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Biochemistry/Interactive Tools/pH & Buffer Calculator

pH & Buffer Calculator

Interactive Tool -- Visualize amino acid titration curves, buffer capacity as a function of pH, and compare common biochemical buffer systems. The Henderson-Hasselbalch equation is applied to calculate buffer composition at physiological pH.

Introduction to pH and Buffers

Biological systems require precise pH control. Most enzymes have narrow pH optima, and even small deviations can dramatically alter protein structure, enzyme activity, and metabolic pathways. Blood pH is maintained between 7.35 and 7.45 -- a deviation of just 0.3 units can be life-threatening.

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They consist of a weak acid and its conjugate base (or a weak base and its conjugate acid). The effectiveness of a buffer depends on the relationship between its $\text{p}K_a$ and the desired pH.

Key Biochemical Buffer Systems

Bicarbonate buffer: The primary extracellular buffer in blood ($\text{H}_2\text{CO}_3/\text{HCO}_3^-$, $\text{p}K_a = 6.35$)
Phosphate buffer: Important intracellular buffer ($\text{H}_2\text{PO}_4^-/\text{HPO}_4^{2-}$, $\text{p}K_a = 7.20$)
Protein buffers: Histidine residues ($\text{p}K_a \approx 6.0$) provide buffering near physiological pH
Tris buffer: Widely used laboratory buffer ($\text{p}K_a = 8.07$ at 25 degrees C)

Key Equations

Henderson-Hasselbalch Equation

The fundamental equation relating pH to the ratio of conjugate base to weak acid:

$$\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}$$

When $[\text{A}^-] = [\text{HA}]$, the log term is zero and $\text{pH} = \text{p}K_a$. A buffer is most effective within $\pm 1$ pH unit of its $\text{p}K_a$ (where the ratio of conjugate base to acid is between 1:10 and 10:1).

Buffer Capacity

Buffer capacity ($\beta$) quantifies a buffer's resistance to pH change:

$$\beta = 2.303\left(\frac{K_a[\text{H}^+]C}{(K_a + [\text{H}^+])^2}\right)$$

Where $C$ is the total buffer concentration, $K_a$ is the acid dissociation constant, and $[\text{H}^+]$ is the hydrogen ion concentration. Buffer capacity is maximal when $\text{pH} = \text{p}K_a$ (i.e., when $[\text{H}^+] = K_a$), giving$\beta_{\max} = 2.303 \cdot C/4$.

Isoelectric Point of Amino Acids

For amino acids with no ionizable side chain, the isoelectric point is the average of the two $\text{p}K_a$ values:

$$\text{pI} = \frac{\text{p}K_{a1} + \text{p}K_{a2}}{2}$$

At the isoelectric point, the amino acid carries no net charge and exists predominantly as the zwitterion. For amino acids with ionizable side chains, the pI is the average of the two $\text{p}K_a$ values that bracket the zwitterionic form.

Python: pH & Buffer Simulator

This interactive simulator generates three visualizations: a glycine titration curve showing both ionization stages, a buffer capacity plot comparing common buffers, and a speciation diagram for biochemical buffer systems. The Henderson-Hasselbalch equation is used to calculate buffer composition at physiological pH (7.4).

pH & Buffer Calculator

Python

Titration curves, buffer capacity analysis, and Henderson-Hasselbalch calculations for biochemical buffers

ph_buffer.py180 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# ========================================
# pH & Buffer Calculator
# ========================================

fig, axes = plt.subplots(1, 3, figsize=(18, 6))
fig.patch.set_facecolor('#0a0a0a')
fig.suptitle('pH & Buffer Analysis', fontsize=16, color='#6ee7b7', fontweight='bold', y=1.02)

for ax in axes.flat:
    ax.set_facecolor('#0a0a0a')
    ax.tick_params(colors='white')
    ax.xaxis.label.set_color('white')
    ax.yaxis.label.set_color('white')
    ax.title.set_color('#6ee7b7')
    for spine in ax.spines.values():
        spine.set_color('#333')

