Space Time for First Order Reaction using Recycle Ratio Calculator

✖Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.ⓘ Recycle Ratio [R]			+10% -10%
✖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%
✖Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.ⓘ Final Reactant Concentration [C_f]			+10% -10%

✖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.ⓘ Space Time for First Order Reaction using Recycle Ratio [𝛕]

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Space Time for First Order Reaction using Recycle Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))
𝛕 = ((R+1)/k^')*ln((C_o+(R*C_f))/((R+1)*C_f))
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 - (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.
Recycle Ratio - Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.
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.
Final Reactant Concentration - (Measured in Mole per Cubic Meter) - Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.

STEP 1: Convert Input(s) to Base Unit

Recycle Ratio: 0.3 --> No Conversion Required
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
Final Reactant Concentration: 20 Mole per Cubic Meter --> 20 Mole per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛕 = ((R+1)/k^')*ln((C_o+(R*C_f))/((R+1)*C_f)) --> ((0.3+1)/2.508)*ln((80+(0.3*20))/((0.3+1)*20))

Evaluating ... ...

𝛕 = 0.620066182496664

STEP 3: Convert Result to Output's Unit

0.620066182496664 Second --> No Conversion Required

FINAL ANSWER

0.620066182496664 ≈ 0.620066 Second <-- Space Time

(Calculation completed in 00.004 seconds)

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< Recycle Reactor Calculators

Rate Constant for First Order Reaction using Recycle Ratio

LaTeX Go Rate Constant for First Order Reaction = ((Recycle Ratio+1)/Space Time)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration))

Recycle Ratio using Reactant Conversion

LaTeX Go Recycle Ratio = 1/((Final Reactant Conversion/Total Feed Reactant Conversion)-1)

Recycle Ratio using Total Feed Rate

LaTeX Go Recycle Ratio = (Total Molar Feed Rate/Fresh Molar Feed Rate)-1

Recycle Ratio

LaTeX Go Recycle Ratio = Volume Returned/Volume Discharged

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

Initial Reactant Concentration for First Order Reaction using Reaction Rate

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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 using Recycle Ratio Formula

LaTeX Go

What is recycle in chemical engineering?

The essentials of the recycling method are that the mixture of both reacted and unreacted products reaches a separating system beyond the reactor where these products are separated from each other; then the unreacted part mixes with the fresh feed stock and the resulting mixture is passed into the reactor.

Why is chemical recycling important?

Chemical recycling could reduce the amount of plastic that ends up in landfills, thereby potentially reducing the release of harmful chemicals into the environment. Chemical recycling can also produce high-quality raw materials, thereby decreasing demand for fossil fuels and other natural resources.

How to Calculate Space Time for First Order Reaction using Recycle Ratio?

Space Time for First Order Reaction using Recycle Ratio calculator uses Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)) to calculate the Space Time, The Space Time for First Order Reaction using Recycle Ratio formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor for first order reaction for zero fractional volume change. Space Time is denoted by 𝛕 symbol.

How to calculate Space Time for First Order Reaction using Recycle Ratio using this online calculator? To use this online calculator for Space Time for First Order Reaction using Recycle Ratio, enter Recycle Ratio (R), Rate Constant for First Order Reaction (k^'), Initial Reactant Concentration (C_o) & Final Reactant Concentration (C_f) and hit the calculate button. Here is how the Space Time for First Order Reaction using Recycle Ratio calculation can be explained with given input values -> 0.062007 = ((0.3+1)/2.508)*ln((80+(0.3*20))/((0.3+1)*20)).

FAQ

What is Space Time for First Order Reaction using Recycle Ratio?

The Space Time for First Order Reaction using Recycle Ratio formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor for first order reaction for zero fractional volume change and is represented as 𝛕 = ((R+1)/k^')*ln((C_o+(R*C_f))/((R+1)*C_f)) or Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)). Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams, 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 & Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.

How to calculate Space Time for First Order Reaction using Recycle Ratio?

The Space Time for First Order Reaction using Recycle Ratio formula is defined as the time taken by the amount of fluid to either completely enter or completely exit the reactor for first order reaction for zero fractional volume change is calculated using Space Time = ((Recycle Ratio+1)/Rate Constant for First Order Reaction)*ln((Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration))/((Recycle Ratio+1)*Final Reactant Concentration)). To calculate Space Time for First Order Reaction using Recycle Ratio, you need Recycle Ratio (R), Rate Constant for First Order Reaction (k^'), Initial Reactant Concentration (C_o) & Final Reactant Concentration (C_f). With our tool, you need to enter the respective value for Recycle Ratio, Rate Constant for First Order Reaction, Initial Reactant Concentration & Final 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?

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

Space Time = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Rate Constant for Second Order Reaction*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))
Space Time = ((Recycle Ratio+1)*Initial Reactant Concentration*(Initial Reactant Concentration-Final Reactant Concentration))/(Initial Reactant Concentration*Rate Constant for Second Order Reaction*Final Reactant Concentration*(Initial Reactant Concentration+(Recycle Ratio*Final Reactant Concentration)))

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