## Time at Max Intermediate in First Order followed by Zero Order Reaction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns)
τR,max = (1/k1)*ln((k1*CAo)/k0)
This formula uses 1 Functions, 4 Variables
Functions Used
ln - Natural logarithm function (base e), 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 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.
Initial Reactant Concentration for Multiple Rxns - (Measured in Mole per Cubic Meter) - The Initial Reactant Concentration for Multiple Rxns refers to the amount of reactant present in the solvent before the considered process.
Rate Constant for Zero Order Rxn for Multiple Rxns - (Measured in Mole per Cubic Meter Second) - The Rate Constant for Zero Order Rxn for Multiple Rxns is equal to the rate of the reaction because in this case the rate of reaction is proportional to zero power of the conc of the reactant.
STEP 1: Convert Input(s) to Base Unit
Rate Constant for First Step First Order Reaction: 0.42 1 Per Second --> 0.42 1 Per Second No Conversion Required
Initial Reactant Concentration for Multiple Rxns: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Rate Constant for Zero Order Rxn for Multiple Rxns: 6.5 Mole per Cubic Meter Second --> 6.5 Mole per Cubic Meter Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τR,max = (1/k1)*ln((k1*CAo)/k0) --> (1/0.42)*ln((0.42*80)/6.5)
Evaluating ... ...
τR,max = 3.91124735730373
STEP 3: Convert Result to Output's Unit
3.91124735730373 Second --> No Conversion Required
3.91124735730373 3.911247 Second <-- Time at Maximum Intermediate Concentration
(Calculation completed in 00.004 seconds)
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## < 10+ First Order followed by Zero Order Reaction Calculators

Maximum Intermediate Concentration in First Order followed by Zero Order Reaction
Maximum Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns*(1-(Rate Constant for Zero Order Rxn for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction)*(1-ln(Rate Constant for Zero Order Rxn for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction)))))
Rate Constant for Zero Order Reaction using Rate Constant for First Order Reaction
Rate Constant for Zero Order Rxn for Multiple Rxns = (Initial Reactant Concentration for Multiple Rxns/Time Interval)*(1-exp((-Rate Constant for First Step First Order Reaction)*Time Interval)-(Intermediate Concentration/Initial Reactant Concentration for Multiple Rxns))
Intermediate Concentration for First Order followed by Zero Order Reaction
Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns*(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval)-((Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval)/Initial Reactant Concentration for Multiple Rxns))
Rate Constant for First Order Reaction using Rate Constant for Zero Order Reaction
Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns-(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval)-Intermediate Concentration))
Time at Max Intermediate in First Order followed by Zero Order Reaction
Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns)
Initial Reactant Concentration using Intermediate for First Order followed by Zero Order Reaction
Initial Reactant Concentration for Multiple Rxns = (Intermediate Concentration+(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval))/(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval))
Rate Constant for First Order Reaction in First Order followed by Zero Order Reaction
Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration for Multiple Rxns/Reactant Concentration for Multiple Rxns)
Time Interval for First Order Reaction in First Order followed by Zero Order Reaction
Time Interval = (1/Rate Constant for First Step First Order Reaction)*ln(Initial Reactant Concentration for Multiple Rxns/Reactant Concentration for Multiple Rxns)
Initial Reactant Concentration in First Order followed by Zero Order Reaction
Initial Reactant Concentration for Multiple Rxns = Reactant Concentration for Multiple Rxns/exp(-Rate Constant for First Step First Order Reaction*Time Interval)
Reactant Concentration in First Order followed by Zero Order Reaction
Reactant Concentration for Multiple Rxns = Initial Reactant Concentration for Multiple Rxns*exp(-Rate Constant for First Step First Order Reaction*Time Interval)

