Space Time for Second Order Reaction using Rate Constant for Plug Flow Calculator

✖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 [k_'']			+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%
✖Fractional Volume Change is the ratio of the change in volume and the initial volume.ⓘ Fractional Volume Change [ε]			+10% -10%
✖Reactant Conversion gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.ⓘ Reactant Conversion [X_A]			+10% -10%

✖Space Time for Plug Flow is the time necessary to process volume of reactor fluid at the entrance conditions.ⓘ Space Time for Second Order Reaction using Rate Constant for Plug Flow [𝛕_PlugFlow]

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Formula

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Space Time for Second Order Reaction using Rate Constant for Plug Flow

Formula

`"𝛕"_{"PlugFlow"} = (1/("k"_{"''"}*"C"_{"o"}))*(2*"ε"*(1+"ε")*ln(1-"X"_{"A"})+"ε"^2*"X"_{"A"}+(("ε"+1)^2*"X"_{"A"}/(1-"X"_{"A"})))`

Example

`"0.05829s"=(1/("0.608m³/(mol*s)"*"80mol/m³"))*(2*"0.21"*(1+"0.21")*ln(1-"0.7")+("0.21")^2*"0.7"+(("0.21"+1)^2*"0.7"/(1-"0.7")))`

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Space Time for Second Order Reaction using Rate Constant for Plug Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
𝛕_PlugFlow = (1/(k_''*C_o))*(2*ε*(1+ε)*ln(1-X_A)+ε^2*X_A+((ε+1)^2*X_A/(1-X_A)))
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

Space Time for Plug Flow - (Measured in Second) - Space Time for Plug Flow 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.
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

Rate Constant for Second Order Reaction: 0.608 Cubic Meter per Mole Second --> 0.608 Cubic Meter per Mole 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

𝛕_PlugFlow = (1/(k_''*C_o))*(2*ε*(1+ε)*ln(1-X_A)+ε^2*X_A+((ε+1)^2*X_A/(1-X_A))) --> (1/(0.608*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 ... ...

𝛕_PlugFlow = 0.0582903855710299

STEP 3: Convert Result to Output's Unit

0.0582903855710299 Second --> No Conversion Required

FINAL ANSWER

0.0582903855710299 ≈ 0.05829 Second <-- Space Time for Plug Flow

(Calculation completed in 00.004 seconds)

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< 3 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)))

Space Time for Second Order Reaction using Rate Constant for Plug Flow Formula

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 Space Time for Second Order Reaction using Rate Constant for Plug Flow?

Space Time for Second Order Reaction using Rate Constant for Plug Flow calculator uses 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))) to calculate the Space Time for Plug Flow, The Space Time for Second Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for second order reaction where fractional volume change is considerable. Space Time for Plug Flow is denoted by 𝛕_PlugFlow symbol.

How to calculate Space Time for Second Order Reaction using Rate Constant for Plug Flow using this online calculator? To use this online calculator for Space Time for Second Order Reaction using Rate Constant for Plug Flow, enter Rate Constant for Second Order Reaction (k_''), Initial Reactant Concentration (C_o), Fractional Volume Change (ε) & Reactant Conversion (X_A) and hit the calculate button. Here is how the Space Time for Second Order Reaction using Rate Constant for Plug Flow calculation can be explained with given input values -> 0.582904 = (1/(0.608*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 Space Time for Second Order Reaction using Rate Constant for Plug Flow?

The Space Time for Second Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for second order reaction where fractional volume change is considerable and is represented as 𝛕_PlugFlow = (1/(k_''*C_o))*(2*ε*(1+ε)*ln(1-X_A)+ε^2*X_A+((ε+1)^2*X_A/(1-X_A))) or 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))). 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 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 Space Time for Second Order Reaction using Rate Constant for Plug Flow?

The Space Time for Second Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for second order reaction where fractional volume change is considerable is calculated using 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))). To calculate Space Time for Second Order Reaction using Rate Constant for Plug Flow, you need Rate Constant for Second Order Reaction (k_''), Initial Reactant Concentration (C_o), Fractional Volume Change (ε) & Reactant Conversion (X_A). With our tool, you need to enter the respective value for Rate Constant for Second Order Reaction, 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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