Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation Calculator

✖Reactant Concentration for Strong Pore Diffusion refers to the amount of reactant present at any given point of time during the process, at Strong Resistance of Pore, in Catalyst Deactivation.ⓘ Reactant Concentration for Strong Pore Diffusion [C_A,SP]			+10% -10%
✖The Rate Constant based on Weight of Catalyst is a specific form of expressing the rate constant in a catalytic reaction with respect to the mass of the catalyst.ⓘ Rate Constant based on Weight of Catalyst [k']			+10% -10%
✖Space Time for 1st Order Catalyzed Reactions is a parameter used to quantify the time required for a given volume of reactant to pass through a catalytic reactor.ⓘ Space Time for 1st Order Catalyzed Reactions [𝛕 ']			+10% -10%
✖Thiele Modulus for Deactivation without a is the parameter, which is used for Calculating Effectiveness Factor, in Catalyst Deactivation, without Activity Coefficient.ⓘ Thiele Modulus for Deactivation without a [M_T]			+10% -10%
✖Rate of Deactivation refers to the speed or rate at which the activity of a catalyst decreases over time in a chemical reaction.ⓘ Rate of Deactivation [k_d]			+10% -10%
✖A Time Interval is the amount of time required for the change from initial to the final state.ⓘ Time Interval [t]			+10% -10%

✖Initial Conc. for 1st Order Catalyzed Reactions is the first measured Concentration of a Compound in a Substance.ⓘ Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation [C_A0]

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Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation

Formula

`"C"_{"A0"} = "C"_{"A,SP"}*exp((("k'"*"𝛕 '")/"M"_{"T"})*exp((-"k"_{"d"}*"t")/2))`

Example

`"80.32263mol/m³"="37.9mol/m³"*exp((("0.988s⁻¹"*"2.72s")/"3.4")*exp((-"0.034s⁻¹"*"3s")/2))`

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Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2))
C_A0 = C_A,SP*exp(((k'*𝛕 ')/M_T)*exp((-k_d*t)/2))
This formula uses 1 Functions, 7 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

Initial Conc. for 1st Order Catalyzed Reactions - (Measured in Mole per Cubic Meter) - Initial Conc. for 1st Order Catalyzed Reactions is the first measured Concentration of a Compound in a Substance.
Reactant Concentration for Strong Pore Diffusion - (Measured in Mole per Cubic Meter) - Reactant Concentration for Strong Pore Diffusion refers to the amount of reactant present at any given point of time during the process, at Strong Resistance of Pore, in Catalyst Deactivation.
Rate Constant based on Weight of Catalyst - (Measured in 1 Per Second) - The Rate Constant based on Weight of Catalyst is a specific form of expressing the rate constant in a catalytic reaction with respect to the mass of the catalyst.
Space Time for 1st Order Catalyzed Reactions - (Measured in Second) - Space Time for 1st Order Catalyzed Reactions is a parameter used to quantify the time required for a given volume of reactant to pass through a catalytic reactor.
Thiele Modulus for Deactivation without a - Thiele Modulus for Deactivation without a is the parameter, which is used for Calculating Effectiveness Factor, in Catalyst Deactivation, without Activity Coefficient.
Rate of Deactivation - (Measured in 1 Per Second) - Rate of Deactivation refers to the speed or rate at which the activity of a catalyst decreases over time in a chemical reaction.
Time Interval - (Measured in Second) - A Time Interval is the amount of time required for the change from initial to the final state.

STEP 1: Convert Input(s) to Base Unit

Reactant Concentration for Strong Pore Diffusion: 37.9 Mole per Cubic Meter --> 37.9 Mole per Cubic Meter No Conversion Required
Rate Constant based on Weight of Catalyst: 0.988 1 Per Second --> 0.988 1 Per Second No Conversion Required
Space Time for 1st Order Catalyzed Reactions: 2.72 Second --> 2.72 Second No Conversion Required
Thiele Modulus for Deactivation without a: 3.4 --> No Conversion Required
Rate of Deactivation: 0.034 1 Per Second --> 0.034 1 Per Second No Conversion Required
Time Interval: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_A0 = C_A,SP*exp(((k'*𝛕 ')/M_T)*exp((-k_d*t)/2)) --> 37.9*exp(((0.988*2.72)/3.4)*exp((-0.034*3)/2))

Evaluating ... ...

