Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
kbatch = (1/𝛕Batch)*ln(Co Batch/CBatch)
This formula uses 1 Functions, 4 Variables
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)
Variables Used
Rate Constant for First Order in Batch Reactor - (Measured in 1 Per Second) - The Rate Constant for First Order in Batch Reactor is defined as the rate of the reaction divided by the concentration of the reactant.
Space Time in Batch Reactor - (Measured in Second) - Space Time in Batch Reactor is the time necessary to process volume of reactor fluid at the entrance conditions.
Initial Reactant Concentration in Batch Reactor - (Measured in Mole per Cubic Meter) - The Initial Reactant Concentration in Batch Reactor refers to the amount of reactant present in the solvent before the considered process.
Reactant Conc at any Time in Batch Reactor - (Measured in Mole per Cubic Meter) - The Reactant Conc at any Time in Batch Reactor refers to the amount of reactant present in the solvent at any given point of time during the process.
STEP 1: Convert Input(s) to Base Unit
Space Time in Batch Reactor: 0.051 Second --> 0.051 Second No Conversion Required
Initial Reactant Concentration in Batch Reactor: 81.5 Mole per Cubic Meter --> 81.5 Mole per Cubic Meter No Conversion Required
Reactant Conc at any Time in Batch Reactor: 23 Mole per Cubic Meter --> 23 Mole per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kbatch = (1/𝛕Batch)*ln(Co Batch/CBatch) --> (1/0.051)*ln(81.5/23)
Evaluating ... ...
kbatch = 24.8060549866209
STEP 3: Convert Result to Output's Unit
24.8060549866209 1 Per Second --> No Conversion Required
FINAL ANSWER
24.8060549866209 24.80605 1 Per Second <-- Rate Constant for First Order in Batch Reactor
(Calculation completed in 00.004 seconds)

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14 Plug Flow or Batch Calculators

Rate Constant for Second Order Reaction using Reactant Concentration for Plug Flow
Go Rate Constant for Second Order in Batch Reactor = (Initial Reactant Concentration in Batch Reactor-Reactant Conc at any Time in Batch Reactor)/(Space Time in Batch Reactor*Initial Reactant Concentration in Batch Reactor*Reactant Conc at any Time in Batch Reactor)
Space Time for Second Order Reaction using Reactant Concentration for Plug Flow
Go Space Time in Batch Reactor = (Initial Reactant Concentration in Batch Reactor-Reactant Conc at any Time in Batch Reactor)/(Rate Constant for Second Order in Batch Reactor*Initial Reactant Concentration in Batch Reactor*Reactant Conc at any Time in Batch Reactor)
Initial Reactant Concentration for Second Order Reaction using Space Time for Plug Flow
Go Initial Reactant Concentration in Batch Reactor = (1/(Rate Constant for Second Order in Batch Reactor*Space Time in Batch Reactor))*(Reactant Conversion in Batch/(1-Reactant Conversion in Batch))
Rate Constant for Second Order Reaction using Space Time for Plug Flow
Go Rate Constant for Second Order in Batch Reactor = (1/(Space Time in Batch Reactor*Initial Reactant Concentration in Batch Reactor))*(Reactant Conversion in Batch/(1-Reactant Conversion in Batch))
Space Time for Second Order Reaction for Plug Flow
Go Space Time in Batch Reactor = (1/(Rate Constant for Second Order in Batch Reactor*Initial Reactant Concentration in Batch Reactor))*(Reactant Conversion in Batch/(1-Reactant Conversion in Batch))
Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow
Go Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
Space Time for First Order Reaction using Reactant Concentration for Plug Flow
Go Space Time in Batch Reactor = (1/Rate Constant for First Order in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
Reactant Concentration for Zero Order Reaction using Space Time for Plug Flow
Go Reactant Conc at any Time in Batch Reactor = Initial Reactant Concentration in Batch Reactor-(Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)
Initial Reactant Concentration for Zero Order Reaction using Space Time for Plug Flow
Go Initial Reactant Concentration in Batch Reactor = (Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)/Reactant Conversion in Batch
Reactant Conversion for Zero Order Reaction using Space Time for Plug Flow
Go Reactant Conversion in Batch = (Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)/Initial Reactant Concentration in Batch Reactor
Rate Constant for Zero Order Reaction using Space Time for Plug Flow
Go Rate Constant for Zero Order in Batch = (Reactant Conversion in Batch*Initial Reactant Concentration in Batch Reactor)/Space Time in Batch Reactor
Space Time for Zero Order Reaction for Plug Flow
Go Space Time in Batch Reactor = (Reactant Conversion in Batch*Initial Reactant Concentration in Batch Reactor)/Rate Constant for Zero Order in Batch
Rate Constant for First Order Reaction using Space Time for Plug Flow
Go Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))
Space Time for First Order Reaction for Plug Flow
Go Space Time in Batch Reactor = (1/Rate Constant for First Order in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))