# ---- Plot 1: Amino acid titration curve (Glycine) ----
# Glycine: pKa1 = 2.34 (\u03b1-COOH), pKa2 = 9.60 (\u03b1-NH3+)
pKa1 = 2.34
pKa2 = 9.60

# Simulate adding base (equivalents of OH-) from 0 to 2
equiv_OH = np.linspace(0, 2, 1000)
pH_values = []

for eq in equiv_OH:
    # Two-stage titration
    if eq < 0.001:
        pH_values.append(pKa1 - 1.0)
    elif eq < 1.0:
        # First buffer region: HA2+/HA (\u03b1-COOH ionization)
        ratio = eq / (1.0 - eq)
        pH_values.append(pKa1 + np.log10(ratio))
    elif abs(eq - 1.0) < 0.001:
        # Isoelectric point
        pH_values.append((pKa1 + pKa2) / 2)
    elif eq < 2.0:
        # Second buffer region: HA/A- (\u03b1-NH3+ ionization)
        ratio = (eq - 1.0) / (2.0 - eq)
        pH_values.append(pKa2 + np.log10(ratio))
    else:
        pH_values.append(pKa2 + 1.0)

pH_values = np.array(pH_values)
pH_values = np.clip(pH_values, 0, 14)

axes[0].plot(equiv_OH, pH_values, color='#10b981', linewidth=2.5)
axes[0].axhline(y=pKa1, color='#34d399', linestyle='--', alpha=0.5, linewidth=1)
axes[0].axhline(y=pKa2, color='#6ee7b7', linestyle='--', alpha=0.5, linewidth=1)
axes[0].axhline(y=(pKa1+pKa2)/2, color='#fbbf24', linestyle=':', alpha=0.5, linewidth=1)

axes[0].annotate(f'pKa1 = {pKa1}', xy=(0.5, pKa1), fontsize=9, color='#34d399',
                 xytext=(0.15, pKa1+0.8), arrowprops=dict(arrowstyle='->', color='#34d399', lw=1.2))
axes[0].annotate(f'pKa2 = {pKa2}', xy=(1.5, pKa2), fontsize=9, color='#6ee7b7',
                 xytext=(1.55, pKa2-1.0), arrowprops=dict(arrowstyle='->', color='#6ee7b7', lw=1.2))
axes[0].annotate(f'pI = {(pKa1+pKa2)/2:.2f}', xy=(1.0, (pKa1+pKa2)/2), fontsize=9, color='#fbbf24',
                 xytext=(0.2, (pKa1+pKa2)/2+1.5), arrowprops=dict(arrowstyle='->', color='#fbbf24', lw=1.2))

# Shade buffer regions
axes[0].axvspan(0.1, 0.9, alpha=0.08, color='#10b981')
axes[0].axvspan(1.1, 1.9, alpha=0.08, color='#6ee7b7')
axes[0].text(0.5, 1.2, 'Buffer\nRegion 1', ha='center', fontsize=8, color='#34d399', alpha=0.7)
axes[0].text(1.5, 12.5, 'Buffer\nRegion 2', ha='center', fontsize=8, color='#6ee7b7', alpha=0.7)

axes[0].set_xlabel('Equivalents of OH\u207b added', fontsize=11)
axes[0].set_ylabel('pH', fontsize=11)
axes[0].set_title('Glycine Titration Curve', fontsize=13, fontweight='bold')
axes[0].set_ylim(0, 14)
axes[0].set_xlim(0, 2)
axes[0].grid(True, alpha=0.15, color='gray')

# ---- Plot 2: Buffer capacity vs pH ----
# Buffer capacity: \u03b2 = 2.303 * (Ka * [H+] * C) / (Ka + [H+])^2
C = 0.1  # 100 mM total buffer concentration
pH_range = np.linspace(1, 13, 500)
H_range = 10**(-pH_range)

