Temperature in Arrhenius Equation for First Order Reaction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
TempFirstOrder = modulus(Ea1/[R]*(ln(Afactor-firstorder/kfirst)))
This formula uses 1 Constants, 2 Functions, 4 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus
Variables Used
Temperature in Arrhenius Eq for 1st Order Reaction - (Measured in Kelvin) - Temperature in Arrhenius Eq for 1st Order Reaction is the degree or intensity of heat present in a substance or object.
Activation Energy - (Measured in Joule Per Mole) - Activation Energy is the minimum amount of energy that is required to activate atoms or molecules to a condition in which they can undergo chemical transformation.
Frequency Factor from Arrhenius Eqn for 1st Order - (Measured in 1 Per Second) - Frequency Factor from Arrhenius Eqn for 1st Order is also known as the pre-exponential factor and it describes the frequency of reaction and correct molecular orientation.
Rate Constant for First Order Reaction - (Measured in 1 Per Second) - The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.
STEP 1: Convert Input(s) to Base Unit
Activation Energy: 197.3778 Joule Per Mole --> 197.3778 Joule Per Mole No Conversion Required
Frequency Factor from Arrhenius Eqn for 1st Order: 0.687535 1 Per Second --> 0.687535 1 Per Second No Conversion Required
Rate Constant for First Order Reaction: 0.520001 1 Per Second --> 0.520001 1 Per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TempFirstOrder = modulus(Ea1/[R]*(ln(Afactor-firstorder/kfirst))) --> modulus(197.3778/[R]*(ln(0.687535/0.520001)))
Evaluating ... ...
TempFirstOrder = 6.62990139004984
STEP 3: Convert Result to Output's Unit
6.62990139004984 Kelvin --> No Conversion Required
FINAL ANSWER
6.62990139004984 6.629901 Kelvin <-- Temperature in Arrhenius Eq for 1st Order Reaction
(Calculation completed in 00.020 seconds)

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18 First Order Reaction Calculators

Graphical Representation of Time for Completion
Go Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Concentration for First Order Reaction)-(2.303/Rate Constant for First Order Reaction)*log10(Concentration at Time t)
Temperature in Arrhenius Equation for First Order Reaction
Go Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
Rate Constant for First Order Reaction from Arrhenius Equation
Go Rate Constant for First Order Reaction = Frequency Factor from Arrhenius Eqn for 1st Order*exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Arrhenius Constant for First Order Reaction
Go Frequency Factor from Arrhenius Eqn for 1st Order = Rate Constant for First Order Reaction/exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Activation Energy for First Order Reaction
Go Energy of Activation = [R]*Temperature of Gas*(ln(Frequency Factor from Arrhenius Equation/Rate Constant for First Order Reaction))
Time for Completion for First Order given Rate Constant and Initial Concentration
Go Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Concentration for First Order Reaction/Concentration at Time t)
Rate Constant of First Order Reaction using Logarithm to base 10
Go Rate Constant for First Order Reaction = 2.303/Time for completion*log10(Initial Concentration for First Order Reaction/Concentration at Time t)
Time for Completion of First Order Reaction
Go Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A)
Time for Completion by Titration Method for First Order Reaction
Go Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Reactant Volume/Volume at Time t)
Rate Constant by Titration Method for First Order Reaction
Go Rate Constant for First Order Reaction = (2.303/Time for completion)*log10(Initial Reactant Volume/Volume at Time t)
Relaxation Time of Reversible First Order
Go Relaxation Time of Reversible First Order = 1/(Forward Rate Constant+Rate Constant of Backward First Order)
Quarter Life of First Order Reaction
Go Quarter Life of First Order Reaction = ln(4)/Rate Constant for First Order Reaction
Rate Constant at Half Time for First Order Reaction
Go Rate Constant for First Order Reaction = 0.693/Half Time
Half Time Completion of First Order Reaction
Go Half Time = 0.693/Rate Constant for First Order Reaction
Average Time of Completion for First Order Reaction
Go Average time = 1/Rate Constant for First Order Reaction
Rate constant given average time
Go Rate Constant for First Order Reaction = 1/Average time
Half Time for Completion given Average Time
Go Half Time = Average time/1.44
Average Time of Completion given Half Time
Go Average time = 1.44*Half Time

