Initial Reactant Concentration for Second Order Reaction for Plug Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR)))
CoPlugFlow = (1/(𝛕pfr*k''))*(2*εPFR*(1+εPFR)*ln(1-XA-PFR)+εPFR^2*XA-PFR+((εPFR+1)^2*XA-PFR/(1-XA-PFR)))
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
Initial Reactant Conc for 2nd Order Plug Flow - (Measured in Mole per Cubic Meter) - Initial Reactant Conc for 2nd Order Plug Flow refers to the amount of reactant present in the solvent before the considered process.
Space Time in PFR - (Measured in Second) - Space Time in PFR is the time necessary to process volume of reactor fluid at the entrance conditions.
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.
Fractional Volume Change in PFR - Fractional Volume Change in PFR is the ratio of the change in volume and the initial volume.
Reactant Conversion in PFR - Reactant Conversion in PFR gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.
STEP 1: Convert Input(s) to Base Unit
Space Time in PFR: 0.05009 Second --> 0.05009 Second No Conversion Required
Rate Constant for Second Order Reaction: 0.0608 Cubic Meter per Mole Second --> 0.0608 Cubic Meter per Mole Second No Conversion Required
Fractional Volume Change in PFR: 0.22 --> No Conversion Required
Reactant Conversion in PFR: 0.715 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
CoPlugFlow = (1/(𝛕pfr*k''))*(2*εPFR*(1+εPFR)*ln(1-XA-PFR)+εPFR^2*XA-PFR+((εPFR+1)^2*XA-PFR/(1-XA-PFR))) --> (1/(0.05009*0.0608))*(2*0.22*(1+0.22)*ln(1-0.715)+0.22^2*0.715+((0.22+1)^2*0.715/(1-0.715)))
Evaluating ... ...
CoPlugFlow = 1016.20875140585
STEP 3: Convert Result to Output's Unit
1016.20875140585 Mole per Cubic Meter --> No Conversion Required
FINAL ANSWER
1016.20875140585 1016.209 Mole per Cubic Meter <-- Initial Reactant Conc for 2nd Order Plug Flow
(Calculation completed in 00.004 seconds)

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Plug Flow or Batch Calculators

Initial Reactant Concentration for Zero Order Reaction for Plug Flow
​ LaTeX ​ Go Initial Reactant Concentration in PFR = (Rate Constant for Zero Order Reaction*Space Time in PFR)/Reactant Conversion in PFR
Space Time for Zero Order Reaction using Rate Constant for Plug Flow
​ LaTeX ​ Go Space Time in PFR = (Reactant Conversion in PFR*Initial Reactant Concentration in PFR)/Rate Constant for Zero Order Reaction
Reactant Conversion for Zero Order Reaction for Plug Flow
​ LaTeX ​ Go Reactant Conversion in PFR = (Rate Constant for Zero Order Reaction*Space Time in PFR)/Initial Reactant Concentration in PFR
Rate Constant for Zero Order Reaction for Plug Flow
​ LaTeX ​ Go Rate Constant for Zero Order Reaction = (Reactant Conversion in PFR*Initial Reactant Concentration in PFR)/Space Time in PFR

Reactor Performance Equations for Variable Volume Reactions Calculators

Initial Reactant Concentration for Second Order Reaction for Mixed Flow
​ LaTeX ​ Go Initial Reactant Conc for 2nd Order Mixed Flow = (1/Space Time in MFR*Rate Constant for Second Order Reaction in MFR)*((Reactant Conversion in MFR*(1+(Fractional Volume Change in Reactor*Reactant Conversion in MFR))^2)/(1-Reactant Conversion in MFR)^2)
Rate Constant for Second Order Reaction for Mixed Flow
​ LaTeX ​ Go Rate Constant for 2ndOrder Reaction for Mixed Flow = (1/Space Time in MFR*Initial Reactant Concentration in MFR)*((Reactant Conversion in MFR*(1+(Fractional Volume Change in Reactor*Reactant Conversion in MFR))^2)/(1-Reactant Conversion in MFR)^2)
Rate Constant for First Order Reaction for Mixed Flow
​ LaTeX ​ Go Rate Constant for First Order Reaction in MFR = (1/Space Time in MFR)*((Reactant Conversion in MFR*(1+(Fractional Volume Change in Reactor*Reactant Conversion in MFR)))/(1-Reactant Conversion in MFR))
Initial Reactant Concentration for Zero Order Reaction for Mixed Flow
​ LaTeX ​ Go Initial Reactant Concentration in MFR = (Rate Constant for Zero Order Reaction in MFR*Space Time in MFR)/Reactant Conversion in MFR

