Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series Calculator

✖The Initial Reactant Concentration for Multiple Rxns refers to the amount of reactant present in the solvent before the considered process.ⓘ Initial Reactant Concentration for Multiple Rxns [C_A0]			+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%
✖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%
✖Space Time for PFR is the time necessary to process volume of reactor fluid at the entrance conditions, the time taken by the amount of fluid to either completely enter or completely exit the reactor.ⓘ Space Time for PFR [τ]			+10% -10%

✖Intermediate Concentration for Series Rxn is the concentration of product of first step or intermediate, of second step of first order irreversible reaction.ⓘ Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series [C_R]

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Formula

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Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series

Formula

`"C"_{"R"} = "C"_{"A0"}*("k"_{"I"}/("k"_{"2"}-"k"_{"I"}))*(exp(-"k"_{"I"}*"τ")-exp(-"k"_{"2"}*"τ"))`

Example

`"8.964735mol/m³"="80mol/m³"*("0.42s⁻¹"/("0.08s⁻¹"-"0.42s⁻¹"))*(exp(-"0.42s⁻¹"*"30s")-exp(-"0.08s⁻¹"*"30s"))`

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Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
C_R = C_A0*(k_I/(k₂-k_I))*(exp(-k_I*τ)-exp(-k₂*τ))
This formula uses 1 Functions, 5 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Intermediate Concentration for Series Rxn - (Measured in Mole per Cubic Meter) - Intermediate Concentration for Series Rxn is the concentration of product of first step or intermediate, of second step of first order irreversible reaction.
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 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.
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.
Space Time for PFR - (Measured in Second) - Space Time for PFR is the time necessary to process volume of reactor fluid at the entrance conditions, the time taken by the amount of fluid to either completely enter or completely exit the reactor.

STEP 1: Convert Input(s) to Base Unit

Initial Reactant Concentration for Multiple Rxns: 80 Mole per Cubic Meter --> 80 Mole per Cubic Meter No Conversion Required
Rate Constant for First Step First Order Reaction: 0.42 1 Per Second --> 0.42 1 Per Second No Conversion Required
Rate Constant for Second Step First Order Reaction: 0.08 1 Per Second --> 0.08 1 Per Second No Conversion Required
Space Time for PFR: 30 Second --> 30 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_R = C_A0*(k_I/(k₂-k_I))*(exp(-k_I*τ)-exp(-k₂*τ)) --> 80*(0.42/(0.08-0.42))*(exp(-0.42*30)-exp(-0.08*30))

Evaluating ... ...

C_R = 8.96473509062469

STEP 3: Convert Result to Output's Unit

8.96473509062469 Mole per Cubic Meter --> No Conversion Required

FINAL ANSWER

8.96473509062469 ≈ 8.964735 Mole per Cubic Meter <-- Intermediate Concentration for Series Rxn

(Calculation completed in 00.004 seconds)

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

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

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))

Maximum Intermediate Concentration in First Order followed by Zero Order Reaction

Go 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 Rxn in Series for MFR using Product Concentration

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))

Product Concentration for First Order Reaction for Mixed Flow Reactor

Go 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 Rxn for MFR using Intermediate Concentration

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)

Intermediate Concentration for First Order Reaction for Mixed Flow Reactor

Go Intermediate Concentration for Series Rxn = (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)))

Intermediate Concentration for First Order followed by Zero Order Reaction

Go Intermediate Conc. for 1st Order Series Rxn = Initial Reactant Concentration for Multiple Rxns*(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval for Multiple Reactions)-((Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval for Multiple Reactions)/Initial Reactant Concentration for Multiple Rxns))

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

Go Rate Constant for First Step First Order Reaction = (1/Time Interval for Multiple Reactions)*ln(Initial Reactant Concentration for Multiple Rxns/(Initial Reactant Concentration for Multiple Rxns-(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval for Multiple Reactions)-Intermediate Concentration for Series Rxn))

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

Go Rate Constant for Zero Order Rxn using k1 = (Initial Reactant Concentration for Multiple Rxns/Time Interval for Multiple Reactions)*(1-exp((-Rate Constant for First Step First Order Reaction)*Time Interval for Multiple Reactions)-(Intermediate Concentration for Series Rxn/Initial Reactant Concentration for Multiple Rxns))

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

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))

Maximum Intermediate Concentration for First Order Irreversible Reaction in Series

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))

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

Go Initial Reactant Concentration using Intermediate = (Intermediate Concentration for Series Rxn+(Rate Constant for Zero Order Rxn for Multiple Rxns*Time Interval for Multiple Reactions))/(1-exp(-Rate Constant for First Step First Order Reaction*Time Interval for Multiple Reactions))

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

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 for Multiple Rxns)/Rate Constant for Zero Order Rxn for Multiple Rxns)

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

Go 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 First Order Reaction in First Order followed by Zero Order Reaction

Go Rate Constant for First Step First Order Reaction = (1/Time Interval for Multiple Reactions)*ln(Initial Reactant Concentration for Multiple Rxns/Reactant Concentration for Zero Order Series Rxn)

Initial Reactant Concentration in First Order followed by Zero Order Reaction

Go Initial Reactant Concentration for Multiple Rxns = Reactant Concentration for Zero Order Series Rxn/exp(-Rate Constant for First Step First Order Reaction*Time Interval for Multiple Reactions)

Reactant Concentration in First Order followed by Zero Order Reaction

Go Reactant Concentration for Zero Order Series Rxn = Initial Reactant Concentration for Multiple Rxns*exp(-Rate Constant for First Step First Order Reaction*Time Interval for Multiple Reactions)

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

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)

Maximum Intermediate Concentration for First Order Irreversible Reaction in MFR

Go 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)

Initial Reactant Concentration for Two Steps First Order Reaction for Mixed Flow Reactor

Go Initial Reactant Concentration for Multiple Rxns = Reactant Concentration for 1st Order Series 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

Go Reactant Concentration for Zero Order Series Rxn = 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

Go 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

Go 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

Go Rate Constant for First Step First Order Reaction = 1/(Rate Constant for Second Step First Order Reaction*(Time at Maximum Intermediate Concentration^2))

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