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

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Plug Flow or Batch Mixed Flow

✖The Rate Constant for First Order in Plug Flow is defined as the rate of the reaction divided by the concentration of the reactant.ⓘ Rate Constant for First Order in Plug Flow [k_{plug flow}]			+10% -10%
✖Fractional Volume Change in PFR is the ratio of the change in volume and the initial volume.ⓘ Fractional Volume Change in PFR [ε_PFR]			+10% -10%
✖Reactant Conversion in PFR gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.ⓘ Reactant Conversion in PFR [X_A-PFR]			+10% -10%

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

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

STEP 0: Pre-Calculation Summary

Formula Used

Space Time in PFR = (1/Rate Constant for First Order in Plug Flow)*((1+Fractional Volume Change in PFR)*ln(1/(1-Reactant Conversion in PFR))-(Fractional Volume Change in PFR*Reactant Conversion in PFR))
𝛕_pfr = (1/k_{plug flow})*((1+ε_PFR)*ln(1/(1-X_A-PFR))-(ε_PFR*X_A-PFR))
This formula uses 1 Functions, 4 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 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 First Order in Plug Flow - (Measured in 1 Per Second) - The Rate Constant for First Order in Plug Flow is defined as the rate of the reaction divided by the concentration of the reactant.
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

Rate Constant for First Order in Plug Flow: 39.5 1 Per Second --> 39.5 1 Per 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

𝛕_pfr = (1/k_{plug flow})*((1+ε_PFR)*ln(1/(1-X_A-PFR))-(ε_PFR*X_A-PFR)) --> (1/39.5)*((1+0.22)*ln(1/(1-0.715))-(0.22*0.715))

Evaluating ... ...

𝛕_pfr = 0.0347879655805178

STEP 3: Convert Result to Output's Unit

0.0347879655805178 Second --> No Conversion Required

FINAL ANSWER

0.0347879655805178 ≈ 0.034788 Second <-- Space Time in PFR

(Calculation completed in 00.020 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

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

LaTeX Go

What is Plug Flow Reactor?

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

How to Calculate Space Time for First Order Reaction using Rate Constant for Plug Flow?

Space Time for First Order Reaction using Rate Constant for Plug Flow calculator uses Space Time in PFR = (1/Rate Constant for First Order in Plug Flow)*((1+Fractional Volume Change in PFR)*ln(1/(1-Reactant Conversion in PFR))-(Fractional Volume Change in PFR*Reactant Conversion in PFR)) to calculate the Space Time in PFR, The Space Time for First Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable. Space Time in PFR is denoted by 𝛕_pfr symbol.

How to calculate Space Time for First Order Reaction using Rate Constant for Plug Flow using this online calculator? To use this online calculator for Space Time for First Order Reaction using Rate Constant for Plug Flow, enter Rate Constant for First Order in Plug Flow (k_{plug flow}), Fractional Volume Change in PFR (ε_PFR) & Reactant Conversion in PFR (X_A-PFR) and hit the calculate button. Here is how the Space Time for First Order Reaction using Rate Constant for Plug Flow calculation can be explained with given input values -> 0.034788 = (1/39.5)*((1+0.22)*ln(1/(1-0.715))-(0.22*0.715)).

FAQ

What is Space Time for First Order Reaction using Rate Constant for Plug Flow?

The Space Time for First Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable and is represented as 𝛕_pfr = (1/k_{plug flow})*((1+ε_PFR)*ln(1/(1-X_A-PFR))-(ε_PFR*X_A-PFR)) or Space Time in PFR = (1/Rate Constant for First Order in Plug Flow)*((1+Fractional Volume Change in PFR)*ln(1/(1-Reactant Conversion in PFR))-(Fractional Volume Change in PFR*Reactant Conversion in PFR)). The Rate Constant for First Order in Plug Flow is defined as the rate of the reaction divided by the concentration of the reactant, 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 Space Time for First Order Reaction using Rate Constant for Plug Flow?

The Space Time for First Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for first order reaction where fractional volume change is considerable is calculated using Space Time in PFR = (1/Rate Constant for First Order in Plug Flow)*((1+Fractional Volume Change in PFR)*ln(1/(1-Reactant Conversion in PFR))-(Fractional Volume Change in PFR*Reactant Conversion in PFR)). To calculate Space Time for First Order Reaction using Rate Constant for Plug Flow, you need Rate Constant for First Order in Plug Flow (k_{plug flow}), Fractional Volume Change in PFR (ε_PFR) & Reactant Conversion in PFR (X_A-PFR). With our tool, you need to enter the respective value for Rate Constant for First Order in Plug Flow, 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.

How many ways are there to calculate Space Time in PFR?

In this formula, Space Time in PFR uses Rate Constant for First Order in Plug Flow, Fractional Volume Change in PFR & Reactant Conversion in PFR. We can use 2 other way(s) to calculate the same, which is/are as follows -

Space Time in PFR = (Reactant Conversion in PFR*Initial Reactant Concentration in PFR)/Rate Constant for Zero Order Reaction
Space Time in PFR = (Reactant Conversion in PFR*Initial Reactant Concentration in PFR)/Rate Constant for Zero Order Reaction

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