Transform equilibrium constants with exact reaction statements
A constant is not a property of a chemical name alone; the complete written equation matters.
Learning outcome: Derive each transformation by multiplying or inverting activity quotients. Compare formal coefficient scaling with a real concentration perturbation.
Starting recap
Refresh dimensionless activities, component balances, admissible roots, normalized partial pressures and independent versus shared measurement errors.
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For A⇌B with K1=4 and B⇌C with K2=3, A⇌C has K=12, B⇌A has .25, and 2A⇌2B has 16.
Open the experimentPredict
Does doubling a written reaction make the physical sample twice as product-rich?
Experiment
Derive each transformation by multiplying or inverting activity quotients. Compare formal coefficient scaling with a real concentration perturbation.
Transform a constant together with its reaction
Worked teaching model · synthetic values · Fictional isomer reactions at one temperature and compatible activity standard states. Reverse inverts K, multiply coefficients by two squares K, add reactions multiplies constants. Changing notation does not create a new physical mixture.
Reset keeps your prediction, captures and practice history.
- K for coefficients multiplied by lambda: solid
Axes rescale. A quotient comparison, inventory intersection and relaxation trajectory have different horizontal meanings; inspect labels rather than treating every curve as elapsed time.
All calculated plot coordinates
| reaction coefficient multiplier | transformed K |
|---|---|
| 0 | 1 |
| 0.03333333 | 1.047294 |
| 0.06666667 | 1.096825 |
| 0.1 | 1.148698 |
| 0.1333333 | 1.203025 |
| 0.1666667 | 1.259921 |
| 0.2 | 1.319508 |
| 0.2333333 | 1.381913 |
| 0.2666667 | 1.447269 |
| 0.3 | 1.515717 |
| 0.3333333 | 1.587401 |
| 0.3666667 | 1.662476 |
| 0.4 | 1.741101 |
| 0.4333333 | 1.823445 |
| 0.4666667 | 1.909683 |
| 0.5 | 2 |
| 0.5333333 | 2.094588 |
| 0.5666667 | 2.19365 |
| 0.6 | 2.297397 |
| 0.6333333 | 2.40605 |
| 0.6666667 | 2.519842 |
| 0.7 | 2.639016 |
| 0.7333333 | 2.763826 |
| 0.7666667 | 2.894538 |
| 0.8 | 3.031433 |
| 0.8333333 | 3.174802 |
| 0.8666667 | 3.324952 |
| 0.9 | 3.482202 |
| 0.9333333 | 3.64689 |
| 0.9666667 | 3.819366 |
| 1 | 4 |
| 1.033333 | 4.189176 |
| 1.066667 | 4.3873 |
| 1.1 | 4.594793 |
| 1.133333 | 4.8121 |
| 1.166667 | 5.039684 |
| 1.2 | 5.278032 |
| 1.233333 | 5.527652 |
| 1.266667 | 5.789077 |
| 1.3 | 6.062866 |
| 1.333333 | 6.349604 |
| 1.366667 | 6.649903 |
| 1.4 | 6.964405 |
| 1.433333 | 7.29378 |
| 1.466667 | 7.638733 |
| 1.5 | 8 |
| 1.533333 | 8.378353 |
| 1.566667 | 8.7746 |
| 1.6 | 9.189587 |
| 1.633333 | 9.6242 |
| 1.666667 | 10.07937 |
| 1.7 | 10.55606 |
| 1.733333 | 11.0553 |
| 1.766667 | 11.57815 |
| 1.8 | 12.12573 |
| 1.833333 | 12.69921 |
| 1.866667 | 13.29981 |
| 1.9 | 13.92881 |
| 1.933333 | 14.58756 |
| 1.966667 | 15.27747 |
| 2 | 16 |
| Quantity | Value | Unit |
|---|---|---|
| A to B constant | 4 | dimensionless |
| B to A constant | 0.25 | dimensionless |
| 2A to 2B constant | 16 | dimensionless |
| A to C coupled constant | 12 | dimensionless |
| C to A coupled reverse constant | 0.08333333 | dimensionless |
A constant belongs to an exact written reaction and its standard-state convention.
Multiply activity quotients when adding reactions so intermediate activities cancel. Do not add K values, and do not compare the magnitude of K for differently scaled reactions as evidence that one physical mixture is more complete. Fractional scaling is a formal thermodynamic transformation, not a fractional molecule event.
These calculated packets are not performed chemical measurements. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.
A constant belongs to an exact written reaction and its standard-state convention.
Multiply activity quotients when adding reactions so intermediate activities cancel. Do not add K values, and do not compare the magnitude of K for differently scaled reactions as evidence that one physical mixture is more complete. Fractional scaling is a formal thermodynamic transformation, not a fractional molecule event.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
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Public practice checks a specific claim. It does not establish independent mastery.
Why is comparing K magnitudes across differently scaled reaction equations misleading?
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