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Rate Constant for First Order Reaction using Recycle Ratio Formula

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

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

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

Rate Constant for First Order Reaction using Recycle Ratio Example

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

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

Here is how the Rate Constant for First Order Reaction using Recycle Ratio equation looks like.

31.1025 = (\frac{0.3 + 1}{0.05}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

31.1025s⁻¹ = (\frac{0.3 + 1}{0.05s}) \cdot \ln (\frac{80mol/m³ + (0.3 \cdot 20mol/m³)}{(0.3 + 1) \cdot 20mol/m³})

31.1025 = (\frac{0.3 + 1}{0.05}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

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Rate Constant for First Order Reaction using Recycle Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k' = (\frac{0.3 + 1}{0.05s}) \cdot \ln (\frac{80mol/m³ + (0.3 \cdot 20mol/m³)}{(0.3 + 1) \cdot 20mol/m³})

Next Step Prepare to Evaluate

∴

k' = (\frac{0.3 + 1}{0.05}) \cdot \ln (\frac{80 + (0.3 \cdot 20)}{(0.3 + 1) \cdot 20})

Next Step Evaluate

∴

k' = 31.1025197140327s⁻¹

LAST Step Rounding Answer

∴

k' = 31.1025s⁻¹

Rate Constant for First Order Reaction using Recycle Ratio Formula Elements

Variables

Functions

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

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

Space Time

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.

Symbol: 𝛕

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Space Time

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 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 Rate Constant for First Order Reaction using Recycle Ratio?

Rate Constant for First Order Reaction using Recycle Ratio evaluator uses 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)) to evaluate the Rate Constant for First Order Reaction, The Rate Constant for First Order Reaction using Recycle Ratio formula is defined as the constant of proportionality which gives the relation between rate for first order reaction and the first power of concentration of one of the reactants for zero fractional volume change. Rate Constant for First Order Reaction is denoted by k^' symbol.

How to evaluate Rate Constant for First Order Reaction using Recycle Ratio using this online evaluator? To use this online evaluator for Rate Constant for First Order Reaction using Recycle Ratio, enter Recycle Ratio (R), Space Time (𝛕), Initial Reactant Concentration (C_o) & Final Reactant Concentration (C_f) and hit the calculate button.

FAQs on Rate Constant for First Order Reaction using Recycle Ratio

What is the formula to find Rate Constant for First Order Reaction using Recycle Ratio?

The formula of Rate Constant for First Order Reaction using Recycle Ratio is expressed as 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)). Here is an example- 31.10252 = ((0.3+1)/0.05)*ln((80+(0.3*20))/((0.3+1)*20)).

How to calculate Rate Constant for First Order Reaction using Recycle Ratio?

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

Can the Rate Constant for First Order Reaction using Recycle Ratio be negative?

Yes, the Rate Constant for First Order Reaction using Recycle Ratio, measured in First Order Reaction Rate Constant can be negative.

Which unit is used to measure Rate Constant for First Order Reaction using Recycle Ratio?

Rate Constant for First Order Reaction using Recycle Ratio is usually measured using the 1 Per Second[s⁻¹] for First Order Reaction Rate Constant. 1 Per Millisecond[s⁻¹], 1 Per Day[s⁻¹], 1 Per Hour[s⁻¹] are the few other units in which Rate Constant for First Order Reaction using Recycle Ratio can be measured.

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Rate Constant for First Order Reaction using Recycle Ratio Formula

Rate Constant for First Order Reaction using Recycle Ratio Example

Rate Constant for First Order Reaction using Recycle Ratio Solution

Rate Constant for First Order Reaction using Recycle Ratio Formula Elements

Other formulas in Recycle Reactor category

How to Evaluate Rate Constant for First Order Reaction using Recycle Ratio?

FAQs on Rate Constant for First Order Reaction using Recycle Ratio

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