Rate Constant for Second Order Reaction using Recycle Ratio Calculator

✖Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.ⓘ Recycle Ratio [R]			+10% -10%
✖The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process.ⓘ Initial Reactant Concentration [C_o]			+10% -10%
✖Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.ⓘ Final Reactant Concentration [C_f]			+10% -10%
✖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.ⓘ Space Time [𝛕]			+10% -10%

✖The Rate Constant for Second Order Reaction is defined as the average rate of the reaction per concentration of the reactant having power raised to 2.ⓘ Rate Constant for Second Order Reaction using Recycle Ratio [k^'']

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Rate Constant for Second Order Reaction using Recycle Ratio

Formula

`"k"^{"''"} = (("R"+1)*"C"_{"o"}*("C"_{"o"}-"C"_{"f"}))/("C"_{"o"}*"𝛕"*"C"_{"f"}*("C"_{"o"}+("R"*"C"_{"f"})))`

Example

`"0.906977m³/(mol*s)"=(("0.3"+1)*"80mol/m³"*("80mol/m³"-"20mol/m³"))/("80mol/m³"*"0.05s"*"20mol/m³"*("80mol/m³"+("0.3"*"20mol/m³")))`

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Rate Constant for Second Order Reaction using Recycle Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
k^'' = ((R+1)*C_o*(C_o-C_f))/(C_o*𝛕*C_f*(C_o+(R*C_f)))
This formula uses 5 Variables

Variables Used

Rate Constant for Second Order Reaction - (Measured in Cubic Meter per Mole Second) - The Rate Constant for Second Order Reaction is defined as the average rate of the reaction per concentration of the reactant having power raised to 2.
Recycle Ratio - Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Recycle Ratio: 0.3 --> 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
Space Time: 0.05 Second --> 0.05 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k^'' = ((R+1)*C_o*(C_o-C_f))/(C_o*𝛕*C_f*(C_o+(R*C_f))) --> ((0.3+1)*80*(80-20))/(80*0.05*20*(80+(0.3*20)))

Evaluating ... ...

k^'' = 0.906976744186046

STEP 3: Convert Result to Output's Unit

0.906976744186046 Cubic Meter per Mole Second --> No Conversion Required

FINAL ANSWER

0.906976744186046 ≈ 0.906977 Cubic Meter per Mole Second <-- Rate Constant for Second 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

Space Time for Second Order Reaction using Recycle Ratio

Rate Constant for First Order Reaction using Recycle Ratio

Space Time for First Order Reaction using Recycle Ratio

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 Second Order Reaction using Recycle Ratio Formula

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 Second Order Reaction using Recycle Ratio?

Rate Constant for Second Order Reaction using Recycle Ratio calculator uses 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))) to calculate the Rate Constant for Second Order Reaction, The Rate Constant for Second Order Reaction using Recycle Ratio formula is defined as the proportionality constant for second order reaction for zero fractional volume change. Rate Constant for Second Order Reaction is denoted by k^'' symbol.

How to calculate Rate Constant for Second Order Reaction using Recycle Ratio using this online calculator? To use this online calculator for Rate Constant for Second Order Reaction using Recycle Ratio, enter Recycle Ratio (R), Initial Reactant Concentration (C_o), Final Reactant Concentration (C_f) & Space Time (𝛕) and hit the calculate button. Here is how the Rate Constant for Second Order Reaction using Recycle Ratio calculation can be explained with given input values -> 0.906977 = ((0.3+1)*80*(80-20))/(80*0.05*20*(80+(0.3*20))).

FAQ

What is Rate Constant for Second Order Reaction using Recycle Ratio?

The Rate Constant for Second Order Reaction using Recycle Ratio formula is defined as the proportionality constant for second order reaction for zero fractional volume change and is represented as k^'' = ((R+1)*C_o*(C_o-C_f))/(C_o*𝛕*C_f*(C_o+(R*C_f))) or 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))). Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams, 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 & 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.

How to calculate Rate Constant for Second Order Reaction using Recycle Ratio?

The Rate Constant for Second Order Reaction using Recycle Ratio formula is defined as the proportionality constant for second order reaction for zero fractional volume change is calculated using 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))). To calculate Rate Constant for Second Order Reaction using Recycle Ratio, you need Recycle Ratio (R), Initial Reactant Concentration (C_o), Final Reactant Concentration (C_f) & Space Time (𝛕). With our tool, you need to enter the respective value for Recycle Ratio, Initial Reactant Concentration, Final Reactant Concentration & Space Time 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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