragment ion. What is the m/z value of the McLafferty rearrangement peak, and what neutral molecule is lost? (The McLafferty rearrangement requires a carbonyl compound with a gamma hydrogen atom relative to the carbonyl group. It involves a six-membered cyclic transition state with transfer of the gamma hydrogen to the carbonyl oxygen, followed by cleavage of the alpha-beta bond.)

The FTIR spectrum of acetone (CH₃COCH₃) shows a strong absorption at approximately 1715 cm⁻¹. This band corresponds to:

The IR spectrum of a molecule shows a strong absorption band at 1715 cm⁻¹ and a characteristic C-H stretch at 2720 cm⁻¹. The molecule is most likely:

The Cramer's rule is applied to solve simultaneous linear equations in various areas of chemistry. In the context of solving for the composition of a binary mixture using absorbance measurements at two wavelengths, the system of equations is: A₁ = ε₁ₐcₐl + ε₁ᵦcᵦl and A₂ = ε₂ₐcₐl + ε₂ᵦcᵦl. Using Cramer's rule, the concentration cₐ is given by (where Δ = ε₁ₐε₂ᵦ - ε₁ᵦε₂ₐ):

In high-performance liquid chromatography (HPLC) using a reversed-phase column (C₁₈ stationary phase and polar mobile phase such as methanol/water), which of the following compounds would have the longest retention time? (Consider the hydrophobic interactions between the non-polar C₁₈ stationary phase and the analytes.)

Sodium chloride (NaCl) crystallises in a face-centred cubic lattice. What is the coordination number of Na⁺ and Cl⁻ ions, respectively, and how many formula units of NaCl are present per unit cell?