25 Reactor Performance Equations for Constant Volume Reactions Calculators

Rate Constant for Second Order Reaction using Reactant Concentration for Plug Flow
Go Rate Constant for Second Order in Batch Reactor = (Initial Reactant Concentration in Batch Reactor-Reactant Conc at any Time in Batch Reactor)/(Space Time in Batch Reactor*Initial Reactant Concentration in Batch Reactor*Reactant Conc at any Time in Batch Reactor)
Rate Constant for Second Order Reaction using Reactant Concentration for Mixed Flow
Go Rate Constant for Second Order in Mixed Flow = (Initial Reactant Concentration in Mixed Flow-Reactant Concentration at given Time)/((Space Time in Mixed Flow)*(Reactant Concentration at given Time)^2)
Space Time for Second Order Reaction using Reactant Concentration for Mixed Flow
Go Space Time in Mixed Flow = (Initial Reactant Concentration in Mixed Flow-Reactant Concentration at given Time)/((Rate Constant for Second Order in Mixed Flow)*(Reactant Concentration at given Time)^2)
Initial Reactant Concentration for Second Order Reaction using Space Time for Mixed Flow
Go Initial Reactant Concentration in Mixed Flow = (Reactant Conversion in Mixed Flow)/((1-Reactant Conversion in Mixed Flow)^2*(Space Time in Mixed Flow)*(Rate Constant for Second Order in Mixed Flow))
Rate Constant for Second Order Reaction using Space Time for Mixed Flow
Go Rate Constant for Second Order in Mixed Flow = (Reactant Conversion in Mixed Flow)/((1-Reactant Conversion in Mixed Flow)^2*(Space Time in Mixed Flow)*(Initial Reactant Concentration in Mixed Flow))
Space Time for Second Order Reaction for Mixed Flow
Go Space Time in Mixed Flow = (Reactant Conversion in Mixed Flow)/((1-Reactant Conversion in Mixed Flow)^2*(Rate Constant for Second Order in Mixed Flow)*(Initial Reactant Concentration in Mixed Flow))
Initial Reactant Concentration for Second Order Reaction using Space Time for Plug Flow
Go Initial Reactant Concentration in Batch Reactor = (1/(Rate Constant for Second Order in Batch Reactor*Space Time in Batch Reactor))*(Reactant Conversion in Batch/(1-Reactant Conversion in Batch))
Rate Constant for Second Order Reaction using Space Time for Plug Flow
Go Rate Constant for Second Order in Batch Reactor = (1/(Space Time in Batch Reactor*Initial Reactant Concentration in Batch Reactor))*(Reactant Conversion in Batch/(1-Reactant Conversion in Batch))
Rate Constant for First Order Reaction using Reactant Concentration for Mixed Flow
Go Rate Constant for First Order Reaction = (1/Space Time in Mixed Flow)*((Initial Reactant Concentration in Mixed Flow-Reactant Concentration at given Time)/Reactant Concentration at given Time)
Space Time for First Order Reaction using Reactant Concentration for Mixed Flow
Go Space Time in Mixed Flow = (1/Rate Constant for First Order Reaction)*((Initial Reactant Concentration in Mixed Flow-Reactant Concentration at given Time)/Reactant Concentration at given Time)
Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow
Go Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
Space Time for First Order Reaction using Reactant Concentration for Plug Flow
Go Space Time in Batch Reactor = (1/Rate Constant for First Order in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
Reactant Concentration for Zero Order Reaction using Space Time for Plug Flow
Go Reactant Conc at any Time in Batch Reactor = Initial Reactant Concentration in Batch Reactor-(Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)
Reactant Concentration for Zero Order Reaction using Space Time for Mixed Flow
Go Reactant Concentration at given Time = Initial Reactant Concentration in Mixed Flow-(Rate Constant for Zero Order in Mixed Flow*Space Time in Mixed Flow)
Initial Reactant Concentration for Zero Order Reaction using Space Time for Mixed Flow
Go Initial Reactant Concentration in Mixed Flow = (Rate Constant for Zero Order in Mixed Flow*Space Time in Mixed Flow)/Reactant Conversion in Mixed Flow
Reactant Conversion for Zero Order Reaction using Space Time for Mixed Flow
Go Reactant Conversion in Mixed Flow = (Rate Constant for Zero Order in Mixed Flow*Space Time in Mixed Flow)/Initial Reactant Concentration in Mixed Flow
Rate Constant for Zero Order Reaction using Space Time for Mixed Flow
Go Rate Constant for Zero Order in Mixed Flow = (Reactant Conversion in Mixed Flow*Initial Reactant Concentration in Mixed Flow)/Space Time in Mixed Flow
Space Time for Zero Order Reaction for Mixed Flow
Go Space Time in Mixed Flow = (Reactant Conversion in Mixed Flow*Initial Reactant Concentration in Mixed Flow)/Rate Constant for Zero Order in Mixed Flow
Initial Reactant Concentration for Zero Order Reaction using Space Time for Plug Flow
Go Initial Reactant Concentration in Batch Reactor = (Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)/Reactant Conversion in Batch
Reactant Conversion for Zero Order Reaction using Space Time for Plug Flow
Go Reactant Conversion in Batch = (Rate Constant for Zero Order in Batch*Space Time in Batch Reactor)/Initial Reactant Concentration in Batch Reactor
Rate Constant for Zero Order Reaction using Space Time for Plug Flow
Go Rate Constant for Zero Order in Batch = (Reactant Conversion in Batch*Initial Reactant Concentration in Batch Reactor)/Space Time in Batch Reactor
Rate Constant for First Order Reaction using Space Time for Mixed Flow
Go Rate Constant for First Order Reaction = (1/Space Time in Mixed Flow)*(Reactant Conversion in Mixed Flow/(1-Reactant Conversion in Mixed Flow))
Space Time for First Order Reaction for Mixed Flow
Go Space Time in Mixed Flow = (1/Rate Constant for First Order Reaction)*(Reactant Conversion in Mixed Flow/(1-Reactant Conversion in Mixed Flow))
Rate Constant for First Order Reaction using Space Time for Plug Flow
Go Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))
Space Time for First Order Reaction for Plug Flow
Go Space Time in Batch Reactor = (1/Rate Constant for First Order in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))

Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow Formula

Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor)
kbatch = (1/𝛕Batch)*ln(Co Batch/CBatch)

What is Plug Flow Reactor?

The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.

How to Calculate Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow?

Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow calculator uses Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor) to calculate the Rate Constant for First Order in Batch Reactor, The Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow formula is defined as the constant of proportionality which gives the relation between rate of reaction and the first power of concentration of one of the reactants. Rate Constant for First Order in Batch Reactor is denoted by kbatch symbol.

How to calculate Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow using this online calculator? To use this online calculator for Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow, enter Space Time in Batch Reactor (𝛕Batch), Initial Reactant Concentration in Batch Reactor (Co Batch) & Reactant Conc at any Time in Batch Reactor (CBatch) and hit the calculate button. Here is how the Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow calculation can be explained with given input values -> 24.68539 = (1/0.051)*ln(81.5/23).

FAQ

What is Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow?
The Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow formula is defined as the constant of proportionality which gives the relation between rate of reaction and the first power of concentration of one of the reactants and is represented as kbatch = (1/𝛕Batch)*ln(Co Batch/CBatch) or Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor). Space Time in Batch Reactor is the time necessary to process volume of reactor fluid at the entrance conditions, The Initial Reactant Concentration in Batch Reactor refers to the amount of reactant present in the solvent before the considered process & The Reactant Conc at any Time in Batch Reactor refers to the amount of reactant present in the solvent at any given point of time during the process.
How to calculate Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow?
The Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow formula is defined as the constant of proportionality which gives the relation between rate of reaction and the first power of concentration of one of the reactants is calculated using Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(Initial Reactant Concentration in Batch Reactor/Reactant Conc at any Time in Batch Reactor). To calculate Rate Constant for First Order Reaction using Reactant Concentration for Plug Flow, you need Space Time in Batch Reactor (𝛕Batch), Initial Reactant Concentration in Batch Reactor (Co Batch) & Reactant Conc at any Time in Batch Reactor (CBatch). With our tool, you need to enter the respective value for Space Time in Batch Reactor, Initial Reactant Concentration in Batch Reactor & Reactant Conc at any Time in Batch Reactor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Rate Constant for First Order in Batch Reactor?
In this formula, Rate Constant for First Order in Batch Reactor uses Space Time in Batch Reactor, Initial Reactant Concentration in Batch Reactor & Reactant Conc at any Time in Batch Reactor. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))
  • Rate Constant for First Order in Batch Reactor = (1/Space Time in Batch Reactor)*ln(1/(1-Reactant Conversion in Batch))
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