Model host guest association with practical equilibrium inputs. See complex levels and binding fractions instantly. Built for clear supramolecular planning and comparison workflows today.
Pseudorotaxane formation is treated as a 1:1 host guest equilibrium.
H + G ⇌ HG
Ka = [HG] / ([H][G])
Mass balance gives:
[H]T = [H] + [HG]
[G]T = [G] + [HG]
Let x = [HG]. Then the equilibrium solution becomes:
x = (([H]T + [G]T + 1/Ka) - √(([H]T + [G]T + 1/Ka)² - 4[H]T[G]T)) / 2
After solving for x, the free concentrations are:
[H]eq = [H]T - x
[G]eq = [G]T - x
The bound percentages come from the ratio of complex to starting totals.
These example rows are useful for testing the calculator.
| Case | Ka (L/mol) | Host Total (M) | Guest Total (M) | Complex [HG]eq (M) | Free Host (M) | Free Guest (M) | Host Bound (%) |
|---|---|---|---|---|---|---|---|
| Case 1 | 1500 | 0.002000 | 0.003000 | 0.001409 | 0.000591 | 0.001591 | 70.466635 |
| Case 2 | 5000 | 0.001500 | 0.001500 | 0.001043 | 0.000457 | 0.000457 | 69.548238 |
| Case 3 | 800 | 0.004000 | 0.002500 | 0.001635 | 0.002365 | 0.000865 | 40.886022 |
| Case 4 | 12000 | 0.000800 | 0.001000 | 0.000647 | 0.000153 | 0.000353 | 80.894589 |
Pseudorotaxane systems are central to supramolecular chemistry. They form when a linear guest threads through a host. The assembly remains noncovalent. Yet it can be strong and highly useful. Researchers study this equilibrium to understand recognition, selectivity, and responsive molecular behavior.
This calculator estimates the balance between free host, free guest, and threaded complex. It uses a standard 1:1 binding model. That model fits many host guest screening studies. It is especially helpful during early design, titration planning, and comparative binding analysis.
The association constant Ka controls how strongly the components prefer the assembled state. A larger Ka usually means greater complex formation. A smaller Ka leaves more free species in solution. Total concentrations also matter. Even strong systems can show incomplete binding when one component is scarce.
The complex concentration shows the amount of pseudorotaxane present at equilibrium. Free host and free guest show the unbound fractions. Bound percentages help you compare formulations fast. Kd gives the inverse view of affinity. The initial guest to host ratio helps you judge stoichiometric balance.
You can use this page for feasibility checks, presentation support, lab notes, and teaching examples. It is useful before synthesis campaigns and before detailed spectroscopic fitting. It also helps when selecting concentration windows for NMR, UV visible, fluorescence, or calorimetry experiments.
This calculator assumes a simple 1:1 equilibrium. Real systems may show cooperativity, solvent effects, ion pairing, or competing complexes. Even so, this model offers a clear starting point. It gives fast, consistent estimates for planning and communication.
It solves a 1:1 host guest equilibrium for pseudorotaxane formation. The output includes complex concentration, free host, free guest, bound percentages, Kd, and the initial guest to host ratio.
Ka is the association constant. It measures binding strength. Higher Ka values usually produce more complex at equilibrium when the same total concentrations are used.
Free concentrations show how much host and guest remain unbound. They help you estimate whether additional material, different stoichiometry, or another experimental window is needed.
No. This version assumes one host binds one guest. Systems with multiple sites, sequential binding, or cooperative effects need an expanded model.
Enter concentrations in mol/L. Then choose your preferred display unit for the result. This keeps the equilibrium math consistent and the output easier to read.
Kd is the inverse of Ka. Lower Kd values indicate stronger binding. Some users prefer Kd because it is familiar in affinity comparison workflows.
Yes. Use the CSV button for spreadsheet export. Use the PDF button to print the page or save it as a PDF from your browser.
Yes. It is useful for quick screening, concentration planning, and result communication. It gives a solid first estimate before deeper fitting or full titration analysis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.