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Space Time for First Order Reaction using Recycle Ratio Formula

GoSpace Time for Second Order Reaction using Recycle Ratio Formula

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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. Check FAQs

𝛕 = (\frac{R + 1}{k'}) \cdot \ln (\frac{C o + (R \cdot C f)}{(R + 1) \cdot C f})

𝛕 - Space Time?R - Recycle Ratio?k^' - Rate Constant for First Order Reaction?C_o - Initial Reactant Concentration?C_f - Final Reactant Concentration?

Space Time for First Order Reaction using Recycle Ratio Example

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Here is how the Space Time for First Order Reaction using Recycle Ratio equation looks like with Values.

Here is how the Space Time for First Order Reaction using Recycle Ratio equation looks like with Units.

Here is how the Space Time for First Order Reaction using Recycle Ratio equation looks like.

0.6201 = (\frac{0.3 + 1}{2.508}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

0.6201s = (\frac{0.3 + 1}{2.508s⁻¹}) \cdot \ln (\frac{80mol/m³ + (0.3 \cdot 20mol/m³)}{(0.3 + 1) \cdot 20mol/m³})

0.6201 = (\frac{0.3 + 1}{2.508}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

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Space Time for First Order Reaction using Recycle Ratio Solution

Follow our step by step solution on how to calculate Space Time for First Order Reaction using Recycle Ratio?

FIRST Step Consider the formula

𝛕 = (\frac{R + 1}{k'}) \cdot \ln (\frac{C o + (R \cdot C f)}{(R + 1) \cdot C f})

Next Step Substitute values of Variables

∴

𝛕 = (\frac{0.3 + 1}{2.508s⁻¹}) \cdot \ln (\frac{80mol/m³ + (0.3 \cdot 20mol/m³)}{(0.3 + 1) \cdot 20mol/m³})

Next Step Prepare to Evaluate

∴

𝛕 = (\frac{0.3 + 1}{2.508}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

Next Step Evaluate

∴

𝛕 = 0.620066182496664s

LAST Step Rounding Answer

∴

𝛕 = 0.6201s

Space Time for First Order Reaction using Recycle Ratio Formula Elements

Variables

Functions

Space Time

Symbol: 𝛕

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Space Time

Recycle Ratio

Recycle Ratio is defined as volume of feed, returned to the reactor entrance divided by the volume of the leaving streams.

Symbol: R

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Recycle Ratio

Rate Constant for First Order Reaction

The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.

Symbol: k^'

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value can be positive or negative.

Formulas to find Rate Constant for First Order Reaction

Initial Reactant Concentration

The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process.

Symbol: C_o

Measurement: Molar ConcentrationUnit: mol/m³

Note: Value should be greater than 0.

Formulas to find Initial Reactant Concentration

Final Reactant Concentration

Final Reactant Concentration refers to the amount of reactant present in solution after the considered process.

Symbol: C_f

Measurement: Molar ConcentrationUnit: mol/m³

Note: Value can be positive or negative.

Formulas to find Final Reactant Concentration

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Space Time

Go Space Time for Second Order Reaction using Recycle Ratio

𝛕 = \frac{(R + 1) \cdot C o \cdot (C o - C f)}{C o \cdot k'' \cdot C f \cdot (C o + (R \cdot C f))}

Other formulas in Recycle Reactor category

Go Initial Reactant Concentration for First Order Reaction in Vessel i

C i-1 = C i \cdot (1 + (k' \cdot trC2'))

Go Initial Reactant Concentration for First Order Reaction using Reaction Rate

C o = \frac{trC2' \cdot r i}{X i-1 - X i}

Go Initial Reactant Concentration for Second Order Reaction for Plug Flow or Infinite Reactors

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

Go Reactant Concentration for First Order Reaction in Vessel i

C i = \frac{C i-1}{1 + (k' \cdot trC2')}

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

Space Time for First Order Reaction using Recycle Ratio evaluator 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 evaluate 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 evaluate Space Time for First Order Reaction using Recycle Ratio using this online evaluator? To use this online evaluator 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.

FAQs on Space Time for First Order Reaction using Recycle Ratio

What is the formula to find Space Time for First Order Reaction using Recycle Ratio?

The formula of Space Time for First Order Reaction using Recycle Ratio is expressed as 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)). Here is an example- 0.062007 = ((0.3+1)/2.508)*ln((80+(0.3*20))/((0.3+1)*20)).

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

With Recycle Ratio (R), Rate Constant for First Order Reaction (k^'), Initial Reactant Concentration (C_o) & Final Reactant Concentration (C_f) we can find Space Time for First Order Reaction using Recycle Ratio using the formula - 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)). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Space Time?

Here are the different ways to Calculate Space Time-

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)))

Can the Space Time for First Order Reaction using Recycle Ratio be negative?

No, the Space Time for First Order Reaction using Recycle Ratio, measured in Time cannot be negative.

Which unit is used to measure Space Time for First Order Reaction using Recycle Ratio?

Space Time for First Order Reaction using Recycle Ratio is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Space Time for First Order Reaction using Recycle Ratio can be measured.

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Space Time for First Order Reaction using Recycle Ratio Formula

​GoSpace Time for Second Order Reaction using Recycle Ratio Formula

Space Time for First Order Reaction using Recycle Ratio Example

Space Time for First Order Reaction using Recycle Ratio Solution

Space Time for First Order Reaction using Recycle Ratio Formula Elements

Other Formulas to find Space Time

Other formulas in Recycle Reactor category

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

FAQs on Space Time for First Order Reaction using Recycle Ratio

Variable Name

GoSpace Time for Second Order Reaction using Recycle Ratio Formula