# Show buffer capacity for three pKa values
buffer_pKas = [('Acetate', 4.76, '#10b981'), ('Phosphate', 7.20, '#34d399'), ('Tris', 8.07, '#6ee7b7')]

for name, pKa, color in buffer_pKas:
    Ka = 10**(-pKa)
    beta = 2.303 * (Ka * H_range * C) / (Ka + H_range)**2
    axes[1].plot(pH_range, beta * 1000, color=color, linewidth=2.5, label=f'{name} (pKa={pKa})')
    # Mark the peak
    peak_idx = np.argmax(beta)
    axes[1].plot(pH_range[peak_idx], beta[peak_idx]*1000, 'o', color=color, markersize=6)

axes[1].axvline(x=7.4, color='#f87171', linestyle='--', alpha=0.4, linewidth=1, label='pH 7.4 (physiol.)')
axes[1].set_xlabel('pH', fontsize=11)
axes[1].set_ylabel('Buffer Capacity \u03b2 (mM/pH unit)', fontsize=11)
axes[1].set_title('Buffer Capacity vs pH', fontsize=13, fontweight='bold')
axes[1].legend(facecolor='#1a1a1a', edgecolor='#333', labelcolor='white', fontsize=9)
axes[1].set_xlim(2, 12)
axes[1].grid(True, alpha=0.15, color='gray')

# ---- Plot 3: Common biochemical buffers comparison ----
buffers = [
    ('Acetate', 4.76, '#10b981'),
    ('Bicarbonate', 6.35, '#059669'),
    ('Phosphate', 7.20, '#34d399'),
    ('Tris', 8.07, '#6ee7b7'),
]

pH_range2 = np.linspace(2, 12, 500)
bar_positions = []
bar_colors = []
bar_labels = []

for name, pKa, color in buffers:
    Ka = 10**(-pKa)
    H_vals = 10**(-pH_range2)
    # Fraction of conjugate base: [A-]/C = Ka/(Ka + [H+])
    frac_base = Ka / (Ka + H_vals)
    axes[2].plot(pH_range2, frac_base, color=color, linewidth=2.5, label=f'{name} (pKa={pKa})')
    # Mark pKa point (fraction = 0.5)
    axes[2].plot(pKa, 0.5, 's', color=color, markersize=7, zorder=5)
    # Shade effective buffer range (pKa +/- 1)
    axes[2].axvspan(pKa-1, pKa+1, alpha=0.04, color=color)

axes[2].axhline(y=0.5, color='gray', linestyle=':', alpha=0.3)
axes[2].axvline(x=7.4, color='#f87171', linestyle='--', alpha=0.4, linewidth=1, label='pH 7.4')
axes[2].set_xlabel('pH', fontsize=11)
axes[2].set_ylabel('Fraction as conjugate base [A\u207b]/C', fontsize=11)
axes[2].set_title('Biochemical Buffer Systems', fontsize=13, fontweight='bold')
axes[2].legend(facecolor='#1a1a1a', edgecolor='#333', labelcolor='white', fontsize=8, loc='upper left')
axes[2].set_xlim(2, 12)
axes[2].set_ylim(-0.05, 1.05)
axes[2].grid(True, alpha=0.15, color='gray')

plt.tight_layout(pad=3.0)
plt.savefig('ph_buffer.png', dpi=150, bbox_inches='tight', facecolor='#0a0a0a')
plt.show()

# ---- Summary Output ----
print("=" * 55)
print("  pH & BUFFER CALCULATOR RESULTS")
print("=" * 55)

print(f"\n--- Glycine Titration ---")
print(f"  pKa1 (\u03b1-COOH) = {pKa1}")
print(f"  pKa2 (\u03b1-NH3+) = {pKa2}")
print(f"  Isoelectric point (pI) = ({pKa1} + {pKa2}) / 2 = {(pKa1+pKa2)/2:.2f}")
print(f"  Buffer region 1: pH {pKa1-1:.2f} to {pKa1+1:.2f}")
print(f"  Buffer region 2: pH {pKa2-1:.2f} to {pKa2+1:.2f}")

