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)/Rate Constant for Zero Order Reaction)
τR,max = (1/k1)*ln((k1*Co)/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 - (Measured in Mole per Cubic Meter) - The Initial Reactant Concentration refers to the amount of reactant present in the solvent before the considered process.
Rate Constant for Zero Order Reaction - (Measured in Mole per Cubic Meter Second) - The Rate Constant for Zero Order Reaction is equal to the rate of the reaction because in a zero-order reaction the rate of reaction is proportional to zero power of the concentration 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: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Rate Constant for Zero Order Reaction: 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*Co)/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
FINAL ANSWER
3.91124735730373 Second <-- Time at Maximum Intermediate Concentration
(Calculation completed in 00.016 seconds)

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9 First Order followed by Zero Order Reaction Calculators

Rate Constant for Zero Order Reaction using Rate Constant for First Order Reaction

Rate Constant for Zero Order Reaction using Rate Constant for First Order Reaction

Formula
`"k"_{"0"} = ("C"_{"o"}/"Δt")*(1-exp((-"k"_{"1"})*"Δt")-("C"_{"R"}/"C"_{"o"}))`

Example
`"9.596361mol/m³*s"=("80mol/m³"/"0.48s")*(1-exp((-"0.42s⁻¹")*"0.48s")-("10mol/m³"/"80mol/m³"))`

Calculator
LaTeX
Go Rate Constant for Zero Order Reaction = (Initial Reactant Concentration/Time Interval)*(1-exp((-Rate Constant for First Step First Order Reaction)*Time Interval)-(Intermediate Concentration/Initial Reactant Concentration))
Intermediate Concentration for First Order followed by Zero Order Reaction

Intermediate Concentration for First Order followed by Zero Order Reaction

Formula
`"C"_{"R"} = "C"_{"o"}*(1-exp(-"k"_{"1"}*"Δt")-(("k"_{"0"}*"Δt")/"C"_{"o"}))`

Example
`"11.48625mol/m³"="80mol/m³"*(1-exp(-"0.42s⁻¹"*"0.48s")-(("6.5mol/m³*s"*"0.48s")/"80mol/m³"))`

Calculator
LaTeX
Go Intermediate Concentration = Initial Reactant Concentration*(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval)-((Rate Constant for Zero Order Reaction*Time Interval)/Initial Reactant Concentration))
Rate Constant for First Order Reaction using Rate Constant for Zero Order Reaction

Rate Constant for First Order Reaction using Rate Constant for Zero Order Reaction

Formula
`"k"_{"1"} = (1/"Δt")*ln("C"_{"o"}/("C"_{"o"}-("k"_{"0"}*"Δt")-"C"_{"R"}))`

Example
`"0.373181s⁻¹"=(1/"0.48s")*ln("80mol/m³"/("80mol/m³"-("6.5mol/m³*s"*"0.48s")-"10mol/m³"))`

Calculator
LaTeX
Go Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration/(Initial Reactant Concentration-(Rate Constant for Zero Order Reaction*Time Interval)-Intermediate Concentration))
Time at Max Intermediate in First Order followed by Zero Order Reaction

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

Formula
`"τ"_{"R,"max""} = (1/"k"_{"1"})*ln(("k"_{"1"}*"C"_{"o"})/"k"_{"0"})`

Example
`"3.911247s"=(1/"0.42s⁻¹")*ln(("0.42s⁻¹"*"80mol/m³")/"6.5mol/m³*s")`

Calculator
LaTeX
Go 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)/Rate Constant for Zero Order Reaction)
Initial Reactant Concentration using Intermediate for First Order followed by Zero Order Reaction

Initial Reactant Concentration using Intermediate for First Order followed by Zero Order Reaction

Formula
`"C"_{"o"} = ("C"_{"R"}+("k"_{"0"}*"Δt"))/(1-exp(-"k"_{"1"}*"Δt"))`

Example
`"71.85963mol/m³"=("10mol/m³"+("6.5mol/m³*s"*"0.48s"))/(1-exp(-"0.42s⁻¹"*"0.48s"))`

Calculator
LaTeX
Go Initial Reactant Concentration = (Intermediate Concentration+(Rate Constant for Zero Order Reaction*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 Order Reaction in First Order followed by Zero Order Reaction

Formula
`"k"_{"1"} = (1/"Δt")*ln("C"_{"o"}/"C")`

Example
`"2.508277s⁻¹"=(1/"0.48s")*ln("80mol/m³"/"24mol/m³")`

Calculator
LaTeX
Go Rate Constant for First Step First Order Reaction = (1/Time Interval)*ln(Initial Reactant Concentration/Reactant Concentration)
Time Interval for First Order Reaction in First Order followed by Zero Order Reaction

Time Interval for First Order Reaction in First Order followed by Zero Order Reaction

Formula
`"Δt" = (1/"k"_{"1"})*ln("C"_{"o"}/"C")`

Example
`"2.866602s"=(1/"0.42s⁻¹")*ln("80mol/m³"/"24mol/m³")`

Calculator
LaTeX
Go Time Interval = (1/Rate Constant for First Step First Order Reaction)*ln(Initial Reactant Concentration/Reactant Concentration)
Initial Reactant Concentration in First Order followed by Zero Order Reaction

Initial Reactant Concentration in First Order followed by Zero Order Reaction

Formula
`"C"_{"o"} = "C"/exp(-"k"_{"1"}*"Δt")`

Example
`"29.36061mol/m³"="24mol/m³"/exp(-"0.42s⁻¹"*"0.48s")`

Calculator
LaTeX
Go Initial Reactant Concentration = Reactant Concentration/exp(-Rate Constant for First Step First Order Reaction*Time Interval)
Reactant Concentration in First Order followed by Zero Order Reaction

Reactant Concentration in First Order followed by Zero Order Reaction

Formula
`"C" = "C"_{"o"}*exp(-"k"_{"1"}*"Δt")`

Example
`"65.39375mol/m³"="80mol/m³"*exp(-"0.42s⁻¹"*"0.48s")`

Calculator
LaTeX
Go Reactant Concentration = Initial Reactant Concentration*exp(-Rate Constant for First Step First Order Reaction*Time Interval)

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)/Rate Constant for Zero Order Reaction)
τR,max = (1/k1)*ln((k1*Co)/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)/Rate Constant for Zero Order Reaction) 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 (Co) & Rate Constant for Zero Order Reaction (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 -> -12.535789 = (1/0.42)*ln((0.42*80)/6500).

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*Co)/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)/Rate Constant for Zero Order Reaction). 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 refers to the amount of reactant present in the solvent before the considered process & The Rate Constant for Zero Order Reaction is equal to the rate of the reaction because in a zero-order reaction the rate of reaction is proportional to zero power of the concentration 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)/Rate Constant for Zero Order Reaction). 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 (Co) & Rate Constant for Zero Order Reaction (k0). With our tool, you need to enter the respective value for Rate Constant for First Step First Order Reaction, Initial Reactant Concentration & Rate Constant for Zero Order Reaction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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