## < 25 Important Formulas in Potpourri of Multiple Reactions Calculators

Initial Reactant Concentration for Two Steps First Order Irreversible Reaction in Series
Initial Reactant Concentration for Multiple Rxns = (Intermediate Concentration*(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)-exp(-Rate Constant for Second Step First Order Reaction*Space Time)))
Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series
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 First Step First Order Reaction))*(exp(-Rate Constant for First Step First Order Reaction*Space Time)-exp(-Rate Constant for Second Step First Order Reaction*Space Time))
Maximum Intermediate Concentration in First Order followed by Zero Order Reaction
Maximum Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns*(1-(Rate Constant for Zero Order Rxn for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction)*(1-ln(Rate Constant for Zero Order Rxn for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction)))))
Initial Reactant Concentration for First Order Reaction for MFR using Product Concentration
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))
Product Concentration for First Order Reaction for Mixed Flow Reactor
Final Product Concentration = (Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction*(Space Time for Mixed Flow Reactor^2))/((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)))
Initial Reactant Concentration for First Order Reaction for MFR using Intermediate Concentration
Initial Reactant Concentration for Multiple Rxns = (Intermediate 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*Space Time for Mixed Flow Reactor)
Intermediate Concentration for First Order Reaction for Mixed Flow Reactor
Intermediate Concentration = (Initial Reactant Concentration for Multiple Rxns*Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor)/((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)))
Initial Reactant Concentration for First Order Reaction for Maximum Intermediate Concentration
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))
Maximum Intermediate Concentration for First Order Irreversible Reaction in Series
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))
Rate Constant for Zero Order Reaction using Rate Constant for First Order Reaction
Rate Constant for Zero Order Rxn for Multiple Rxns = (Initial Reactant Concentration for Multiple Rxns/Time Interval)*(1-exp((-Rate Constant for First Step First Order Reaction)*Time Interval)-(Intermediate Concentration/Initial Reactant Concentration for Multiple Rxns))
Intermediate Concentration for First Order followed by Zero Order Reaction
Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns*(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval)-((Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval)/Initial Reactant Concentration for Multiple Rxns))
Rate Constant for First Order Reaction using Rate Constant for Zero Order Reaction
Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns-(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval)-Intermediate Concentration))
Time at Max Intermediate in First Order followed by Zero Order Reaction
Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns)
Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series
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)
Initial Reactant Concentration using Intermediate for First Order followed by Zero Order Reaction
Initial Reactant Concentration for Multiple Rxns = (Intermediate Concentration+(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval))/(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval))
Initial Reactant Concentration for First Order Reaction in MFR at Maximum Intermediate Concentration
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)
Maximum Intermediate Concentration for First Order Irreversible Reaction in MFR
Maximum Intermediate Concentration = Initial Reactant Concentration for Multiple Rxns/((((Rate Constant for Second Step First Order Reaction/Rate Constant for First Step First Order Reaction)^(1/2))+1)^2)
Rate Constant for First Order Reaction in First Order followed by Zero Order Reaction
Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration for Multiple Rxns/Reactant Concentration for Multiple Rxns)
Initial Reactant Concentration in First Order followed by Zero Order Reaction
Initial Reactant Concentration for Multiple Rxns = Reactant Concentration for Multiple Rxns/exp(-Rate Constant for First Step First Order Reaction*Time Interval)
Reactant Concentration in First Order followed by Zero Order Reaction
Reactant Concentration for Multiple Rxns = Initial Reactant Concentration for Multiple Rxns*exp(-Rate Constant for First Step First Order Reaction*Time Interval)
Initial Reactant Concentration for Two Steps First Order Reaction for Mixed Flow Reactor
Initial Reactant Concentration for Multiple Rxns = Reactant Concentration for Multiple Rxns*(1+(Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor))
Reactant Concentration for Two Steps First Order Reaction for Mixed Flow Reactor
Reactant Concentration for Multiple Rxns = Initial Reactant Concentration for Multiple Rxns/(1+(Rate Constant for First Step First Order Reaction*Space Time for Mixed Flow Reactor))
Time at Maximum Intermediate Concentration for First Order Irreversible Reaction in Series in MFR
Time at Maximum Intermediate Concentration = 1/sqrt(Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction)
Rate Constant for Second Step First Order Reaction for MFR at Maximum Intermediate Concentration
Rate Constant for Second Step First Order Reaction = 1/(Rate Constant for First Step First Order Reaction*(Time at Maximum Intermediate Concentration^2))
Rate Constant for First Step First Order Reaction for MFR at Maximum Intermediate Concentration
Rate Constant for First Step First Order Reaction = 1/(Rate Constant for Second Step First Order Reaction*(Time at Maximum Intermediate Concentration^2))