C_A0 = 80.3226278992389

STEP 3: Convert Result to Output's Unit

80.3226278992389 Mole per Cubic Meter --> No Conversion Required

FINAL ANSWER

80.3226278992389 ≈ 80.32263 Mole per Cubic Meter <-- Initial Conc. for 1st Order Catalyzed Reactions

(Calculation completed in 00.035 seconds)

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< 15 Deactivating Catalysts Calculators

Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids

Go Rate Constant based on Weight of Catalyst = ((Volume of Reactor*Rate of Deactivation)/Weight of Catalyst in Deactivation of Catalyst)*exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)

Weight of Catalyst in Batch Solids and Batch Fluids

Go Weight of Catalyst in Deactivation of Catalyst = ((Volume of Reactor*Rate of Deactivation)/Rate Constant based on Weight of Catalyst)*exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)

Volume of Reactor for Batch Solids and Batch Fluids

Go Volume of Reactor = (Rate Constant based on Weight of Catalyst*Weight of Catalyst in Deactivation of Catalyst)/(exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)*Rate of Deactivation)

Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation

Go Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2))

Deactivation rate for Batch Solids and Mixed Changing Flow of Fluids

Go Rate of Deactivation for Mixed Flow = (ln(Space Time for 1st Order Catalyzed Reactions)-ln((Initial Conc. for 1st Order Catalyzed Reactions-Reactant Concentration)/(Rate Constant based on Weight of Catalyst*Reactant Concentration)))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Mixed Changing Flow of Fluids

Go Rate Constant based on Weight of Catalyst = (Initial Conc. for 1st Order Catalyzed Reactions-Reactant Concentration)/(Reactant Concentration*exp(ln(Space Time for 1st Order Catalyzed Reactions)-Rate of Deactivation for Mixed Flow*Time Interval))

Rate Constant based on Weight of Catalyst in Batch Solids and Plug Changing Flow of Fluids

Go Rate Constant based on Weight of Catalyst = ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)*(1/exp((ln(Space Time for 1st Order Catalyzed Reactions)-Rate of Deactivation for Plug Flow*Time Interval)))

Deactivation Rate for Batch Solids and Plug Changing Flow of Fluids

Go Rate of Deactivation for Plug Flow = (ln(Space Time for 1st Order Catalyzed Reactions)-ln((1/Rate Constant based on Weight of Catalyst)*ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)))/Time Interval

Deactivation rate for Batch Solids and Plug Constant Flow of Fluids

Go Rate of Deactivation for Plug Flow = (ln(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)-ln(ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Plug Constant Flow of Fluids

Go Rate Constant based on Weight of Catalyst = exp(ln(ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration))+Rate of Deactivation for Plug Flow*Time Interval)/Space Time for 1st Order Catalyzed Reactions

Initial Reactant Concentration of Reactant for No Pore Resistance in Catalyst Deactivation

Go Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for No Pore Diffusion*exp(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions*exp(-Rate of Deactivation*Time Interval))

Deactivation Rate in Batch Solids and Mixed Constant Flow of Fluids

Go Rate of Deactivation for Mixed Flow = (ln(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)-ln((Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)-1))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Mixed Constant Flow of Fluids

Go Rate Constant based on Weight of Catalyst = exp(ln((Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)-1)+Rate of Deactivation for Mixed Flow*Time Interval)/Space Time for 1st Order Catalyzed Reactions

Thiele Modulus for Deactivation

Go Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation)

Activity of Catalyst

Go Activity of Catalyst = -(Rate at which Pellet converts Reactant A)/-(Rate of Reaction of A with a Fresh Pellet)

Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation Formula

What is Strong Pore Resistance?

