Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order Calculator

✖The Reactant Concentration refers to the amount of reactant present at any given point of time during the process.ⓘ Reactant Concentration [C]			+10% -10%
✖Reaction Rate based on Volume of Catalyst Pellets is the Reaction rate calculated based on Volume of Catalyst pellets, where Catalyst is present in the Reactor.ⓘ Reaction Rate based on Volume of Catalyst Pellets [r_a''']			+10% -10%
✖Solid Fraction is defined as the Solid Fraction of the Catalyst which varies with the Initial Weight of Catalyst laid in the Reactor.ⓘ Solid Fraction [f]			+10% -10%
✖Height of Catalyst Bed is Height of the laid Catalyst in the Reactor.ⓘ Height of Catalyst Bed [H]			+10% -10%
✖Superficial Gas Velocity is the Velocity recorded where the solids are absent.ⓘ Superficial Gas Velocity [u₀]			+10% -10%

✖Initial Concentration of Reactant is the first measured Concentration of a Compound in a Substance.ⓘ Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order [C_AO]

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Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order

Formula

`"C"_{"AO"} = "C"*(exp((("r"_{"a"}"'''")*"f"*"H")/"u"_{"0"}))`

Example

`"41.5108mol/m³"="24mol/m³"*(exp(("1.908mol/m³*s"*"0.78"*"2.89m")/"7.85m/s"))`

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Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity))
C_AO = C*(exp((r_a'''*f*H)/u₀))
This formula uses 1 Functions, 6 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 Concentration of Reactant - (Measured in Mole per Cubic Meter) - Initial Concentration of Reactant is the first measured Concentration of a Compound in a Substance.
Reactant Concentration - (Measured in Mole per Cubic Meter) - The Reactant Concentration refers to the amount of reactant present at any given point of time during the process.
Reaction Rate based on Volume of Catalyst Pellets - (Measured in Mole per Cubic Meter Second) - Reaction Rate based on Volume of Catalyst Pellets is the Reaction rate calculated based on Volume of Catalyst pellets, where Catalyst is present in the Reactor.
Solid Fraction - Solid Fraction is defined as the Solid Fraction of the Catalyst which varies with the Initial Weight of Catalyst laid in the Reactor.
Height of Catalyst Bed - (Measured in Meter) - Height of Catalyst Bed is Height of the laid Catalyst in the Reactor.
Superficial Gas Velocity - (Measured in Meter per Second) - Superficial Gas Velocity is the Velocity recorded where the solids are absent.

STEP 1: Convert Input(s) to Base Unit

Reactant Concentration: 24 Mole per Cubic Meter --> 24 Mole per Cubic Meter No Conversion Required
Reaction Rate based on Volume of Catalyst Pellets: 1.908 Mole per Cubic Meter Second --> 1.908 Mole per Cubic Meter Second No Conversion Required
Solid Fraction: 0.78 --> No Conversion Required
Height of Catalyst Bed: 2.89 Meter --> 2.89 Meter No Conversion Required
Superficial Gas Velocity: 7.85 Meter per Second --> 7.85 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_AO = C*(exp((r_a'''*f*H)/u₀)) --> 24*(exp((1.908*0.78*2.89)/7.85))

Evaluating ... ...

C_AO = 41.510800733093

STEP 3: Convert Result to Output's Unit

41.510800733093 Mole per Cubic Meter --> No Conversion Required

FINAL ANSWER

41.510800733093 ≈ 41.5108 Mole per Cubic Meter <-- Initial Concentration of Reactant

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Chemical Reaction Engineering » Reactions Catalyzed by Solids » Solid Catalyzed Reactions » Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order

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Mass Transfer Coefficient of Fluid passing through Single Particle

Go Overall Gas Phase Mass Transfer Coefficient = (2+0.6*(((Density*Velocity in Tube*Diameter of Tube)/Dynamic Viscosity of Liquid)^(1/2))*((Dynamic Viscosity of Liquid/(Density*Diffusivity of Flow))^(1/3)))*(Diffusivity of Flow/Diameter of Tube)

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order

Go Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity))

