Physical Chemistry

Code Examples

import numpy as np
from typing import Dict, Tuple, Callable

class Thermodynamics:
    def __init__(self, delta_h: float, delta_s: float, temp: float = 298.15):
        self.delta_h = delta_h
        self.delta_s = delta_s
        self.temp = temp

    def calculate_delta_g(self) -> float:
        return self.delta_h - self.temp * self.delta_s

    def equilibrium_constant(self, r_gas: float = 8.314) -> float:
        delta_g = self.calculate_delta_g()
        return np.exp(-delta_g / (r_gas * self.temp))

    def spontaneity_check(self) -> str:
        delta_g = self.calculate_delta_g()
        if delta_g < 0:
            return "spontaneous"
        elif delta_g > 0:
            return "non-spontaneous"
        return "equilibrium"

class QuantumChemistry:
    def __init__(self, mass: float = 9.109e-31, planck: float = 6.626e-34):
        self.m = mass
        self.h = planck

    def particle_in_box_energy(self, n: int, box_length: float) -> float:
        return (n**2 * self.h**2) / (8 * self.m * box_length**2)

    def hydrogen_wavefunction(self, n: int, l: int, m: int, r: float) -> complex:
        from scipy.special import spherical_yn, eval_hermite
        from mpmath import sqrt, exp, pi, factorial
        rho = 2 * r / n  # Bohr radius units
        radial = np.exp(-rho/2) * rho**l * eval_hermite(2*l+1, rho)
        normalization = sqrt(2/(n * factorial(2*l+1))) * (2/(n**(3/2)))
        return normalization * radial

    def calculate_spectral_line(self, energy_diff: float) -> float:
        return (energy_diff * 6.626e-34) / (3e8 * 6.626e-25)  # wavelength

thermo = Thermodynamics(delta_h=-285.8, delta_s=163.2)
print(f"ΔG: {thermo.calculate_delta_g():.2f} kJ/mol")
print(f"Keq: {thermo.equilibrium_constant():.2e}")
print(f"Reaction is: {thermo.spontaneity_check()}")

Best Practices

1. Always use consistent units throughout thermodynamic calculations
2. Apply Hess's law and Born-Haber cycles for indirect enthalpy measurements
3. Consider temperature dependence of thermodynamic parameters
4. Use appropriate approximations (Born-Oppenheimer, Hartree-Fock) in quantum calculations
5. Validate kinetic models with experimental rate data
6. Account for non-ideal behavior in concentrated solutions
7. Use partition functions correctly for statistical mechanical calculations
8. Consider selection rules when interpreting spectroscopic data
9. Apply proper error analysis to experimental measurements
10. Use computational chemistry software for complex molecular calculations