11 Temperature Dependency from Arrhenius' Law Calculators

Activation Energy using Rate Constant at Two Different Temperatures
Go Activation Energy Rate Constant = [R]*ln(Rate Constant at Temperature 2/Rate Constant at Temperature 1)*Reaction 1 Temperature*Reaction 2 Temperature/(Reaction 2 Temperature-Reaction 1 Temperature)
Activation Energy using Reaction Rate at Two Different Temperatures
Go Activation Energy = [R]*ln(Reaction Rate 2/Reaction Rate 1)*Reaction 1 Temperature*Reaction 2 Temperature/(Reaction 2 Temperature-Reaction 1 Temperature)
Temperature in Arrhenius Equation for First Order Reaction
Go Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
Temperature in Arrhenius Equation for Zero Order Reaction
Go Temperature in Arrhenius Eq Zero Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for Zero Order/Rate Constant for Zero Order Reaction)))
Temperature in Arrhenius Equation for Second Order Reaction
Go Temperature in Arrhenius Eq for 2nd Order Reaction = Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 2nd Order/Rate Constant for Second Order Reaction))
Rate Constant for Second Order Reaction from Arrhenius Equation
Go Rate Constant for Second Order Reaction = Frequency Factor from Arrhenius Eqn for 2nd Order*exp(-Activation Energy/([R]*Temperature for Second Order Reaction))
Arrhenius Constant for Second Order Reaction
Go Frequency Factor from Arrhenius Eqn for 2nd Order = Rate Constant for Second Order Reaction/exp(-Activation Energy/([R]*Temperature for Second Order Reaction))
Rate Constant for First Order Reaction from Arrhenius Equation
Go Rate Constant for First Order Reaction = Frequency Factor from Arrhenius Eqn for 1st Order*exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Arrhenius Constant for First Order Reaction
Go Frequency Factor from Arrhenius Eqn for 1st Order = Rate Constant for First Order Reaction/exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Rate Constant for Zero Order Reaction from Arrhenius Equation
Go Rate Constant for Zero Order Reaction = Frequency Factor from Arrhenius Eqn for Zero Order*exp(-Activation Energy/([R]*Temperature for Zero Order Reaction))
Arrhenius Constant for Zero Order Reaction
Go Frequency Factor from Arrhenius Eqn for Zero Order = Rate Constant for Zero Order Reaction/exp(-Activation Energy/([R]*Temperature for Zero Order Reaction))

20 Basics of Reactor Design and Temperature Dependency from Arrhenius Law Calculators

Key Reactant Conversion with Varying Density,Temperature and Total Pressure
Go Key-Reactant Conversion = (1-((Key-Reactant Concentration/Initial Key-Reactant Concentration)*((Temperature*Initial Total Pressure)/(Initial Temperature*Total Pressure))))/(1+Fractional Volume Change*((Key-Reactant Concentration/Initial Key-Reactant Concentration)*((Temperature*Initial Total Pressure)/(Initial Temperature*Total Pressure))))
Initial Key Reactant Concentration with Varying Density,Temperature and Total Pressure
Go Initial Key-Reactant Concentration = Key-Reactant Concentration*((1+Fractional Volume Change*Key-Reactant Conversion)/(1-Key-Reactant Conversion))*((Temperature*Initial Total Pressure)/(Initial Temperature*Total Pressure))
Key Reactant Concentration with Varying Density,Temperature and Total Pressure
Go Key-Reactant Concentration = Initial Key-Reactant Concentration*((1-Key-Reactant Conversion)/(1+Fractional Volume Change*Key-Reactant Conversion))*((Initial Temperature*Total Pressure)/(Temperature*Initial Total Pressure))
Activation Energy using Rate Constant at Two Different Temperatures
Go Activation Energy Rate Constant = [R]*ln(Rate Constant at Temperature 2/Rate Constant at Temperature 1)*Reaction 1 Temperature*Reaction 2 Temperature/(Reaction 2 Temperature-Reaction 1 Temperature)
Activation Energy using Reaction Rate at Two Different Temperatures
Go Activation Energy = [R]*ln(Reaction Rate 2/Reaction Rate 1)*Reaction 1 Temperature*Reaction 2 Temperature/(Reaction 2 Temperature-Reaction 1 Temperature)
Temperature in Arrhenius Equation for First Order Reaction
Go Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
Temperature in Arrhenius Equation for Zero Order Reaction
Go Temperature in Arrhenius Eq Zero Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for Zero Order/Rate Constant for Zero Order Reaction)))
Temperature in Arrhenius Equation for Second Order Reaction
Go Temperature in Arrhenius Eq for 2nd Order Reaction = Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 2nd Order/Rate Constant for Second Order Reaction))
Reactant Concentration using Reactant Conversion with Varying Density
Go Reactant Concentration with Varying Density = ((1-Reactant Conversion with Varying Density)*(Initial Reactant Concentration))/(1+Fractional Volume Change*Reactant Conversion with Varying Density)
Rate Constant for Second Order Reaction from Arrhenius Equation
Go Rate Constant for Second Order Reaction = Frequency Factor from Arrhenius Eqn for 2nd Order*exp(-Activation Energy/([R]*Temperature for Second Order Reaction))
Arrhenius Constant for Second Order Reaction
Go Frequency Factor from Arrhenius Eqn for 2nd Order = Rate Constant for Second Order Reaction/exp(-Activation Energy/([R]*Temperature for Second Order Reaction))
Rate Constant for First Order Reaction from Arrhenius Equation
Go Rate Constant for First Order Reaction = Frequency Factor from Arrhenius Eqn for 1st Order*exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Arrhenius Constant for First Order Reaction
Go Frequency Factor from Arrhenius Eqn for 1st Order = Rate Constant for First Order Reaction/exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Initial Reactant Conversion using Reactant Concentration with Varying Density
Go Reactant Conversion = (Initial Reactant Concentration-Reactant Concentration)/(Initial Reactant Concentration+Fractional Volume Change*Reactant Concentration)
Rate Constant for Zero Order Reaction from Arrhenius Equation
Go Rate Constant for Zero Order Reaction = Frequency Factor from Arrhenius Eqn for Zero Order*exp(-Activation Energy/([R]*Temperature for Zero Order Reaction))
Arrhenius Constant for Zero Order Reaction
Go Frequency Factor from Arrhenius Eqn for Zero Order = Rate Constant for Zero Order Reaction/exp(-Activation Energy/([R]*Temperature for Zero Order Reaction))
Initial Reactant Concentration using Reactant Conversion with Varying Density
Go Initial Reactant Conc with Varying Density = ((Reactant Concentration)*(1+Fractional Volume Change*Reactant Conversion))/(1-Reactant Conversion)
Initial Reactant Concentration using Reactant Conversion
Go Initial Reactant Concentration = Reactant Concentration/(1-Reactant Conversion)
Reactant Concentration using Reactant Conversion
Go Reactant Concentration = Initial Reactant Concentration*(1-Reactant Conversion)
Reactant Conversion using Reactant Concentration
Go Reactant Conversion = 1-(Reactant Concentration/Initial Reactant Concentration)

