## Rate Constant for Second Order Reaction for Plug Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
kPlugFlow'' = (1/(𝛕*Co))*(2*ε*(1+ε)*ln(1-XA)+ε^2*XA+((ε+1)^2*XA/(1-XA)))
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 2nd Order Reaction for Plug Flow - (Measured in Cubic Meter per Mole Second) - Rate Constant for 2nd Order Reaction for Plug Flow is defined as the average rate of the reaction per concentration of the reactant having power raised to 2.
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.
Fractional Volume Change - Fractional Volume Change is the ratio of the change in volume and the initial volume.
Reactant Conversion - Reactant Conversion 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: 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
Fractional Volume Change: 0.21 --> No Conversion Required
Reactant Conversion: 0.7 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kPlugFlow'' = (1/(𝛕*Co))*(2*ε*(1+ε)*ln(1-XA)+ε^2*XA+((ε+1)^2*XA/(1-XA))) --> (1/(0.05*80))*(2*0.21*(1+0.21)*ln(1-0.7)+0.21^2*0.7+((0.21+1)^2*0.7/(1-0.7)))
Evaluating ... ...
kPlugFlow'' = 0.708811088543723
STEP 3: Convert Result to Output's Unit
0.708811088543723 Cubic Meter per Mole Second --> No Conversion Required
FINAL ANSWER
0.708811088543723 0.708811 Cubic Meter per Mole Second <-- Rate Constant for 2nd Order Reaction for Plug Flow
(Calculation completed in 00.009 seconds)
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## <Reactor Performance Equations for Variable Volume Reactions Calculators

Initial Reactant Concentration for Second Order Reaction for Mixed Flow
​ 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
​ 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
​ 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
​ 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
​ 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
​ 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
​ 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)))

## Rate Constant for Second Order Reaction for Plug Flow Formula

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)))
kPlugFlow'' = (1/(𝛕*Co))*(2*ε*(1+ε)*ln(1-XA)+ε^2*XA+((ε+1)^2*XA/(1-XA)))

## 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 Rate Constant for Second Order Reaction for Plug Flow?

Rate Constant for Second Order Reaction for Plug Flow calculator uses 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))) to calculate the Rate Constant for 2nd Order Reaction for Plug Flow, The Rate Constant for Second Order Reaction for Plug Flow formula is defined as the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances for considerable fractional volume change. Rate Constant for 2nd Order Reaction for Plug Flow is denoted by kPlugFlow'' symbol.

How to calculate Rate Constant for Second Order Reaction for Plug Flow using this online calculator? To use this online calculator for Rate Constant for Second Order Reaction for Plug Flow, enter Space Time (𝛕), Initial Reactant Concentration (Co), Fractional Volume Change (ε) & Reactant Conversion (XA) and hit the calculate button. Here is how the Rate Constant for Second Order Reaction for Plug Flow calculation can be explained with given input values -> 0.708811 = (1/(0.05*80))*(2*0.21*(1+0.21)*ln(1-0.7)+0.21^2*0.7+((0.21+1)^2*0.7/(1-0.7))).

### FAQ

What is Rate Constant for Second Order Reaction for Plug Flow?
The Rate Constant for Second Order Reaction for Plug Flow formula is defined as the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances for considerable fractional volume change and is represented as kPlugFlow'' = (1/(𝛕*Co))*(2*ε*(1+ε)*ln(1-XA)+ε^2*XA+((ε+1)^2*XA/(1-XA))) or 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))). 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, Fractional Volume Change is the ratio of the change in volume and the initial volume & Reactant Conversion gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.
How to calculate Rate Constant for Second Order Reaction for Plug Flow?
The Rate Constant for Second Order Reaction for Plug Flow formula is defined as the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances for considerable fractional volume change is calculated using 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))). To calculate Rate Constant for Second Order Reaction for Plug Flow, you need Space Time (𝛕), Initial Reactant Concentration (Co), Fractional Volume Change (ε) & Reactant Conversion (XA). With our tool, you need to enter the respective value for Space Time, Initial Reactant Concentration, Fractional Volume Change & Reactant Conversion 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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