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

✖Volume of Reactor is a measure of the space within the reactor vessel available for the chemical reaction to take place.ⓘ Volume of Reactor [V]			+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%
✖Weight of Catalyst in Deactivation of Catalyst is the measure of mass of Catalyst, in the Chemical Process.ⓘ Weight of Catalyst in Deactivation of Catalyst [W_d]			+10% -10%
✖Reactant concentration is a measure of the quantity of a specific reactant in relation to the total volume or mass of the system in which a chemical reaction is taking place.ⓘ Reactant Concentration [C_A]			+10% -10%
✖Concentration at Infinite Time refers to the Concentration of Reactant at Infinite Time in an Irreversible Reaction.ⓘ Concentration at Infinite Time [C_A∞]			+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%

✖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 in Batch Solids and Batch Fluids [k']

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

Formula

`"k'" = (("V"*"k"_{"d"})/"W"_{"d"})*exp(ln(ln("C"_{"A"}/"C"_{"A∞"}))+"k"_{"d"}*"t")`

Example

`"0.982634s⁻¹"=(("999m³"*"0.034s⁻¹")/"49kg")*exp(ln(ln("24.1mol/m³"/"6.7mol/m³"))+"0.034s⁻¹"*"3s")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
k' = ((V*k_d)/W_d)*exp(ln(ln(C_A/C_A∞))+k_d*t)
This formula uses 2 Functions, 7 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)
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

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.
Volume of Reactor - (Measured in Cubic Meter) - Volume of Reactor is a measure of the space within the reactor vessel available for the chemical reaction to take place.
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.
Weight of Catalyst in Deactivation of Catalyst - (Measured in Kilogram) - Weight of Catalyst in Deactivation of Catalyst is the measure of mass of Catalyst, in the Chemical Process.
Reactant Concentration - (Measured in Mole per Cubic Meter) - Reactant concentration is a measure of the quantity of a specific reactant in relation to the total volume or mass of the system in which a chemical reaction is taking place.
Concentration at Infinite Time - (Measured in Mole per Cubic Meter) - Concentration at Infinite Time refers to the Concentration of Reactant at Infinite Time in an Irreversible 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

Volume of Reactor: 999 Cubic Meter --> 999 Cubic Meter No Conversion Required
Rate of Deactivation: 0.034 1 Per Second --> 0.034 1 Per Second No Conversion Required
Weight of Catalyst in Deactivation of Catalyst: 49 Kilogram --> 49 Kilogram No Conversion Required
Reactant Concentration: 24.1 Mole per Cubic Meter --> 24.1 Mole per Cubic Meter No Conversion Required
Concentration at Infinite Time: 6.7 Mole per Cubic Meter --> 6.7 Mole per Cubic Meter No Conversion Required
Time Interval: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k' = ((V*k_d)/W_d)*exp(ln(ln(C_A/C_A∞))+k_d*t) --> ((999*0.034)/49)*exp(ln(ln(24.1/6.7))+0.034*3)

Evaluating ... ...

k' = 0.982633856479822

STEP 3: Convert Result to Output's Unit

0.982633856479822 1 Per Second --> No Conversion Required

FINAL ANSWER

0.982633856479822 ≈ 0.982634 1 Per Second <-- Rate Constant based on Weight of Catalyst

(Calculation completed in 00.020 seconds)

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Home » Engineering » Chemical Engineering » Chemical Reaction Engineering » Reactions Catalyzed by Solids » Deactivating Catalysts » Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids

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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)

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

What are Batch Solids and Batch Fluids?

Batch solids refer to solid materials that are processed in a batch mode, meaning that a specific quantity of material is treated or transformed at once in a defined batch or lot. Batch fluids refer to liquid or gaseous materials that are processed in a batch mode, where a specific volume or quantity of fluid is treated or transformed as a distinct batch.

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

Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids calculator uses 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) to calculate the Rate Constant based on Weight of Catalyst, The Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids formula is defined as the Rate Constant based on Weight of the Catalyst, a parameter used to describe the kinetics of a chemical reaction, particularly in the context of catalysis. It is defined by the ratio of the rate of reaction to the weight of the catalyst present. Rate Constant based on Weight of Catalyst is denoted by k' symbol.

How to calculate Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids using this online calculator? To use this online calculator for Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids, enter Volume of Reactor (V), Rate of Deactivation (k_d), Weight of Catalyst in Deactivation of Catalyst (W_d), Reactant Concentration (C_A), Concentration at Infinite Time (C_A∞) & Time Interval (t) and hit the calculate button. Here is how the Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids calculation can be explained with given input values -> 0.982634 = ((999*0.034)/49)*exp(ln(ln(24.1/6.7))+0.034*3).

FAQ

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

The Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids formula is defined as the Rate Constant based on Weight of the Catalyst, a parameter used to describe the kinetics of a chemical reaction, particularly in the context of catalysis. It is defined by the ratio of the rate of reaction to the weight of the catalyst present and is represented as k' = ((V*k_d)/W_d)*exp(ln(ln(C_A/C_A∞))+k_d*t) or 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). Volume of Reactor is a measure of the space within the reactor vessel available for the chemical reaction to take place, Rate of Deactivation refers to the speed or rate at which the activity of a catalyst decreases over time in a chemical reaction, Weight of Catalyst in Deactivation of Catalyst is the measure of mass of Catalyst, in the Chemical Process, Reactant concentration is a measure of the quantity of a specific reactant in relation to the total volume or mass of the system in which a chemical reaction is taking place, Concentration at Infinite Time refers to the Concentration of Reactant at Infinite Time in an Irreversible Reaction & A Time Interval is the amount of time required for the change from initial to the final state.

How to calculate Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids?

The Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids formula is defined as the Rate Constant based on Weight of the Catalyst, a parameter used to describe the kinetics of a chemical reaction, particularly in the context of catalysis. It is defined by the ratio of the rate of reaction to the weight of the catalyst present is calculated using 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). To calculate Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids, you need Volume of Reactor (V), Rate of Deactivation (k_d), Weight of Catalyst in Deactivation of Catalyst (W_d), Reactant Concentration (C_A), Concentration at Infinite Time (C_A∞) & Time Interval (t). With our tool, you need to enter the respective value for Volume of Reactor, Rate of Deactivation, Weight of Catalyst in Deactivation of Catalyst, Reactant Concentration, Concentration at Infinite Time & 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 Rate Constant based on Weight of Catalyst?

In this formula, Rate Constant based on Weight of Catalyst uses Volume of Reactor, Rate of Deactivation, Weight of Catalyst in Deactivation of Catalyst, Reactant Concentration, Concentration at Infinite Time & Time Interval. We can use 4 other way(s) to calculate the same, which is/are as follows -

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
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 = 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
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)))

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