Space Time for Second Order Reaction for Plug Flow or Infinite Reactors Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1)
𝛕p = (1/(Co*k''))*((Co/C)-1)
This formula uses 4 Variables
Variables Used
Space Time for Plug Flow Reactor - (Measured in Second) - Space Time for Plug Flow Reactor is the time taken by the amount of fluid to either completely enter or completely exit the plug flow 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.
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.
Reactant Concentration - (Measured in Mole per Cubic Meter) - The Reactant Concentration 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
Initial Reactant Concentration: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Rate Constant for Second Order Reaction: 0.062 Cubic Meter per Mole Second --> 0.062 Cubic Meter per Mole Second No Conversion Required
Reactant Concentration: 24 Mole per Cubic Meter --> 24 Mole per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝛕p = (1/(Co*k''))*((Co/C)-1) --> (1/(80*0.062))*((80/24)-1)
Evaluating ... ...
𝛕p = 0.470430107526882
STEP 3: Convert Result to Output's Unit
0.470430107526882 Second --> No Conversion Required
FINAL ANSWER
0.470430107526882 0.47043 Second <-- Space Time for Plug Flow Reactor
(Calculation completed in 00.004 seconds)

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22 Design for Single Reactions Calculators

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)
Rate Constant for First Order Reaction in Vessel i
Go Rate Constant for First Order Reaction = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/(Reactant Concentration in Vessel i*Space Time for Vessel i)
Rate Constant for Second Order Reaction for Plug Flow or Infinite Reactors
Go Rate Constant for Second Order Reaction = (1/(Initial Reactant Concentration*Space Time for Plug Flow Reactor))*((Initial Reactant Concentration/Reactant Concentration)-1)
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
Reaction Rate for Vessel i using Space Time
Go Reaction Rate for Vessel i = (Initial Reactant Concentration*(Reactant Conversion of Vessel i-1-Reactant Conversion of Vessel i))/Space Time for Vessel i
Rate Constant for First Order Reaction for Plug Flow or for Infinite Reactors
Go Rate Constant for First Order Reaction = (1/Space Time for Plug Flow Reactor)*ln(Initial Reactant Concentration/Reactant Concentration)
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
Initial Reactant Concentration for First Order Reaction using Molar Feed Rate
Go Initial Reactant Concentration = (Space Time for Vessel i*Molar Feed Rate)/Volume of Vessel i
Molar Feed Rate for First Order Reaction for Vessel i
Go Molar Feed Rate = (Volume of Vessel i*Initial Reactant Concentration)/Space Time for Vessel i
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

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

Space Time for Second Order Reaction for Plug Flow or Infinite Reactors Formula

Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1)
𝛕p = (1/(Co*k''))*((Co/C)-1)

What is Plug Flow Reactor?

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

What is second order reaction?

Second order reactions can be defined as chemical reactions wherein the sum of the exponents in the corresponding rate law of the chemical reaction is equal to two.

How to Calculate Space Time for Second Order Reaction for Plug Flow or Infinite Reactors?

Space Time for Second Order Reaction for Plug Flow or Infinite Reactors calculator uses Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1) to calculate the Space Time for Plug Flow Reactor, The Space Time for Second Order Reaction for Plug Flow or Infinite Reactors formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable for plug flow. Space Time for Plug Flow Reactor is denoted by 𝛕p symbol.

How to calculate Space Time for Second Order Reaction for Plug Flow or Infinite Reactors using this online calculator? To use this online calculator for Space Time for Second Order Reaction for Plug Flow or Infinite Reactors, enter Initial Reactant Concentration (Co), Rate Constant for Second Order Reaction (k'') & Reactant Concentration (C) and hit the calculate button. Here is how the Space Time for Second Order Reaction for Plug Flow or Infinite Reactors calculation can be explained with given input values -> 0.47043 = (1/(80*0.062))*((80/24)-1).

FAQ

What is Space Time for Second Order Reaction for Plug Flow or Infinite Reactors?
The Space Time for Second Order Reaction for Plug Flow or Infinite Reactors formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable for plug flow and is represented as 𝛕p = (1/(Co*k''))*((Co/C)-1) or Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1). The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process, 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 & The Reactant Concentration refers to the amount of reactant present in the solvent at any given point of time during the process.
How to calculate Space Time for Second Order Reaction for Plug Flow or Infinite Reactors?
The Space Time for Second Order Reaction for Plug Flow or Infinite Reactors formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable for plug flow is calculated using Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1). To calculate Space Time for Second Order Reaction for Plug Flow or Infinite Reactors, you need Initial Reactant Concentration (Co), Rate Constant for Second Order Reaction (k'') & Reactant Concentration (C). With our tool, you need to enter the respective value for Initial Reactant Concentration, Rate Constant for Second Order Reaction & Reactant Concentration 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 Space Time for Plug Flow Reactor?
In this formula, Space Time for Plug Flow Reactor uses Initial Reactant Concentration, Rate Constant for Second Order Reaction & Reactant Concentration. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
  • Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
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