Reaction Rate Arrhenius
Computes the rate constant k of a reaction via Arrhenius equation given A, Ea and T.
—
Arrhenius equation: temperature dependence of rate constants
The Arrhenius equation k = A·e^(−Ea/RT) ties the rate constant k of a reaction to the absolute temperature T in kelvin. A is the pre-exponential factor, which folds in collision frequency and orientation; Ea is the activation energy in J/mol; and R = 8.314 J/(mol·K). Svante Arrhenius put it forward in 1889 and won the Nobel Prize in Chemistry in 1903 for the broader work. It explains the old bench rule that a 10°C rise roughly doubles the reaction rate. Work an example: with A = 1×10¹⁰, Ea = 50,000 J/mol, and T = 298.15 K, you get k ≈ 1.96×10¹⁰·e^(−20.17) ≈ 19. Take the natural log of both sides and it becomes ln k = ln A − Ea/(RT), a straight line when you plot ln k against 1/T. Read Ea off its slope.
Applications and context
It shows up in chemical kinetics, in food shelf-life prediction through the Q10 coefficient, in pharmaceutical stability testing under ICH Q1A accelerated aging, in industrial chemistry for reactor design, and in work on battery degradation and polymer cure rates. Open almost any catalysis paper and you will find an Ea pulled from an Arrhenius plot.
FAQ
Why exponential? Only the molecules carrying energy above Ea can react, and the Maxwell–Boltzmann distribution puts that fraction at e^(−Ea/RT).
Does it always hold? Not quite. At very high T, or for reactions that proceed by tunneling, the straight ln k versus 1/T line bends. In those cases reach for the Eyring equation from transition-state theory.
How do I get Ea experimentally? Measure k at a handful of temperatures, plot ln k against 1/T, then multiply the slope by −R.
Related Tools
Space Mean Speed
Calculate the space mean speed of two vehicles by the harmonic mean, v_s = 2 ÷ (1/v₁ + 1/v₂), from the individual speeds v₁ and v₂. The result, in the same unit as the speeds, is the harmonic mean — not the arithmetic — which is the correct way to compute the mean speed of a traffic stream when observing a road section (average over space). Space mean speed is always less than or equal to the time mean speed (the arithmetic mean observed at a point), because it gives more weight to slow vehicles, which spend more time in the section. It is the speed used in the fundamental equation q = k·v. Enter the two speeds.
Minimum Shutter Handheld by Focal
Applies the focal length reciprocal rule for handheld shooting.
TGV Cruise Trip Time
Estimates TGV high-speed train travel time at 300 km/h cruise speed.
Half-Wave Dipole Length
Calculate the physical length of a half-wave dipole, L = (150 ÷ f)·VF, from the frequency f (MHz) and the velocity factor VF (typically ~0.95 for wires, correcting the end effect). The result, in metres, is the total length of the dipole antenna resonant at the desired frequency — each arm is half this value. The half-wave dipole is the most used reference antenna, with 2.15 dBi gain. The velocity factor makes the antenna slightly shorter than a half wavelength in vacuum. Enter the frequency and the velocity factor.
Tool Life (Taylor's Equation)
Calculate a cutting tool's life by Taylor's equation, T = (C ÷ Vc)^(1/n), from the constant C (the cutting speed giving 1 minute of life, characteristic of the tool-material pair), the cutting speed Vc (m/min) and the exponent n (depending on tool material). Formulated by F. W. Taylor in 1907 from thousands of tests, this is machining's most famous relation and describes a fundamental trade-off: the HIGHER the cutting speed, the SHORTER the tool life — and steeply, since it is a power law. The exponent n quantifies the sensitivity: for HSS n ≈ 0.1 (life drops very fast with speed), for carbide n ≈ 0.2-0.3, for ceramic n ≈ 0.4-0.6 (less sensitive, allowing much higher speeds). Taylor's equation is the basis of economic OPTIMIZATION of machining: there is an optimal cutting speed minimizing total cost per part, balancing cutting time (falling with speed) against tool and change-downtime cost (rising with speed). Speeds above optimum 'burn' costly tools too fast; below, waste machine time. Enter the constant C, the cutting speed and the exponent n.
Mach Number Speed Altitude Calculator
Computes aircraft Mach number from true airspeed in knots and altitude in feet using the speed of sound in the ISA standard atmosphere.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.