Plug Flow Reactor Calculators

Initial Reactant Concentration for Second Order Reaction for Plug Flow
​ LaTeX ​ Go Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR)))
Space Time for Second Order Reaction using Rate Constant for Plug Flow
​ LaTeX ​ Go Space Time for Plug Flow = (1/(Rate Constant for Second Order Reaction*Initial Reactant Concentration))*(2*Fractional Volume Change*(1+Fractional Volume Change)*ln(1-Reactant Conversion)+Fractional Volume Change^2*Reactant Conversion+((Fractional Volume Change+1)^2*Reactant Conversion/(1-Reactant Conversion)))
Rate Constant for Second Order Reaction for Plug Flow
​ LaTeX ​ Go Rate Constant for 2nd Order Reaction for Plug Flow = (1/(Space Time*Initial Reactant Concentration))*(2*Fractional Volume Change*(1+Fractional Volume Change)*ln(1-Reactant Conversion)+Fractional Volume Change^2*Reactant Conversion+((Fractional Volume Change+1)^2*Reactant Conversion/(1-Reactant Conversion)))

Initial Reactant Concentration for Second Order Reaction for Plug Flow Formula

​LaTeX ​Go
Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR)))
CoPlugFlow = (1/(𝛕pfr*k''))*(2*εPFR*(1+εPFR)*ln(1-XA-PFR)+εPFR^2*XA-PFR+((εPFR+1)^2*XA-PFR/(1-XA-PFR)))

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.

How to Calculate Initial Reactant Concentration for Second Order Reaction for Plug Flow?

Initial Reactant Concentration for Second Order Reaction for Plug Flow calculator uses Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR))) to calculate the Initial Reactant Conc for 2nd Order Plug Flow, The Initial Reactant Concentration for Second Order Reaction for Plug Flow formula is defined as the concentration of reactant before the considered reaction for second order reaction where there is considerable fractional volume change. Initial Reactant Conc for 2nd Order Plug Flow is denoted by CoPlugFlow symbol.

How to calculate Initial Reactant Concentration for Second Order Reaction for Plug Flow using this online calculator? To use this online calculator for Initial Reactant Concentration for Second Order Reaction for Plug Flow, enter Space Time in PFR (𝛕pfr), Rate Constant for Second Order Reaction (k''), Fractional Volume Change in PFR PFR) & Reactant Conversion in PFR (XA-PFR) and hit the calculate button. Here is how the Initial Reactant Concentration for Second Order Reaction for Plug Flow calculation can be explained with given input values -> 989.6288 = (1/(0.05009*0.0608))*(2*0.22*(1+0.22)*ln(1-0.715)+0.22^2*0.715+((0.22+1)^2*0.715/(1-0.715))).

FAQ

What is Initial Reactant Concentration for Second Order Reaction for Plug Flow?
The Initial Reactant Concentration for Second Order Reaction for Plug Flow formula is defined as the concentration of reactant before the considered reaction for second order reaction where there is considerable fractional volume change and is represented as CoPlugFlow = (1/(𝛕pfr*k''))*(2*εPFR*(1+εPFR)*ln(1-XA-PFR)+εPFR^2*XA-PFR+((εPFR+1)^2*XA-PFR/(1-XA-PFR))) or Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR))). Space Time in PFR is the time necessary to process volume of reactor fluid at the entrance conditions, 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, Fractional Volume Change in PFR is the ratio of the change in volume and the initial volume & Reactant Conversion in PFR gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.
How to calculate Initial Reactant Concentration for Second Order Reaction for Plug Flow?
The Initial Reactant Concentration for Second Order Reaction for Plug Flow formula is defined as the concentration of reactant before the considered reaction for second order reaction where there is considerable fractional volume change is calculated using Initial Reactant Conc for 2nd Order Plug Flow = (1/(Space Time in PFR*Rate Constant for Second Order Reaction))*(2*Fractional Volume Change in PFR*(1+Fractional Volume Change in PFR)*ln(1-Reactant Conversion in PFR)+Fractional Volume Change in PFR^2*Reactant Conversion in PFR+((Fractional Volume Change in PFR+1)^2*Reactant Conversion in PFR/(1-Reactant Conversion in PFR))). To calculate Initial Reactant Concentration for Second Order Reaction for Plug Flow, you need Space Time in PFR (𝛕pfr), Rate Constant for Second Order Reaction (k''), Fractional Volume Change in PFR PFR) & Reactant Conversion in PFR (XA-PFR). With our tool, you need to enter the respective value for Space Time in PFR, Rate Constant for Second Order Reaction, Fractional Volume Change in PFR & Reactant Conversion in PFR 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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