Adsorption Capacity Calculator

Calculator inputs

Sample name

Initial concentration, C0 (mg/L)

Equilibrium concentration, Ce (mg/L)

Solution volume, V (L)

Adsorbent mass, m (g)

Contact time (min)

Flow rate (L/min)

Temperature (°C)

pH

Langmuir qmax (mg/g)

Langmuir KL (L/mg)

Freundlich KF

Freundlich n

Run notes

Provide model constants only when you want Langmuir and Freundlich comparison outputs.

Example data table

Sample	C0 (mg/L)	Ce (mg/L)	V (L)	m (g)	qe (mg/g)	Removal (%)
Carbon A	120	18	0.75	1.40	54.64	85.00
Zeolite B	95	30	1.00	2.00	32.50	68.42
Biochar C	150	25	0.50	0.90	69.44	83.33

Formula used

Experimental adsorption capacity: q_e = ((C₀ - C_e) × V) / m

Here, C0 is initial concentration in mg/L, Ce is equilibrium concentration in mg/L, V is solution volume in liters, and m is adsorbent mass in grams.

Removal efficiency: Removal % = ((C₀ - C_e) / C₀) × 100

Distribution coefficient: Kd = ((C₀ - C_e) / C_e) × (V / m)

Langmuir estimate: q_e,L = (q_max × K_L × C_e) / (1 + K_L × C_e)

Langmuir separation factor: R_L = 1 / (1 + K_L × C₀)

Freundlich estimate: q_e,F = K_F × C_e^1/n

These equations help compare measured capacity with common equilibrium model predictions for screening and design work.

How to use this calculator

Enter a sample name to identify the test run.
Fill in initial and equilibrium concentrations from your lab data.
Provide treated solution volume and dry adsorbent mass.
Add optional time, flow, temperature, and pH values for operational context.
Enter Langmuir or Freundlich constants only when model comparison is needed.
Press the calculate button to show results above the form.
Use the CSV button for spreadsheet work or the PDF button for reporting.

Frequently asked questions

1. What does adsorption capacity mean?

Adsorption capacity shows how much solute a sorbent retains per gram. It is usually expressed as mg/g and helps compare adsorbent performance under similar operating conditions.

2. Why must Ce stay below C0?

A higher equilibrium concentration than the starting concentration implies no net removal and usually signals input, sampling, or unit errors. The calculator blocks that condition for consistency.

3. When should I use Langmuir constants?

Use Langmuir inputs when your system follows monolayer adsorption assumptions and you want a theoretical equilibrium estimate. They are useful for model fitting and quick benchmarking.

4. When is the Freundlich model helpful?

Freundlich is helpful for heterogeneous surfaces and non-ideal adsorption behavior. It often fits empirical test data well across moderate concentration ranges.

5. What units should I keep consistent?

Keep concentration in mg/L, volume in liters, and adsorbent mass in grams. Mixing units changes the calculated capacity and makes comparisons unreliable.

6. Why is Kd undefined when Ce equals zero?

The distribution coefficient divides by equilibrium concentration. When Ce is zero, the denominator becomes zero, so the value tends toward an undefined or extremely large limit.

7. Can this calculator support pilot-scale work?

Yes. It is useful for pilot and bench studies, especially when you need quick capacity checks, model comparisons, and residence-time context from flow data.

8. Does temperature or pH change the result directly?

Not in the core capacity equation. They are shown as contextual variables because both can strongly affect adsorption behavior, kinetics, and model suitability.