Temperature in Arrhenius Equation for First Order Reaction Formula

Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
TempFirstOrder = modulus(Ea1/[R]*(ln(Afactor-firstorder/kfirst)))

What is significance of Arrhenius equation?

The Arrhenius equation explains the effect of temperature on the rate constant. There is certainly the minimum amount of energy known as threshold energy which the reactant molecule must possess before it can react to produce products. Most of the molecules of the reactants, however, have much less kinetic energy than the threshold energy at room temperature, and hence, they do not react. As the temperature is increased, the energy of the reactant molecules increases and become equal to or greater than the threshold energy, which causes the occurrence of reaction.

How to Calculate Temperature in Arrhenius Equation for First Order Reaction?

Temperature in Arrhenius Equation for First Order Reaction calculator uses Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction))) to calculate the Temperature in Arrhenius Eq for 1st Order Reaction, The Temperature in Arrhenius equation for first order reaction formula is defined as activation energy per universal gas constant times the difference of natural logarithm of frequency factor and rate constant. Temperature in Arrhenius Eq for 1st Order Reaction is denoted by TempFirstOrder symbol.

How to calculate Temperature in Arrhenius Equation for First Order Reaction using this online calculator? To use this online calculator for Temperature in Arrhenius Equation for First Order Reaction, enter Activation Energy (Ea1), Frequency Factor from Arrhenius Eqn for 1st Order (Afactor-firstorder) & Rate Constant for First Order Reaction (kfirst) and hit the calculate button. Here is how the Temperature in Arrhenius Equation for First Order Reaction calculation can be explained with given input values -> 6.629901 = modulus(197.3778/[R]*(ln(0.687535/0.520001))).

FAQ

What is Temperature in Arrhenius Equation for First Order Reaction?
The Temperature in Arrhenius equation for first order reaction formula is defined as activation energy per universal gas constant times the difference of natural logarithm of frequency factor and rate constant and is represented as TempFirstOrder = modulus(Ea1/[R]*(ln(Afactor-firstorder/kfirst))) or Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction))). Activation Energy is the minimum amount of energy that is required to activate atoms or molecules to a condition in which they can undergo chemical transformation, Frequency Factor from Arrhenius Eqn for 1st Order is also known as the pre-exponential factor and it describes the frequency of reaction and correct molecular orientation & The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.
How to calculate Temperature in Arrhenius Equation for First Order Reaction?
The Temperature in Arrhenius equation for first order reaction formula is defined as activation energy per universal gas constant times the difference of natural logarithm of frequency factor and rate constant is calculated using Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction))). To calculate Temperature in Arrhenius Equation for First Order Reaction, you need Activation Energy (Ea1), Frequency Factor from Arrhenius Eqn for 1st Order (Afactor-firstorder) & Rate Constant for First Order Reaction (kfirst). With our tool, you need to enter the respective value for Activation Energy, Frequency Factor from Arrhenius Eqn for 1st Order & Rate Constant for First Order Reaction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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