In catalytic processes with strong pore diffusion, the internal structure of the catalyst imposes restrictions on the movement of reactants to the active sites where the catalytic reactions occur and the transport of products away from those sites. This can result in a reduced effective reaction rate compared to the idealized or intrinsic reaction rate.

What is Deactivation of Catalyst?

Catalyst deactivation refers to a gradual loss of catalytic activity over time, leading to a decline in the catalyst's effectiveness in promoting a chemical reaction. This phenomenon can occur due to various factors, and understanding the mechanisms of catalyst deactivation is crucial for optimizing and extending the lifespan of catalysts in industrial processes.

How to Calculate Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation?

Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation calculator uses Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2)) to calculate the Initial Conc. for 1st Order Catalyzed Reactions, The Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation formula is defined as Initial Concentration of Reactant Calculated, when there is Strong Resistance to Pore Diffusion in the Catalyst, with Deactivation. Initial Conc. for 1st Order Catalyzed Reactions is denoted by C_A0 symbol.

How to calculate Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation using this online calculator? To use this online calculator for Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation, enter Reactant Concentration for Strong Pore Diffusion (C_A,SP), Rate Constant based on Weight of Catalyst (k'), Space Time for 1st Order Catalyzed Reactions (𝛕 '), Thiele Modulus for Deactivation without a (M_T), Rate of Deactivation (k_d) & Time Interval (t) and hit the calculate button. Here is how the Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation calculation can be explained with given input values -> 51.07587 = 37.9*exp(((0.988*2.72)/3.4)*exp((-0.034*3)/2)).

FAQ

What is Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation?

The Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation formula is defined as Initial Concentration of Reactant Calculated, when there is Strong Resistance to Pore Diffusion in the Catalyst, with Deactivation and is represented as C_A0 = C_A,SP*exp(((k'*𝛕 ')/M_T)*exp((-k_d*t)/2)) or Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2)). Reactant Concentration for Strong Pore Diffusion refers to the amount of reactant present at any given point of time during the process, at Strong Resistance of Pore, in Catalyst Deactivation, The Rate Constant based on Weight of Catalyst is a specific form of expressing the rate constant in a catalytic reaction with respect to the mass of the catalyst, Space Time for 1st Order Catalyzed Reactions is a parameter used to quantify the time required for a given volume of reactant to pass through a catalytic reactor, Thiele Modulus for Deactivation without a is the parameter, which is used for Calculating Effectiveness Factor, in Catalyst Deactivation, without Activity Coefficient, Rate of Deactivation refers to the speed or rate at which the activity of a catalyst decreases over time in a chemical reaction & A Time Interval is the amount of time required for the change from initial to the final state.

How to calculate Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation?

The Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation formula is defined as Initial Concentration of Reactant Calculated, when there is Strong Resistance to Pore Diffusion in the Catalyst, with Deactivation is calculated using Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2)). To calculate Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation, you need Reactant Concentration for Strong Pore Diffusion (C_A,SP), Rate Constant based on Weight of Catalyst (k'), Space Time for 1st Order Catalyzed Reactions (𝛕 '), Thiele Modulus for Deactivation without a (M_T), Rate of Deactivation (k_d) & Time Interval (t). With our tool, you need to enter the respective value for Reactant Concentration for Strong Pore Diffusion, Rate Constant based on Weight of Catalyst, Space Time for 1st Order Catalyzed Reactions, Thiele Modulus for Deactivation without a, Rate of Deactivation & Time Interval 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 Initial Conc. for 1st Order Catalyzed Reactions?

In this formula, Initial Conc. for 1st Order Catalyzed Reactions uses Reactant Concentration for Strong Pore Diffusion, Rate Constant based on Weight of Catalyst, Space Time for 1st Order Catalyzed Reactions, Thiele Modulus for Deactivation without a, Rate of Deactivation & Time Interval. We can use 1 other way(s) to calculate the same, which is/are as follows -

Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for No Pore Diffusion*exp(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions*exp(-Rate of Deactivation*Time Interval))

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