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Space Time for First Order Reaction for Vessel i using Reaction Rate Calculator

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✖The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process.ⓘ Initial Reactant Concentration [Co]
+10%
-10%
✖Reactant Conversion of Vessel i-1 gives us the percentage of reactants converted into products in vessel i-1.ⓘ Reactant Conversion of Vessel i-1 [Xi-1]
+10%
-10%
✖Reactant Conversion of Vessel i gives us the percentage of reactants converted into products in vessel i.ⓘ Reactant Conversion of Vessel i [Xi]
+10%
-10%
✖Reaction Rate for Vessel i is the rate at which a reaction occurs to achieve the desire product.ⓘ Reaction Rate for Vessel i [ri]
+10%
-10%
✖Adjusted Retention Time of Comp 2 is the removal of time taken by the mobile phase to travel the column from the retention time of solute 2.ⓘ Space Time for First Order Reaction for Vessel i using Reaction Rate [trC2']
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Space Time for First Order Reaction for Vessel i using Reaction Rate

Formula
`"trC2"^{"'"} = ("C"_{"o"}*("X"_{"i-1"}-"X"_{"i"}))/"r"_{"i"}`

Example
`"47.05882s"=("80mol/m³"*("0.8"-"0.7"))/"0.17mol/m³*s"`

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Space Time for First Order Reaction for Vessel i using Reaction Rate Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
trC2' = (Co*(Xi-1-Xi))/ri
This formula uses 5 Variables
Variables Used
Adjusted Retention Time of Comp 2 - (Measured in Second) - Adjusted Retention Time of Comp 2 is the removal of time taken by the mobile phase to travel the column from the retention time of solute 2.
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.
Reactant Conversion of Vessel i-1 - Reactant Conversion of Vessel i-1 gives us the percentage of reactants converted into products in vessel i-1.
Reactant Conversion of Vessel i - Reactant Conversion of Vessel i gives us the percentage of reactants converted into products in vessel i.
Reaction Rate for Vessel i - (Measured in Mole per Cubic Meter Second) - Reaction Rate for Vessel i is the rate at which a reaction occurs to achieve the desire product.
STEP 1: Convert Input(s) to Base Unit
Initial Reactant Concentration: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Reactant Conversion of Vessel i-1: 0.8 --> No Conversion Required
Reactant Conversion of Vessel i: 0.7 --> No Conversion Required
Reaction Rate for Vessel i: 0.17 Mole per Cubic Meter Second --> 0.17 Mole per Cubic Meter Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
trC2' = (Co*(Xi-1-Xi))/ri --> (80*(0.8-0.7))/0.17
Evaluating ... ...
trC2' = 47.0588235294118
STEP 3: Convert Result to Output's Unit
47.0588235294118 Second --> No Conversion Required
FINAL ANSWER
47.0588235294118 ≈ 47.05882 Second <-- Adjusted Retention Time of Comp 2
(Calculation completed in 00.020 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 First Order Reaction for Vessel i using Reaction Rate Formula

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
trC2' = (Co*(Xi-1-Xi))/ri

What is continuous stirred-tank reactor?

The continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, mixed flow reactor (MFR), or a continuous-flow stirred-tank reactor (CFSTR), is a common model for a chemical reactor in chemical engineering and environmental engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and slurries.

What is first order reaction?

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants.

How to Calculate Space Time for First Order Reaction for Vessel i using Reaction Rate?

Space Time for First Order Reaction for Vessel i using Reaction Rate calculator uses 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 to calculate the Adjusted Retention Time of Comp 2, The Space Time for First Order Reaction for Vessel i using Reaction Rate formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor vessel i for first order reaction. Adjusted Retention Time of Comp 2 is denoted by trC2' symbol.

How to calculate Space Time for First Order Reaction for Vessel i using Reaction Rate using this online calculator? To use this online calculator for Space Time for First Order Reaction for Vessel i using Reaction Rate, enter Initial Reactant Concentration (Co), Reactant Conversion of Vessel i-1 (Xi-1), Reactant Conversion of Vessel i (Xi) & Reaction Rate for Vessel i (ri) and hit the calculate button. Here is how the Space Time for First Order Reaction for Vessel i using Reaction Rate calculation can be explained with given input values -> 47.05882 = (80*(0.8-0.7))/0.17.

FAQ

What is Space Time for First Order Reaction for Vessel i using Reaction Rate?
The Space Time for First Order Reaction for Vessel i using Reaction Rate formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor vessel i for first order reaction and is represented as trC2' = (Co*(Xi-1-Xi))/ri or 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. The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process, Reactant Conversion of Vessel i-1 gives us the percentage of reactants converted into products in vessel i-1, Reactant Conversion of Vessel i gives us the percentage of reactants converted into products in vessel i & Reaction Rate for Vessel i is the rate at which a reaction occurs to achieve the desire product.
How to calculate Space Time for First Order Reaction for Vessel i using Reaction Rate?
The Space Time for First Order Reaction for Vessel i using Reaction Rate formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor vessel i for first order reaction is calculated using 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. To calculate Space Time for First Order Reaction for Vessel i using Reaction Rate, you need Initial Reactant Concentration (Co), Reactant Conversion of Vessel i-1 (Xi-1), Reactant Conversion of Vessel i (Xi) & Reaction Rate for Vessel i (ri). With our tool, you need to enter the respective value for Initial Reactant Concentration, Reactant Conversion of Vessel i-1, Reactant Conversion of Vessel i & Reaction Rate for Vessel i 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 Adjusted Retention Time of Comp 2?
In this formula, Adjusted Retention Time of Comp 2 uses Initial Reactant Concentration, Reactant Conversion of Vessel i-1, Reactant Conversion of Vessel i & Reaction Rate for Vessel i. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Adjusted Retention Time of Comp 2 = Volume of Vessel i/Volumetric Flow Rate
  • Adjusted Retention Time of Comp 2 = (Volume of Vessel i*Initial Reactant Concentration)/Molar Feed Rate
  • 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)
  • Adjusted Retention Time of Comp 2 = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/Reaction Rate for Vessel i
  • Adjusted Retention Time of Comp 2 = (Volume of Vessel i*Initial Reactant Concentration)/Molar Feed Rate
  • Adjusted Retention Time of Comp 2 = Volume of Vessel i/Volumetric Flow Rate
  • 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)
  • Adjusted Retention Time of Comp 2 = (Reactant Concentration in Vessel i-1-Reactant Concentration in Vessel i)/Reaction Rate for Vessel i
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