Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series Calculator

✖Rate Constant for Second Step First Order Reaction is defined as the constant of proportionality for second step reaction in two steps first order irreversible reaction in series.ⓘ Rate Constant for Second Step First Order Reaction [k₂]			+10% -10%
✖Rate Constant for First Step First Order Reaction is defined as the constant of proportionality for first step reaction in two steps first order irreversible reaction in series.ⓘ Rate Constant for First Step First Order Reaction [k_I]			+10% -10%

✖Time at Maximum Intermediate Concentration is the instant of time at which maximum concentration of intermediate is achieved.ⓘ Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series [τ_R,max]

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Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time at Maximum Intermediate Concentration = ln(Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction)
τ_R,max = ln(k₂/k_I)/(k₂-k_I)
This formula uses 1 Functions, 3 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

Time at Maximum Intermediate Concentration - (Measured in Second) - Time at Maximum Intermediate Concentration is the instant of time at which maximum concentration of intermediate is achieved.
Rate Constant for Second Step First Order Reaction - (Measured in 1 Per Second) - Rate Constant for Second Step First Order Reaction is defined as the constant of proportionality for second step reaction in two steps first order irreversible reaction in series.
Rate Constant for First Step First Order Reaction - (Measured in 1 Per Second) - Rate Constant for First Step First Order Reaction is defined as the constant of proportionality for first step reaction in two steps first order irreversible reaction in series.

STEP 1: Convert Input(s) to Base Unit

Rate Constant for Second Step First Order Reaction: 0.08 1 Per Second --> 0.08 1 Per Second No Conversion Required
Rate Constant for First Step First Order Reaction: 0.42 1 Per Second --> 0.42 1 Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_R,max = ln(k₂/k_I)/(k₂-k_I) --> ln(0.08/0.42)/(0.08-0.42)

Evaluating ... ...

τ_R,max = 4.87714140177509

STEP 3: Convert Result to Output's Unit

4.87714140177509 Second --> No Conversion Required

FINAL ANSWER

4.87714140177509 ≈ 4.877141 Second <-- Time at Maximum Intermediate Concentration

(Calculation completed in 00.006 seconds)

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< Important Formulas in Potpourri of Multiple Reactions Calculators

Initial Reactant Concentration for First Order Rxn in Series for MFR using Product Concentration

LaTeX Go Initial Reactant Concentration for Multiple Rxns = (Final Product Concentration*(1+(Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor))*(1+(Rate Constant for Second Step First Order Reaction*Space Time for Mixed Flow Reactor)))/(Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction*(Space Time for Mixed Flow Reactor^2))

Initial Reactant Concentration for First Order Rxn for MFR using Intermediate Concentration

LaTeX Go Initial Reactant Concentration for Multiple Rxns = (Intermediate Concentration for Series Rxn*(1+(Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor))*(1+(Rate Constant for Second Step First Order Reaction*Space Time for Mixed Flow Reactor)))/(Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor)

Initial Reactant Concentration for First Order Rxn in Series for Maximum Intermediate Concentration

LaTeX Go Initial Reactant Concentration for Multiple Rxns = Maximum Intermediate Concentration/(Rate Constant for First Step First Order Reaction/Rate Constant for Second Step First Order Reaction)^(Rate Constant for Second Step First Order Reaction/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction))

Initial Reactant Concentration for First Order Rxn in MFR at Maximum Intermediate Concentration

LaTeX Go Initial Reactant Concentration for Multiple Rxns = Maximum Intermediate Concentration*((((Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)^(1/2))+1)^2)

< Basics of Potpourri Reactions Calculators

Initial Reactant Concentration for Two Steps First Order Irreversible Reaction in Series

LaTeX Go Initial Reactant Concentration for Multiple Rxns = (Intermediate Concentration for Series Rxn*(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction))/(Rate Constant for First Step First Order Reaction*(exp(-Rate Constant for First Step First Order Reaction*Space Time for PFR)-exp(-Rate Constant for Second Step First Order Reaction*Space Time for PFR)))

Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series

LaTeX Go Intermediate Concentration for Series Rxn = Initial Reactant Concentration for Multiple Rxns*(Rate Constant for First Step First Order Reaction/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction))*(exp(-Rate Constant for First Step First Order Reaction*Space Time for PFR)-exp(-Rate Constant for Second Step First Order Reaction*Space Time for PFR))

Initial Reactant Concentration for First Order Rxn in Series for Maximum Intermediate Concentration

Maximum Intermediate Concentration for First Order Irreversible Reaction in Series

LaTeX Go Maximum Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns*(Rate Constant for First Step First Order Reaction/Rate Constant for Second Step First Order Reaction)^(Rate Constant for Second Step First Order Reaction/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction))

Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series Formula

LaTeX Go

What is Multi-step Reaction?

A multi-step reaction is a combination of two or more elementary steps. An elementary step is a single, simple step involving one or two particles. The rate-determining step is the slowest step in a multi-step reaction, and the overall reaction rate will be exactly the same as the rate of the slowest step.

What is Plug Flow Reactor?

The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.

How to Calculate Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series?

Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series calculator uses Time at Maximum Intermediate Concentration = ln(Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction) to calculate the Time at Maximum Intermediate Concentration, The Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series formula is defined as the time at which maximum concentration of intermediate is achieved for two steps first order irreversible reaction in series. Time at Maximum Intermediate Concentration is denoted by τ_R,max symbol.

How to calculate Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series using this online calculator? To use this online calculator for Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series, enter Rate Constant for Second Step First Order Reaction (k₂) & Rate Constant for First Step First Order Reaction (k_I) and hit the calculate button. Here is how the Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series calculation can be explained with given input values -> 4.877141 = ln(0.08/0.42)/(0.08-0.42).

FAQ

What is Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series?

The Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series formula is defined as the time at which maximum concentration of intermediate is achieved for two steps first order irreversible reaction in series and is represented as τ_R,max = ln(k₂/k_I)/(k₂-k_I) or Time at Maximum Intermediate Concentration = ln(Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction). Rate Constant for Second Step First Order Reaction is defined as the constant of proportionality for second step reaction in two steps first order irreversible reaction in series & Rate Constant for First Step First Order Reaction is defined as the constant of proportionality for first step reaction in two steps first order irreversible reaction in series.

How to calculate Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series?

The Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series formula is defined as the time at which maximum concentration of intermediate is achieved for two steps first order irreversible reaction in series is calculated using Time at Maximum Intermediate Concentration = ln(Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)/(Rate Constant for Second Step First Order Reaction-Rate Constant for First Step First Order Reaction). To calculate Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series, you need Rate Constant for Second Step First Order Reaction (k₂) & Rate Constant for First Step First Order Reaction (k_I). With our tool, you need to enter the respective value for Rate Constant for Second Step First Order Reaction & Rate Constant for First Step First Order Reaction 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 Time at Maximum Intermediate Concentration?

In this formula, Time at Maximum Intermediate Concentration uses Rate Constant for Second Step First Order Reaction & Rate Constant for First Step First Order Reaction. We can use 2 other way(s) to calculate the same, which is/are as follows -

Time at Maximum Intermediate Concentration = 1/sqrt(Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction)
Time at Maximum Intermediate Concentration = 1/sqrt(Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction)

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