Rate Constant for First Order Reaction using Recycle Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
k' = ((R+1)/𝛕)*ln((Co+(R*Cf))/((R+1)*Cf))
This formula uses 1 Functions, 5 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 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.
Recycle Ratio - Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.
Space Time - (Measured in Second) - Space Time is the time necessary to process volume of reactor fluid at the entrance conditions. This is the time taken by the amount of fluid to either completely enter or completely exit the reactor.
Initial Reactant Concentration - (Measured in Mole per Cubic Meter) - The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process.
Final Reactant Concentration - (Measured in Mole per Cubic Meter) - Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.
STEP 1: Convert Input(s) to Base Unit
Recycle Ratio: 0.3 --> No Conversion Required
Space Time: 0.05 Second --> 0.05 Second No Conversion Required
Initial Reactant Concentration: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Final Reactant Concentration: 20 Mole per Cubic Meter --> 20 Mole per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k' = ((R+1)/𝛕)*ln((Co+(R*Cf))/((R+1)*Cf)) --> ((0.3+1)/0.05)*ln((80+(0.3*20))/((0.3+1)*20))
Evaluating ... ...
k' = 31.1025197140327
STEP 3: Convert Result to Output's Unit
31.1025197140327 1 Per Second --> No Conversion Required
FINAL ANSWER
31.1025197140327 31.10252 1 Per Second <-- Rate Constant for First Order Reaction
(Calculation completed in 00.004 seconds)

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13 Recycle Reactor Calculators

Rate Constant for Second Order Reaction using Recycle Ratio
Go Rate Constant for Second Order Reaction = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Space Time*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))
Space Time for Second Order Reaction using Recycle Ratio
Go Space Time = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Rate Constant for Second Order Reaction*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))
Rate Constant for First Order Reaction using Recycle Ratio
Go Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
Space Time for First Order Reaction using Recycle Ratio
Go Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
Total Feed Reactant Conversion
Go Total Feed Reactant Conversion = (Recycle Ratio/(Recycle Ratio+1))*Final Reactant Conversion
Final Reactant Conversion
Go Final Reactant Conversion = ((Recycle Ratio+1)/Recycle Ratio)*Total Feed Reactant Conversion
Recycle Ratio using Reactant Conversion
Go Recycle Ratio = 1/((Final Reactant Conversion/Total Feed Reactant Conversion)-1)
Recycle Ratio using Total Feed Rate
Go Recycle Ratio = (Total Molar Feed Rate/Fresh Molar Feed Rate)-1
Fresh Molar Feed Rate
Go Fresh Molar Feed Rate = Total Molar Feed Rate/(Recycle Ratio+1)
Total Molar Feed Rate
Go Total Molar Feed Rate = (Recycle Ratio+1)*Fresh Molar Feed Rate
Volume of Fluid returned to Reactor Entrance
Go Volume Returned = Volume Discharged*Recycle Ratio
Volume leaving System
Go Volume Discharged = Volume Returned/Recycle Ratio
Recycle Ratio
Go Recycle Ratio = Volume Returned/Volume Discharged