Rate Constant for Mixed Flow Reactor with Weight of Catalyst

Go Rate Const. based on Weight of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Space Time for Reaction for Weight of Catalyst)

Space Time of Mixed Flow Reactor with Weight of Catalyst

Go Space Time for Reaction for Weight of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Rate Const. based on Weight of Catalyst)

Rate Constant for Mixed Flow Reactor with Volume of Catalyst

Go Rate Const. on Volume of Pellets = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Space Time based on Volume of Catalyst)

Space Time of Mixed Flow Reactor with Volume of Catalyst

Go Space Time based on Volume of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Rate Const. on Volume of Pellets)

Mass Transfer Coefficient of Fluid passing through Packed Bed of Particles

Go Overall Gas Phase Mass Transfer Coefficient = (2+1.8*((Reynolds Number)^(1/2)*(Schimdt Number)^(1/3)))*(Diffusivity of Flow/Diameter of Tube)

Rate of Reaction in Mixed Flow Reactor Containing Catalyst

Go Rate of Reaction on Weight of Catalyst Pellets = ((Molar Feed Rate of Reactant*Reactant Conversion)/Weight of Catalyst)

Thiele Modulus

Go Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient)

Effectiveness Factor at First Order

Go Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order Formula

What are Reactions Containing Batch of Catalysts and Batch of Gases?

Reactions containing a batch of catalysts and a batch of gases typically refer to chemical processes where a solid catalyst is employed to facilitate the transformation of gaseous reactants into products. In such systems, the catalyst is usually present in a fixed amount (batch) and does not undergo significant changes in composition during the reaction.

What are Solid Catalyzed Reactions ?

Solid-catalyzed reactions refer to chemical reactions where a solid material, known as a catalyst, facilitates the transformation of reactants into products without itself undergoing any significant change in composition. The use of solid catalysts is widespread in various industrial processes and research applications.

How to Calculate Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order?

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order calculator uses Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity)) to calculate the Initial Concentration of Reactant, Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order formula is defined as The Initial Concentration of Reactant obtained, when Reactant Concentration of Reactant is multiplied with the Exponential function of Rate of Reaction with Volume of Catalyst, for the special case, where ε=0. Initial Concentration of Reactant is denoted by C_AO symbol.

How to calculate Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order using this online calculator? To use this online calculator for Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order, enter Reactant Concentration (C), Reaction Rate based on Volume of Catalyst Pellets (r_a'''), Solid Fraction (f), Height of Catalyst Bed (H) & Superficial Gas Velocity (u₀) and hit the calculate button. Here is how the Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order calculation can be explained with given input values -> 41.5108 = 24*(exp((1.908*0.78*2.89)/7.85)).

FAQ

What is Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order?

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order formula is defined as The Initial Concentration of Reactant obtained, when Reactant Concentration of Reactant is multiplied with the Exponential function of Rate of Reaction with Volume of Catalyst, for the special case, where ε=0 and is represented as C_AO = C*(exp((r_a'''*f*H)/u₀)) or Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity)). The Reactant Concentration refers to the amount of reactant present at any given point of time during the process, Reaction Rate based on Volume of Catalyst Pellets is the Reaction rate calculated based on Volume of Catalyst pellets, where Catalyst is present in the Reactor, Solid Fraction is defined as the Solid Fraction of the Catalyst which varies with the Initial Weight of Catalyst laid in the Reactor, Height of Catalyst Bed is Height of the laid Catalyst in the Reactor & Superficial Gas Velocity is the Velocity recorded where the solids are absent.

How to calculate Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order?

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order formula is defined as The Initial Concentration of Reactant obtained, when Reactant Concentration of Reactant is multiplied with the Exponential function of Rate of Reaction with Volume of Catalyst, for the special case, where ε=0 is calculated using Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity)). To calculate Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order, you need Reactant Concentration (C), Reaction Rate based on Volume of Catalyst Pellets (r_a'''), Solid Fraction (f), Height of Catalyst Bed (H) & Superficial Gas Velocity (u₀). With our tool, you need to enter the respective value for Reactant Concentration, Reaction Rate based on Volume of Catalyst Pellets, Solid Fraction, Height of Catalyst Bed & Superficial Gas Velocity 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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