r"""
The Henderson-Hasselbalch equation and buffer design
======================================================

Hasselbalch's logarithmic form of Henderson's buffer relationship,

.. math::

   \mathrm{pH} = pK_a + \log_{10}\frac{[A^-]}{[HA]},

evaluated with
:func:`~chemistrykit.solutions.systems.acid_base.henderson_hasselbalch_ph`
and inverted by
:meth:`~chemistrykit.solutions.systems.acid_base.Buffer.from_target_ph`
to design an acetate buffer of fixed total concentration for any target
pH. The equation is checked against the exact equilibrium pH of the same
mixture.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from chemistrykit.solutions.systems.acid_base import Buffer, henderson_hasselbalch_ph

pKa = 4.76  # acetic acid
ratios = np.logspace(-2, 2, 200)
pH_hh = [henderson_hasselbalch_ph(pKa, base_conc=r, acid_conc=1.0) for r in ratios]

fig, ax = plt.subplots(figsize=(7, 5))
ax.semilogx(ratios, pH_hh, color="steelblue")
ax.axhline(pKa, color="gray", linestyle=":", label="pH = pKa at [A-]/[HA] = 1")
ax.axvspan(0.1, 10.0, color="steelblue", alpha=0.1, label="useful buffer range, pKa ± 1")
ax.set_xlabel("[A-]/[HA]")
ax.set_ylabel("pH")
ax.set_title("Henderson-Hasselbalch equation, acetate buffer")
ax.legend()
fig.tight_layout()

# %%
# Designing a 0.20 M acetate buffer at pH 5.00, and plotting the required
# composition for every target pH:

buf = Buffer.from_target_ph(pKa=pKa, target_pH=5.0, total_conc=0.20)
print(f"Buffer: [HA] = {buf.acid_conc:.4f} M, [A-] = {buf.base_conc:.4f} M, pH = {buf.pH():.4f}")

pH_targets = np.linspace(pKa - 1.0, pKa + 1.0, 100)
base_fraction = [Buffer.from_target_ph(pKa=pKa, target_pH=pH, total_conc=0.20).base_conc / 0.20 for pH in pH_targets]

fig2, ax2 = plt.subplots(figsize=(7, 5))
ax2.plot(pH_targets, base_fraction, color="darkorange")
ax2.axvline(pKa, color="gray", linestyle=":", label="pH = pKa")
ax2.set_xlabel("target buffer pH")
ax2.set_ylabel("fraction as conjugate base, [A-]/C")
ax2.set_title("Buffer composition from Henderson-Hasselbalch")
ax2.legend()
fig2.tight_layout()

plt.show()