print(f"\n--- Henderson-Hasselbalch at pH 7.4 ---")
print(f"  pH = pKa + log([A\u207b]/[HA])")
print()
target_pH = 7.4
for name, pKa, _ in buffers:
    log_ratio = target_pH - pKa
    ratio = 10**log_ratio
    frac_base = ratio / (1 + ratio)
    frac_acid = 1 / (1 + ratio)
    print(f"  {name} (pKa = {pKa}):")
    print(f"    log([A\u207b]/[HA]) = {log_ratio:+.2f}")
    print(f"    [A\u207b]/[HA] = {ratio:.2f}")
    print(f"    {frac_base*100:.1f}% conjugate base, {frac_acid*100:.1f}% acid")
    if abs(target_pH - pKa) <= 1:
        print(f"    \u2713 EFFECTIVE buffer at pH 7.4 (within pKa \u00b1 1)")
    else:
        print(f"    \u2717 POOR buffer at pH 7.4 (outside pKa \u00b1 1)")
    print()

print(f"--- Buffer Capacity (C = {C*1000:.0f} mM) ---")
for name, pKa, _ in buffers:
    Ka = 10**(-pKa)
    H = 10**(-target_pH)
    beta = 2.303 * (Ka * H * C) / (Ka + H)**2
    beta_max = 2.303 * C / 4  # maximum at pH = pKa
    print(f"  {name}: \u03b2 at pH 7.4 = {beta*1000:.3f} mM/pH unit "
          f"({beta/beta_max*100:.1f}% of max \u03b2)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

How to Use This Tool

Understanding the Plots

Glycine Titration Curve

Shows how pH changes as base (OH$^-$) is progressively added to glycine. The two plateaus correspond to the two buffer regions (near $\text{p}K_{a1}$ and$\text{p}K_{a2}$). The inflection point between them is the isoelectric point (pI).

Buffer Capacity

Each curve peaks at its $\text{p}K_a$, where the buffer is most effective. The red dashed line marks physiological pH (7.4). Phosphate buffer has the highest capacity near pH 7.4 because its $\text{p}K_a$ (7.20) is closest.

Buffer Speciation

Shows the fraction of each buffer present as conjugate base across the pH range. The square markers at 0.5 indicate the $\text{p}K_a$. Shaded regions show the effective buffering range ($\text{p}K_a \pm 1$).

Try Modifying the Code

Change amino acid: Modify pKa1 and pKa2 to simulate different amino acids (e.g., aspartate: 2.09, 3.86, 9.82).
Add buffers: Extend the buffers list with new (name, pKa, color) tuples.
Change concentration: Modify C to see how total buffer concentration affects capacity.
Target different pH: Change target_pH to calculate Henderson-Hasselbalch ratios at a different pH value.
Add a third pKa: For amino acids with ionizable side chains, extend the titration model with a third equilibrium.

Common Biochemical Buffers

Choosing the right buffer for a biochemical experiment requires matching the buffer's $\text{p}K_a$ to the desired working pH. A buffer is effective within approximately $\pm 1$ pH unit of its $\text{p}K_a$.

Buffer	$\text{p}K_a$ (25 degrees C)	Effective Range	Common Use
Acetate	4.76	3.8 -- 5.8	Protein purification, gel electrophoresis
MES	6.15	5.5 -- 6.7	Cell culture, electrophoresis
Bicarbonate	6.35	5.4 -- 7.4	Blood buffer, cell culture media
PIPES	6.76	6.1 -- 7.5	Cell biology, organelle isolation
Phosphate	7.20	6.2 -- 8.2	General biochemistry, PBS
HEPES	7.48	6.8 -- 8.2	Cell culture, structural biology
Tris	8.07	7.0 -- 9.0	Molecular biology, TBE/TAE gels
Glycine	9.60	8.6 -- 10.6	SDS-PAGE running buffer

Note: Good's buffers (MES, PIPES, HEPES, etc.) were specifically designed for biological research. They have minimal interaction with metal ions, minimal membrane permeability, and negligible effects on biochemical reactions -- making them superior to traditional inorganic buffers for many applications.

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