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

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Space Time for Plug Flow is the time necessary to process volume of reactor fluid at the entrance conditions. Check FAQs

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

𝛕_PlugFlow - Space Time for Plug Flow?k_'' - Rate Constant for Second Order Reaction?C_o - Initial Reactant Concentration?ε - Fractional Volume Change?X_A - Reactant Conversion?

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

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

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

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

0.0583 = (\frac{1}{0.608 \cdot 80}) \cdot (2 \cdot 0.21 \cdot (1 + 0.21) \cdot \ln (1 - 0.7) + {0.21}^{2} \cdot 0.7 + ({(0.21 + 1)}^{2} \cdot \frac{0.7}{1 - 0.7}))

0.0583s = (\frac{1}{0.608m³/(mol*s) \cdot 80mol/m³}) \cdot (2 \cdot 0.21 \cdot (1 + 0.21) \cdot \ln (1 - 0.7) + {0.21}^{2} \cdot 0.7 + ({(0.21 + 1)}^{2} \cdot \frac{0.7}{1 - 0.7}))

0.0583 = (\frac{1}{0.608 \cdot 80}) \cdot (2 \cdot 0.21 \cdot (1 + 0.21) \cdot \ln (1 - 0.7) + {0.21}^{2} \cdot 0.7 + ({(0.21 + 1)}^{2} \cdot \frac{0.7}{1 - 0.7}))

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝛕 PlugFlow = (\frac{1}{0.608m³/(mol*s) \cdot 80mol/m³}) \cdot (2 \cdot 0.21 \cdot (1 + 0.21) \cdot \ln (1 - 0.7) + {0.21}^{2} \cdot 0.7 + ({(0.21 + 1)}^{2} \cdot \frac{0.7}{1 - 0.7}))

Next Step Prepare to Evaluate

∴

𝛕 PlugFlow = (\frac{1}{0.608 \cdot 80}) \cdot (2 \cdot 0.21 \cdot (1 + 0.21) \cdot \ln (1 - 0.7) + {0.21}^{2} \cdot 0.7 + ({(0.21 + 1)}^{2} \cdot \frac{0.7}{1 - 0.7}))

Next Step Evaluate

∴

𝛕 PlugFlow = 0.0582903855710299s

LAST Step Rounding Answer

∴

𝛕 PlugFlow = 0.0583s

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

Variables

Functions

Space Time for Plug Flow

Space Time for Plug Flow is the time necessary to process volume of reactor fluid at the entrance conditions.

Symbol: 𝛕_PlugFlow

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Space Time for Plug Flow

Rate Constant for Second Order Reaction

The Rate Constant for Second Order Reaction is defined as the average rate of the reaction per concentration of the reactant having power raised to 2.

Symbol: k_''

Measurement: Second Order Reaction Rate ConstantUnit: m³/(mol*s)

Note: Value can be positive or negative.

Formulas to find Rate Constant for Second 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

Fractional Volume Change

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

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Fractional Volume Change

Reactant Conversion

Reactant Conversion gives us the percentage of reactants converted into products. Enter the percentage as a decimal between 0 and 1.

Symbol: X_A

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Reactant Conversion

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 Plug Flow Reactor category

Go Initial Reactant Concentration for Second Order Reaction for Plug Flow

Co PlugFlow = (\frac{1}{𝛕 pfr \cdot k''}) \cdot (2 \cdot ε PFR \cdot (1 + ε PFR) \cdot \ln (1 - X A-PFR) + {ε PFR}^{2} \cdot X A-PFR + ({(ε PFR + 1)}^{2} \cdot \frac{X A-PFR}{1 - X A-PFR}))

Go Rate Constant for Second Order Reaction for Plug Flow

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

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

Space Time for Second Order Reaction using Rate Constant for Plug Flow evaluator uses Space Time for Plug Flow = (1/(Rate Constant for Second Order Reaction*Initial Reactant Concentration))*(2*Fractional Volume Change*(1+Fractional Volume Change)*ln(1-Reactant Conversion)+Fractional Volume Change^2*Reactant Conversion+((Fractional Volume Change+1)^2*Reactant Conversion/(1-Reactant Conversion))) to evaluate the Space Time for Plug Flow, The Space Time for Second Order Reaction using Rate Constant for Plug Flow formula is defined as the time necessary to process volume of reactor fluid for second order reaction where fractional volume change is considerable. Space Time for Plug Flow is denoted by 𝛕_PlugFlow symbol.

How to evaluate Space Time for Second Order Reaction using Rate Constant for Plug Flow using this online evaluator? To use this online evaluator for Space Time for Second Order Reaction using Rate Constant for Plug Flow, enter Rate Constant for Second Order Reaction (k_''), Initial Reactant Concentration (C_o), Fractional Volume Change (ε) & Reactant Conversion (X_A) and hit the calculate button.

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

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

The formula of Space Time for Second Order Reaction using Rate Constant for Plug Flow is expressed as Space Time for Plug Flow = (1/(Rate Constant for Second Order Reaction*Initial Reactant Concentration))*(2*Fractional Volume Change*(1+Fractional Volume Change)*ln(1-Reactant Conversion)+Fractional Volume Change^2*Reactant Conversion+((Fractional Volume Change+1)^2*Reactant Conversion/(1-Reactant Conversion))). Here is an example- 0.582904 = (1/(0.608*80))*(2*0.21*(1+0.21)*ln(1-0.7)+0.21^2*0.7+((0.21+1)^2*0.7/(1-0.7))).

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

With Rate Constant for Second Order Reaction (k_''), Initial Reactant Concentration (C_o), Fractional Volume Change (ε) & Reactant Conversion (X_A) we can find Space Time for Second Order Reaction using Rate Constant for Plug Flow using the formula - Space Time for Plug Flow = (1/(Rate Constant for Second Order Reaction*Initial Reactant Concentration))*(2*Fractional Volume Change*(1+Fractional Volume Change)*ln(1-Reactant Conversion)+Fractional Volume Change^2*Reactant Conversion+((Fractional Volume Change+1)^2*Reactant Conversion/(1-Reactant Conversion))). This formula also uses Natural Logarithm Function function(s).

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

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

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

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

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