## Time at Max Intermediate in First Order followed by Zero Order Reaction Formula

Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns)
τR,max = (1/k1)*ln((k1*CAo)/k0)

## 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 are first order and zero order reactions?

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants.
Zero-order reaction is a chemical reaction wherein the rate does not vary with the increase or decrease in the concentration of the reactants.

## How to Calculate Time at Max Intermediate in First Order followed by Zero Order Reaction?

Time at Max Intermediate in First Order followed by Zero Order Reaction calculator uses Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns) to calculate the Time at Maximum Intermediate Concentration, The Time at Max Intermediate in First Order followed by Zero Order Reaction formula is defined as the time at which the amount of intermediate formed is maximum in first order reaction followed by zero order reaction. Time at Maximum Intermediate Concentration is denoted by τR,max symbol.

How to calculate Time at Max Intermediate in First Order followed by Zero Order Reaction using this online calculator? To use this online calculator for Time at Max Intermediate in First Order followed by Zero Order Reaction, enter Rate Constant for First Step First Order Reaction (k1), Initial Reactant Concentration for Multiple Rxns (CAo) & Rate Constant for Zero Order Rxn for Multiple Rxns (k0) and hit the calculate button. Here is how the Time at Max Intermediate in First Order followed by Zero Order Reaction calculation can be explained with given input values -> 3.911247 = (1/0.42)*ln((0.42*80)/6.5).

### FAQ

What is Time at Max Intermediate in First Order followed by Zero Order Reaction?
The Time at Max Intermediate in First Order followed by Zero Order Reaction formula is defined as the time at which the amount of intermediate formed is maximum in first order reaction followed by zero order reaction and is represented as τR,max = (1/k1)*ln((k1*CAo)/k0) or Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns). 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, The Initial Reactant Concentration for Multiple Rxns refers to the amount of reactant present in the solvent before the considered process & The Rate Constant for Zero Order Rxn for Multiple Rxns is equal to the rate of the reaction because in this case the rate of reaction is proportional to zero power of the conc of the reactant.
How to calculate Time at Max Intermediate in First Order followed by Zero Order Reaction?
The Time at Max Intermediate in First Order followed by Zero Order Reaction formula is defined as the time at which the amount of intermediate formed is maximum in first order reaction followed by zero order reaction is calculated using Time at Maximum Intermediate Concentration = (1/Rate Constant for First Step First Order Reaction)*ln((Rate Constant for First Step First Order Reaction*Initial Reactant Concentration for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns). To calculate Time at Max Intermediate in First Order followed by Zero Order Reaction, you need Rate Constant for First Step First Order Reaction (k1), Initial Reactant Concentration for Multiple Rxns (CAo) & Rate Constant for Zero Order Rxn for Multiple Rxns (k0). With our tool, you need to enter the respective value for Rate Constant for First Step First Order Reaction, Initial Reactant Concentration for Multiple Rxns & Rate Constant for Zero Order Rxn for Multiple Rxns 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 First Step First Order Reaction, Initial Reactant Concentration for Multiple Rxns & Rate Constant for Zero Order Rxn for Multiple Rxns. We can use 2 other way(s) to calculate the same, which is/are as follows -
• 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)
• Time at Maximum Intermediate Concentration = 1/sqrt(Rate Constant for First Step First Order Reaction*Rate Constant for Second Step First Order Reaction) Let Others Know