// multi-utility computation suite · offline · instant · precise
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sci.batch-reactor-first-order Calculator
Calculates first-order batch reactor conversion X = 1 − exp(−k×t) and required reaction time from rate constant and target conversion. First-order kinetics: X = 90% requires t = 2.3/k; X = 99% requires t = 4.6/k — the factor of 2 more time for an additional 9% conversion.
Inputs
Ca0 Mol L
Amount of solute per unit volume. Higher concentration = more solute dissolved.
K Per S
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
T S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
conversion X at time t
The computed duration or time value.
concentration Ca(t) (mol/L)
The proportional relationship between two quantities.
half-life t₁/₂ (s)
Time for half the radioactive material to decay. After 10 half-lives, less than 0.1% of the original material remains.
time for 90% conversion (s)
The computed duration or time value.
Ca(t) = Ca₀·exp(−kt)
Reference formula or conversion factor shown for context.