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

GoSpace Time for Zero Order Reaction using Rate Constant for Plug Flow Formula

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Space Time in PFR is the time necessary to process volume of reactor fluid at the entrance conditions. Check FAQs

𝛕 pfr = (\frac{1}{k plug flow}) \cdot ((1 + ε PFR) \cdot \ln (\frac{1}{1 - X A-PFR}) - (ε PFR \cdot X A-PFR))

𝛕_pfr - Space Time in PFR?k_{plug flow} - Rate Constant for First Order in Plug Flow?ε_PFR - Fractional Volume Change in PFR?X_A-PFR - Reactant Conversion in PFR?

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

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Here is how the Space Time for First Order Reaction using Rate Constant for Plug Flow equation looks like with Values.

Here is how the Space Time for First Order Reaction using Rate Constant for Plug Flow equation looks like with Units.

Here is how the Space Time for First Order Reaction using Rate Constant for Plug Flow equation looks like.

0.0348 = (\frac{1}{39.5}) \cdot ((1 + 0.22) \cdot \ln (\frac{1}{1 - 0.715}) - (0.22 \cdot 0.715))

0.0348s = (\frac{1}{39.5s⁻¹}) \cdot ((1 + 0.22) \cdot \ln (\frac{1}{1 - 0.715}) - (0.22 \cdot 0.715))

0.0348 = (\frac{1}{39.5}) \cdot ((1 + 0.22) \cdot \ln (\frac{1}{1 - 0.715}) - (0.22 \cdot 0.715))

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

Follow our step by step solution on how to calculate Space Time for First Order Reaction using Rate Constant for Plug Flow?

FIRST Step Consider the formula

𝛕 pfr = (\frac{1}{k plug flow}) \cdot ((1 + ε PFR) \cdot \ln (\frac{1}{1 - X A-PFR}) - (ε PFR \cdot X A-PFR))

Next Step Substitute values of Variables

∴

𝛕 pfr = (\frac{1}{39.5s⁻¹}) \cdot ((1 + 0.22) \cdot \ln (\frac{1}{1 - 0.715}) - (0.22 \cdot 0.715))

Next Step Prepare to Evaluate

∴

𝛕 pfr = (\frac{1}{39.5}) \cdot ((1 + 0.22) \cdot \ln (\frac{1}{1 - 0.715}) - (0.22 \cdot 0.715))

Next Step Evaluate

∴

𝛕 pfr = 0.0347879655805178s

LAST Step Rounding Answer

∴

𝛕 pfr = 0.0348s

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

Variables

Functions

Space Time in PFR

Space Time in PFR is the time necessary to process volume of reactor fluid at the entrance conditions.

Symbol: 𝛕_pfr

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Space Time in PFR

Rate Constant for First Order in Plug 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.

Symbol: k_{plug flow}

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value can be positive or negative.

Formulas to find Rate Constant for First Order in Plug Flow

Fractional Volume Change in PFR

Fractional Volume Change in PFR is the ratio of the change in volume and the initial volume.

Symbol: ε_PFR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Fractional Volume Change in PFR

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.

Symbol: X_A-PFR

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Reactant Conversion in PFR

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 in PFR

Go Space Time for Zero Order Reaction using Rate Constant for Plug Flow

𝛕 pfr = \frac{X A-PFR \cdot C o pfr}{k 0}

Other formulas in Plug Flow or Batch category

Go Initial Reactant Concentration for Second Order Reaction for Mixed Flow

Co MixedFlow = (\frac{1}{𝛕 MFR} \cdot k'' MFR) \cdot (\frac{X MFR \cdot {(1 + (ε \cdot X MFR))}^{2}}{{(1 - X MFR)}^{2}})

Go Initial Reactant Concentration for Zero Order Reaction for Mixed Flow

C o-MFR = \frac{k 0-MFR \cdot 𝛕 MFR}{X MFR}

Go Rate Constant for First Order Reaction for Mixed Flow

k1 MFR = (\frac{1}{𝛕 MFR}) \cdot (\frac{X MFR \cdot (1 + (ε \cdot X MFR))}{1 - X MFR})

Go Rate Constant for Second Order Reaction for Mixed Flow

k MixedFlow'' = (\frac{1}{𝛕 MFR} \cdot C o-MFR) \cdot (\frac{X MFR \cdot {(1 + (ε \cdot X MFR))}^{2}}{{(1 - X MFR)}^{2}})

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

Space Time for First Order Reaction using Rate Constant for Plug Flow evaluator 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 evaluate 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 evaluate Space Time for First Order Reaction using Rate Constant for Plug Flow using this online evaluator? To use this online evaluator 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.

FAQs on Space Time for First Order Reaction using Rate Constant for Plug Flow

What is the formula to find Space Time for First Order Reaction using Rate Constant for Plug Flow?

The formula of Space Time for First Order Reaction using Rate Constant for Plug Flow is expressed as 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)). Here is an example- 0.034788 = (1/39.5)*((1+0.22)*ln(1/(1-0.715))-(0.22*0.715)).

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

With 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) we can find Space Time for First Order Reaction using Rate Constant for Plug Flow using the formula - 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)). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Space Time in PFR?

Here are the different ways to Calculate Space Time in PFR-

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

Can the Space Time for First Order Reaction using Rate Constant for Plug Flow be negative?

No, the Space Time for First Order Reaction using Rate Constant for Plug Flow, measured in Time cannot be negative.

Which unit is used to measure Space Time for First Order Reaction using Rate Constant for Plug Flow?

Space Time for First Order Reaction using Rate Constant for Plug Flow 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 Rate Constant for Plug Flow can be measured.

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