Space Time for First Order Reaction for Plug Flow or for Infinite Reactors Calculator

✖The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.ⓘ Rate Constant for First 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%
✖The Reactant Concentration refers to the amount of reactant present in the solvent at any given point of time during the process.ⓘ Reactant Concentration [C]			+10% -10%

✖Space Time for Plug Flow Reactor is the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor.ⓘ Space Time for First Order Reaction for Plug Flow or for Infinite Reactors [𝛕_p]

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Formula

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Space Time for First Order Reaction for Plug Flow or for Infinite Reactors

Formula

𝛕 p = (\frac{1}{k'}) \cdot \ln (\frac{C o}{C})

Example

0.480053 s = (\frac{1}{2.508 s⁻¹}) \cdot \ln (\frac{80 mol/m³}{24 mol/m³})

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Space Time for First Order Reaction for Plug Flow or for Infinite Reactors Solution

STEP 0: Pre-Calculation Summary

Formula Used

Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
𝛕_p = (1/k^')*ln(C_o/C)
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 for Plug Flow Reactor - (Measured in Second) - Space Time for Plug Flow Reactor is the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor.
Rate Constant for First Order Reaction - (Measured in 1 Per Second) - The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.
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 Concentration - (Measured in Mole per Cubic Meter) - The Reactant Concentration refers to the amount of reactant present in the solvent at any given point of time during the process.

STEP 1: Convert Input(s) to Base Unit

Rate Constant for First Order Reaction: 2.508 1 Per Second --> 2.508 1 Per Second No Conversion Required
Initial Reactant Concentration: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Reactant Concentration: 24 Mole per Cubic Meter --> 24 Mole per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛕_p = (1/k^')*ln(C_o/C) --> (1/2.508)*ln(80/24)

Evaluating ... ...

𝛕_p = 0.480052952283069

STEP 3: Convert Result to Output's Unit

0.480052952283069 Second --> No Conversion Required

FINAL ANSWER

0.480052952283069 ≈ 0.480053 Second <-- Space Time for Plug Flow Reactor

(Calculation completed in 00.004 seconds)

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< Design for Single Reactions Calculators

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

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

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

< Important Formulas in Design of Reactors and Recycle Reactors for Single Reactions Calculators

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)

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))

Space Time for First Order Reaction for Plug Flow or for Infinite Reactors Formula

Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
𝛕_p = (1/k^')*ln(C_o/C)

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.

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 Plug Flow or for Infinite Reactors?

Space Time for First Order Reaction for Plug Flow or for Infinite Reactors calculator uses Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration) to calculate the Space Time for Plug Flow Reactor, The Space Time for First Order Reaction for Plug Flow or for Infinite Reactors formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor or infinite reactors for first order reaction. Space Time for Plug Flow Reactor is denoted by 𝛕_p symbol.

How to calculate Space Time for First Order Reaction for Plug Flow or for Infinite Reactors using this online calculator? To use this online calculator for Space Time for First Order Reaction for Plug Flow or for Infinite Reactors, enter Rate Constant for First Order Reaction (k^'), Initial Reactant Concentration (C_o) & Reactant Concentration (C) and hit the calculate button. Here is how the Space Time for First Order Reaction for Plug Flow or for Infinite Reactors calculation can be explained with given input values -> 0.480053 = (1/2.508)*ln(80/24).

FAQ

What is Space Time for First Order Reaction for Plug Flow or for Infinite Reactors?

The Space Time for First Order Reaction for Plug Flow or for Infinite Reactors formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor or infinite reactors for first order reaction and is represented as 𝛕_p = (1/k^')*ln(C_o/C) or Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration). The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant, The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process & The Reactant Concentration refers to the amount of reactant present in the solvent at any given point of time during the process.

How to calculate Space Time for First Order Reaction for Plug Flow or for Infinite Reactors?

The Space Time for First Order Reaction for Plug Flow or for Infinite Reactors formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor or infinite reactors for first order reaction is calculated using Space Time for Plug Flow Reactor = (1/Rate Constant for First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration). To calculate Space Time for First Order Reaction for Plug Flow or for Infinite Reactors, you need Rate Constant for First Order Reaction (k^'), Initial Reactant Concentration (C_o) & Reactant Concentration (C). With our tool, you need to enter the respective value for Rate Constant for First Order Reaction, Initial Reactant Concentration & Reactant Concentration 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 for Plug Flow Reactor?

In this formula, Space Time for Plug Flow Reactor uses Rate Constant for First Order Reaction, Initial Reactant Concentration & Reactant Concentration. We can use 2 other way(s) to calculate the same, which is/are as follows -

Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1)
Space Time for Plug Flow Reactor = (1/(Initial Reactant Concentration*Rate Constant for Second Order Reaction))*((Initial Reactant Concentration/Reactant Concentration)-1)

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