As an AI, I cannot perform computational chemistry calculations directly. However, I can guide you through the process and help you analyze the results.To calculate the standard enthalpy of formation Hf and the standard entropy S of CH4 g at 298 K, you can use computational chemistry methods such as Density Functional Theory DFT or ab initio methods like Hartree-Fock HF or Mller-Plesset Perturbation Theory MP2 . You will need a suitable software package like Gaussian, ORCA, or NWChem, and a suitable basis set like 6-31G d,p or cc-pVTZ.Here's a general outline of the process:1. Optimize the geometry of CH4 g using the chosen method and basis set. This will provide you with the minimum energy structure.2. Calculate the vibrational frequencies of the optimized structure to ensure that it is a true minimum no imaginary frequencies and to obtain the zero-point vibrational energy ZPVE .3. Calculate the electronic energy of the optimized structure.4. Calculate the Hf and S using the following equations:Hf 298 K = Electronic energy + ZPVE + Enthalpy correctionS 298 K = Sum of translational, rotational, and vibrational entropies5. Compare the calculated values with the experimental values. The experimental values for CH4 g are:Hf 298 K = -74.87 kJ/molS 298 K = 186.3 J/molKPossible explanations for discrepancies between calculated and experimental values:1. Limitations of the computational method: Some methods may not accurately describe the electronic structure of the molecule, leading to discrepancies in the calculated properties.2. Basis set incompleteness: The chosen basis set may not be large enough or flexible enough to accurately describe the wavefunction of the molecule.3. Temperature effects: The calculations are typically performed at 0 K, and the enthalpy and entropy corrections may not fully account for the temperature dependence of these properties.4. Neglect of relativistic effects: For light elements like carbon and hydrogen, relativistic effects are usually negligible. However, for heavier elements, these effects can become significant and may need to be considered.To improve the accuracy of the calculated values, you can try using higher-level methods, larger basis sets, or including additional corrections such as solvation effects or higher-order electron correlation effects.