25 Important Formulas in Design of Reactors & Recycle Reactors for Single Reactions Calculators

Rate Constant for Second Order Reaction using Recycle Ratio
Go Rate Constant for Second Order Reaction = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Space Time*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))
Space Time for Second Order Reaction using Recycle Ratio
Go Space Time = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Rate Constant for Second Order Reaction*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))
Rate Constant for First Order Reaction using Recycle Ratio
Go Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
Space Time for First Order Reaction using Recycle Ratio
Go Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
Space Time for First Order Reaction in Vessel i
Go Adjusted Retention Time of Comp 2 = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/(Reactant Concentration in Vessel i *Rate Constant for First Order Reaction)
Space Time for Second Order Reaction for Plug Flow or Infinite Reactors
Go Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1)
Reactant Concentration for Second Order Reaction for Plug Flow or Infinite Reactors
Go Reactant Concentration = Initial Reactant Concentration/(1+(Initial Reactant Concentration*Rate Constant for Second Order Reaction*Space Time for Plug Flow Reactor))
Initial Reactant Concentration for First Order Reaction using Reaction Rate
Go Initial Reactant Concentration = (Adjusted Retention Time of Comp 2*Reaction Rate for Vessel i)/(Reactant Conversion of Vessel i-1-Reactant Conversion of Vessel i)
Space Time for First Order Reaction for Vessel i using Reaction Rate
Go Adjusted Retention Time of Comp 2 = (Initial Reactant Concentration*(Reactant Conversion of Vessel i-1-Reactant Conversion of Vessel i))/Reaction Rate for Vessel i
Space Time for First Order Reaction for Plug Flow or for Infinite Reactors
Go Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
Initial Reactant Concentration for First Order Reaction in Vessel i
Go Reactant Concentration in Vessel i-1 = Reactant Concentration in Vessel i*(1+(Rate Constant for First Order Reaction*Adjusted Retention Time of Comp 2))
Reactant Concentration for First Order Reaction in Vessel i
Go Reactant Concentration in Vessel i = Reactant Concentration in Vessel i-1/(1+(Rate Constant for First Order Reaction*Adjusted Retention Time of Comp 2))
Initial Reactant Concentration for Second Order Reaction for Plug Flow or Infinite Reactors
Go Initial Reactant Concentration = 1/((1/Reactant Concentration)-(Rate Constant for Second Order Reaction*Space Time for Plug Flow Reactor))
Reaction Rate for Vessel i for Mixed Flow Reactors of Different Sizes in Series
Go Reaction Rate for Vessel i = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/Adjusted Retention Time of Comp 2
Space Time for Vessel i for Mixed Flow Reactors of Different Sizes in Series
Go Adjusted Retention Time of Comp 2 = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/Reaction Rate for Vessel i
Space Time for First Order Reaction for Vessel i using Molar Flow Rate
Go Adjusted Retention Time of Comp 2 = (Volume of Vessel i*Initial Reactant Concentration)/Molar Feed Rate
Volume of Vessel i for First Order Reaction using Molar Feed Rate
Go Volume of Vessel i = (Adjusted Retention Time of Comp 2*Molar Feed Rate)/Initial Reactant Concentration
Total Feed Reactant Conversion
Go Total Feed Reactant Conversion = (Recycle Ratio/(Recycle Ratio+1))*Final Reactant Conversion
Final Reactant Conversion
Go Final Reactant Conversion = ((Recycle Ratio+1)/Recycle Ratio)*Total Feed Reactant Conversion
Recycle Ratio using Reactant Conversion
Go Recycle Ratio = 1/((Final Reactant Conversion/Total Feed Reactant Conversion)-1)
Space Time for First Order Reaction for Vessel i using Volumetric Flow Rate
Go Adjusted Retention Time of Comp 2 = Volume of Vessel i/Volumetric Flow Rate
Volume of Vessel i for First Order Reaction using Volumetric Flow Rate
Go Volume of Vessel i = Volumetric Flow Rate*Adjusted Retention Time of Comp 2
Volumetric Flow Rate for First Order Reaction for Vessel i
Go Volumetric Flow Rate = Volume of Vessel i/Adjusted Retention Time of Comp 2
Recycle Ratio using Total Feed Rate
Go Recycle Ratio = (Total Molar Feed Rate/Fresh Molar Feed Rate)-1
Recycle Ratio
Go Recycle Ratio = Volume Returned/Volume Discharged

Rate Constant for First Order Reaction using Recycle Ratio Formula

Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
k' = ((R+1)/𝛕)*ln((Co+(R*Cf))/((R+1)*Cf))

What is recycle in chemical engineering?

The essentials of the recycling method are that the mixture of both reacted and unreacted products reaches a separating system beyond the reactor where these products are separated from each other; then the unreacted part mixes with the fresh feed stock and the resulting mixture is passed into the reactor.

Why is chemical recycling important?

Chemical recycling could reduce the amount of plastic that ends up in landfills, thereby potentially reducing the release of harmful chemicals into the environment. Chemical recycling can also produce high-quality raw materials, thereby decreasing demand for fossil fuels and other natural resources.

How to Calculate Rate Constant for First Order Reaction using Recycle Ratio?

Rate Constant for First Order Reaction using Recycle Ratio calculator uses Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)) to calculate the Rate Constant for First Order Reaction, The Rate Constant for First Order Reaction using Recycle Ratio formula is defined as the constant of proportionality which gives the relation between rate for first order reaction and the first power of concentration of one of the reactants for zero fractional volume change. Rate Constant for First Order Reaction is denoted by k' symbol.

How to calculate Rate Constant for First Order Reaction using Recycle Ratio using this online calculator? To use this online calculator for Rate Constant for First Order Reaction using Recycle Ratio, enter Recycle Ratio (R), Space Time (𝛕), Initial Reactant Concentration (Co) & Final Reactant Concentration (Cf) and hit the calculate button. Here is how the Rate Constant for First Order Reaction using Recycle Ratio calculation can be explained with given input values -> 31.10252 = ((0.3+1)/0.05)*ln((80+(0.3*20))/((0.3+1)*20)).

FAQ

What is Rate Constant for First Order Reaction using Recycle Ratio?
The Rate Constant for First Order Reaction using Recycle Ratio formula is defined as the constant of proportionality which gives the relation between rate for first order reaction and the first power of concentration of one of the reactants for zero fractional volume change and is represented as k' = ((R+1)/𝛕)*ln((Co+(R*Cf))/((R+1)*Cf)) or Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)). Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams, Space Time is the time necessary to process volume of reactor fluid at the entrance conditions. This is the time taken by the amount of fluid to either completely enter or completely exit the reactor, The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process & Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.
How to calculate Rate Constant for First Order Reaction using Recycle Ratio?
The Rate Constant for First Order Reaction using Recycle Ratio formula is defined as the constant of proportionality which gives the relation between rate for first order reaction and the first power of concentration of one of the reactants for zero fractional volume change is calculated using Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)). To calculate Rate Constant for First Order Reaction using Recycle Ratio, you need Recycle Ratio (R), Space Time (𝛕), Initial Reactant Concentration (Co) & Final Reactant Concentration (Cf). With our tool, you need to enter the respective value for Recycle Ratio, Space Time, Initial Reactant Concentration & Final Reactant Concentration 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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