First-Order Rate Constant Calculator
Calculate first-order rate constant with transparent engineering inputs and the displayed formula.
Run deterministic checks for missing or mixed units, physical bounds, detectable out-of-range values and formula applicability. This is not an engineering approval or a complete code/compliance check.
Export the current calculation inputs and outputs with formula, assumptions, confirmed source credits, automated verification status, tool version and timestamp.
PROFENG Pro unlocks calculation-record exports. The calculation itself remains free.
PROFENG provides this tool for engineering screening and educational use. Check the calculation basis, units, physical assumptions, applicable standards, safety factors, equipment data and project-specific requirements before design, procurement or operation.
Turn this result into a calculation record
Carry the tool context into the PROFENG calculation-check and record workspace without implying certification or engineering approval.
Why use this first-order rate constant calculator?
Calculate first-order rate constant with transparent engineering inputs and the displayed formula. The displayed relationship is k = ln(C₀/C)/t.
What this calculation does
This calculator determines rate constant from initial concentration, final concentration, reaction time. Use it for first-pass mass, energy, reaction and process-balance calculations with a clearly defined calculation basis.
Formula and engineering variables
k = ln(C₀/C)/t
| Variable | Definition | Unit | Working guidance |
|---|---|---|---|
c0 | Initial concentration | mol/L | Illustrative screening band: 0 to about 10 mol/L. This is not a design limit. |
c | Final concentration | mol/L | Illustrative screening band: 0 to about 3 mol/L. This is not a design limit. |
time | Reaction time | s | Illustrative screening band: 0 to about 600 s. This is not a design limit. |
Ranges above are screening guidance or physical bounds where stated. They are not code limits or manufacturer ratings.
Calculated outputs
- Rate constant (1/s): Math.log(c0/c)/time
Worked example
- Initial concentration (c0) = 1 mol/L
- Final concentration (c) = 0.3 mol/L
- Reaction time (time) = 60 s
Math.log((1)/(0.3))/(60) = 0.02007 1/sRate constant: 0.02007 1/sAssumptions
- The material or energy balance uses the entered basis consistently.
- Composition and property inputs represent the process state being evaluated.
- Steady-state behavior is assumed unless time dependence is explicit.
Limitations
- Non-ideal thermodynamics, kinetics, phase equilibrium, transport limitations and process-safety constraints can require more rigorous models.
- Validate design cases against process data, a recognized property method and the governing safety basis.
- Reaction follows first-order kinetics over the evaluated interval.
- Temperature and relevant conditions are treated as constant.
- C0 and C are positive and use the same concentration basis.
- The displayed default values are a worked example only; replace them with traceable project or measurement data.
Formula source and acknowledgement
Relationship used: k = ln(C0/C)/t for an integrated first-order reaction at constant conditions.
The relationship used here follows H. Scott Fogler, Elements of Chemical Reaction Engineering 6th edition (2022 copyright; published 2021), Pearson.
Credit for the underlying method belongs to the cited author(s). PROFENG presents its own implementation and wording and is not affiliated with or endorsed by the authors or publishers.
Limits of use for this relationship
- Reaction follows first-order kinetics over the evaluated interval.
- Temperature and relevant conditions are treated as constant.
- C0 and C are positive and use the same concentration basis.
Read the PROFENG methodology for formula sourcing and automated checks →
How to use it
Start with the inputs shown above, review the assumptions or options, then generate the result. Where the tool creates a file, keep the original until you have opened and checked the downloaded output.
Frequently asked questions
What does First-Order Rate Constant Calculator calculate?
This calculator determines rate constant from initial concentration, final concentration, reaction time. Use it for first-pass mass, energy, reaction and process-balance calculations with a clearly defined calculation basis.
What formula does First-Order Rate Constant Calculator use?
The calculator uses k = ln(C₀/C)/t. Every input used by the implementation is listed in the variable table on this page.
How is the worked example for First-Order Rate Constant Calculator checked?
PROFENG substitutes the displayed default values into the implemented relationship and compares the result against automated verification cases where an independent verifier is available.
What assumptions matter most for First-Order Rate Constant Calculator?
The material or energy balance uses the entered basis consistently. Composition and property inputs represent the process state being evaluated. Steady-state behavior is assumed unless time dependence is explicit.
Can I use this result for final design or procurement?
Use it as an engineering screening calculation. Final design, procurement, operation or compliance decisions require project-specific data and the applicable engineering method, standard or manufacturer information.
QA, changelog and corrections
Last QA update: 30 September 2026.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks, independent cross-checks for calculators, and unit round-trip checks for converters where applicable.
Changelog
30 September 2026 – source/indexation status, metadata and correction pathway reviewed. Engineering tools display the automated verification label only when they are inside the passing Part 3 verification scope.