Arrhenius Equation

The Arrhenius Equation calculator computes the chemical reaction rate (k) based on a collision rate (A), activation energy (E_a) and a temperature (T).

INSTRUCTIONS: Choose units and enter the following:

• (A) Frequency Factor (total number of collisions per second)
• (E_a) Activation Energy
• (T) Temperature

Chemical Reaction Rate (k): The calculator computes the rate in units of per second (s^-1 aka perSec).  However this can be automatically converted in many other frequency units via the pull-down menu.

The Math / Science

Svante Arrhenius found that the fraction of molecules whose energy equals or exceeds the activation energy is proportional to e^-Ea/RT. Therefore, the rate constant k must be proportional to the same factor. The Arrhenius equation is a simple and accurate formula for the temperature dependence of the chemical reaction rate constant. The Arrhenius equation can be used to show the effect of a change of temperature on the rate constant and on the rate of the chemical reaction.

k = A*e^(-E_a/RT)

where:

• k = rate constant of the reaction
• A = pre-exponential or frequency factor.  A is the total number of collisions per second.
• E_a = activation energy (J/mol, cal/mol)
• T = temperature (K)
• R = gas law constant = 8.314 J/(mol_K)

Notes

It is noted that every reaction has an energy barrier or minimum energy to start the reaction. When a reaction increases with increasing temperature, it implies that only molecules with sufficient energy are able to react. The energy barrier or minimum energy a molecule must have to overcome this barrier is called activation energy (Ea).

Molecules must possess an energy that is equal or higher than the activation energy, `E_a` to undergo reaction. At low temperature, only a few molecules have sufficient energy - the reaction will proceed, but at a slow rate. At higher temperate, more molecules are able to surpass the energy barrier and the reaction proceeds at a faster rate.

Related Calculators

• Arrhenius Equation (for two temperatures)
• Ideal Gas Constant (R)
• Arrhenius Equation
• Temperature Coefficient Q10

History

The Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that Van 't Hoff's equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship.:188 It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

A historically useful generalization supported by Arrhenius' equation is that, for many common chemical reactions at room temperature, the reaction rate doubles for every 10 degree Celsius increase in temperature.

Chemistry Calculators

• R - Gas Constant: 8.3144626181532 J/(K⋅mol)
• Boyle's Law Calculator:  P₁ • V₁ = P₂ • V₂
• Charles Law Calculator: V₁• T₂ = V₂ • T₁
• Combined Gas Law Calculator:   P•V / T= k
• Gay-Lussac Law:  T₁•P₂ =T₂•P₁ 
• Ideal Gas Law: P•V = n•R•T
• Bragg's Law:   n·λ = 2d·sinθ
• Hess' Law:  ΔH⁰_rxn=ΔH⁰_a+ΔH⁰_b+ΔH⁰_c+ΔH⁰_d
• Internal Energy: ΔU = q + ω 
• Activation Energy:  E_a = (R*T₁⋅T₂)/(T₁ - T₂) ⋅  ln(k₁/k₂)
• Arrhenius Equation:  k = Ae^E_a/(RT)
• Clausius-Clapeyron Equation:  ln(P₂/P₁) = (ΔH_vap)/R * (1/T₁ - 1/T₂)
• Compressibility Factor: Z = (p*V_m)/(R*T)
• Peng-Robinson Equation of State:  p = (R*T)/(V_m - b) - (a*α)/(V_m² + 2*b*V_m - b²)
• Reduced Specific Volume:  v_r = v/(R* T_cr / P_c)
• Van't Hoff Equation:  ΔH⁰ = R * ( -ln(K₂/K₁))/ (1/T₁ - 1/T₂)

References

• History section is from Wikipedia (wikipedia.org/wiki/Arrhenius_equation)