Explain X-ray diffraction and Hess's Law, and calculate the lattice spacing using Bragg's Law for a given wavelength and diffraction angle.

You're on a roll — e) i) X-ray diffraction is a technique used to determine the atomic and molecular structure of a crystal. It works by observing the interference pattern produced when X-rays are scattered by the atoms in a crystal lattice. ii) Step 1: Identify the given values. Wavelength, = 1.55 × 10^-8 cm Order of diffraction, n = 2 (second-order cone) Angle of diffraction, = 8.92^ Step 2: Use Bragg's Law, which states n = 2d, where d is the spacing between the layers of ions. Rearrange the formula to solve for d: d = (n)/(2) Step 3: Substitute the values and calculate d. d = 2 × (1.55 × 10^-8 cm)2 × (8.92^) d = 1.55 × 10^-8 cm(8.92^) d = 1.55 × 10^-8 cm0.1550 d = 1.0 × 10^-7 cm The spacing between the layers of ions in the crystal is 1.0 × 10^-7 cm. iii) Hess's Law states that the total enthalpy change for a chemical reaction is independent of the pathway taken, provided the initial and final conditions are the same. It means that if a reaction can occur in several steps, the sum of the enthalpy changes for the individual steps is equal to the enthalpy change for the overall reaction. f) Given: Mass of methanol (CH_3OH) = 28 g Mass of ethanol (C_2H_5OH) = 36 g Vapour pressure of pure methanol (P^_methanol) = 32 kPa Vapour pressure of pure ethanol (P^_ethanol) = 20 kPa Step 1: Calculate the molar masses of methanol and ethanol. Molar mass of CH_3OH = (1 × 12.01) + (4 × 1.01) + (1 × 16.00) = 32.05 g/mol Molar mass of C_2H_5OH = (2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 46.08 g/mol (Using approximate integer atomic masses: CH_3OH = 32 g/mol, C_2H_5OH = 46 g/mol) i) Step 2: Calculate the number of moles of each component. Moles of methanol (n_methanol) = mass of methanolmolar mass of methanol = 28 g32.05 g/mol ≈ 0.8736 mol Moles of ethanol (n_ethanol) = mass of ethanolmolar mass of ethanol = 36 g46.08 g/mol ≈ 0.7812 mol Step 3: Calculate the total number of moles. Total moles (n_total) = n_methanol + n_ethanol = 0.8736 mol + 0.7812 mol = 1.6548 mol Step 4: Calculate the mole fraction of each component. Mole fraction of methanol (X_methanol) = n_methanoln_total = 0.8736 mol1.6548 mol ≈ 0.5279 Mole fraction of ethanol (X_ethanol) = n_ethanoln_total = 0.7812 mol1.6548 mol ≈ 0.4721 Mole fraction of methanol: 0.528 Mole fraction of ethanol: 0.472 ii) Step 5: Calculate the partial vapour pressure of each component using Raoult's Law (P_A = X_A P^_A). Partial vapour pressure of methanol (P_methanol) = X_methanol × P^_methanol P_methanol = 0.5279 × 32 kPa ≈ 16.8928 kPa Partial vapour pressure of ethanol (P_ethanol) = X_ethanol × P^_ethanol P_ethanol = 0.4721 × 20 kPa ≈ 9.442 kPa Partial vapour pressure of methanol: 16.9 kPa Partial vapour pressure of ethanol: 9.44 kPa Send me the next one 📸