Time taken for Completion of Reaction given Product Concentration Calculator

✖Forward Reaction Rate Constant is used to define the relationship between the molar concentration of the reactants and the rate of the chemical reaction in forward direction.ⓘ Forward Reaction Rate Constant [k_f]			+10% -10%
✖Backward Reaction Rate Constant is defined as the relationship between the molar concentration of the reactants and the rate of the chemical reaction in backward direction.ⓘ Backward Reaction Rate Constant [k_b]			+10% -10%
✖Initial Concentration of Reactant A is defined as the concentration of the reactant A at time t=0.ⓘ Initial Concentration of Reactant A [A₀]			+10% -10%
✖Concentration of B is defined as the amount of substance B present after reacting for a given interval of time t.ⓘ Concentration of B [B]			+10% -10%

✖Time is used to defined as the period of time that is required for the reactant to given a certain amount of product in a chemical reaction.ⓘ Time taken for Completion of Reaction given Product Concentration [t]

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Formula

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Time taken for Completion of Reaction given Product Concentration

Formula

`"t" = (1/("k"_{"f"}+"k"_{"b"}))*ln("A"_{"0"}*"k"_{"f"}/("k"_{"f"}*("A"_{"0"}-"B")-"k"_{"b"}*"B"))`

Example

`"1107.896s"=(1/("0.0000974s⁻¹"+"0.0000418s⁻¹"))*ln("100mol/L"*"0.0000974s⁻¹"/("0.0000974s⁻¹"*("100mol/L"-"10mol/L")-"0.0000418s⁻¹"*"10mol/L"))`

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Time taken for Completion of Reaction given Product Concentration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time = (1/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*ln(Initial Concentration of Reactant A*Forward Reaction Rate Constant/(Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of B)-Backward Reaction Rate Constant*Concentration of B))
t = (1/(k_f+k_b))*ln(A₀*k_f/(k_f*(A₀-B)-k_b*B))
This formula uses 1 Functions, 5 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)

Variables Used

Time - (Measured in Second) - Time is used to defined as the period of time that is required for the reactant to given a certain amount of product in a chemical reaction.
Forward Reaction Rate Constant - (Measured in 1 Per Second) - Forward Reaction Rate Constant is used to define the relationship between the molar concentration of the reactants and the rate of the chemical reaction in forward direction.
Backward Reaction Rate Constant - (Measured in 1 Per Second) - Backward Reaction Rate Constant is defined as the relationship between the molar concentration of the reactants and the rate of the chemical reaction in backward direction.
Initial Concentration of Reactant A - (Measured in Mole per Cubic Meter) - Initial Concentration of Reactant A is defined as the concentration of the reactant A at time t=0.
Concentration of B - (Measured in Mole per Cubic Meter) - Concentration of B is defined as the amount of substance B present after reacting for a given interval of time t.

STEP 1: Convert Input(s) to Base Unit

Forward Reaction Rate Constant: 9.74E-05 1 Per Second --> 9.74E-05 1 Per Second No Conversion Required
Backward Reaction Rate Constant: 4.18E-05 1 Per Second --> 4.18E-05 1 Per Second No Conversion Required
Initial Concentration of Reactant A: 100 Mole per Liter --> 100000 Mole per Cubic Meter (Check conversion here)
Concentration of B: 10 Mole per Liter --> 10000 Mole per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t = (1/(k_f+k_b))*ln(A₀*k_f/(k_f*(A₀-B)-k_b*B)) --> (1/(9.74E-05+4.18E-05))*ln(100000*9.74E-05/(9.74E-05*(100000-10000)-4.18E-05*10000))

Evaluating ... ...

t = 1107.89603764001

STEP 3: Convert Result to Output's Unit

1107.89603764001 Second --> No Conversion Required

FINAL ANSWER

1107.89603764001 ≈ 1107.896 Second <-- Time

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Chemical Kinetics » Complex Reactions » Reversible Reactions » First Order Opposed by First Order Reactions » Time taken for Completion of Reaction given Product Concentration

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< 17 First Order Opposed by First Order Reactions Calculators

Reactant Concentration at given Time t

Go Concentration of A at Time t = Initial Concentration of Reactant A*(Forward Reaction Rate Constant/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*((Backward Reaction Rate Constant/Forward Reaction Rate Constant)+exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time))

Initial Concentration of Reactant A given Initial Concentration of B greater than 0

Go Initial Concentration of Reactant A = (Initial Concentration of Reactant B+Concentration of Reactant at Equilibrium)*((1/Forward Reaction Rate Constant)*(1/Time)*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))-Initial Concentration of Reactant B

Forward Reaction Rate Constant when Initial B Concentration greater than 0

Go Forward Reaction Rate Constant = 1/Time*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))*((Initial Concentration of Reactant B+Concentration of Reactant at Equilibrium)/(Initial Concentration of Reactant A+Initial Concentration of Reactant B))

Time taken when Initial Concentration of Reactant B greater than 0

Go Time = 1/Forward Reaction Rate Constant*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))*((Initial Concentration of Reactant B+Concentration of Reactant at Equilibrium)/(Initial Concentration of Reactant A+Initial Concentration of Reactant B))

Time taken for Completion of Reaction given Product Concentration

Go Time = (1/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*ln(Initial Concentration of Reactant A*Forward Reaction Rate Constant/(Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of B)-Backward Reaction Rate Constant*Concentration of B))

Product Conc for 1st Order Opposed by 1st Order Rxn given Initial Conc of B greater than 0

Go Concentration of Product at Time t = Concentration of Reactant at Equilibrium*(1-exp(-Forward Reaction Rate Constant*((Initial Concentration of Reactant A+Initial Concentration of Reactant B)/(Initial Concentration of Reactant B+Concentration of Reactant at Equilibrium))*Time))

Initial Concentration of Reactant given Concentration of Product

Go Initial Concentration of Reactant A = Concentration of B*((Forward Reaction Rate Constant+Backward Reaction Rate Constant)/Forward Reaction Rate Constant)*(1/(1-exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time)))

Product Concentration given Initial Concentration of Reactant

Go Concentration of B = ((Initial Concentration of Reactant A*Forward Reaction Rate Constant)/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*(1-exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time))

Forward Reaction Rate Const of 1st Order Opposed by 1st Order Rxn given Initial Conc of Reactant

Go Forward Reaction Rate Constant = (1/Time)*(Concentration of Reactant at Equilibrium/Initial Concentration of Reactant A)*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))

Time taken for 1st Order Opposed by 1st Order Reaction given Initial Concentration of Reactant

Go Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/Initial Concentration of Reactant A)*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))

Initial Concentration of Reactant for First Order Opposed by First Order Reaction

Go Initial Concentration of Reactant A = (1/(Time*Forward Reaction Rate Constant))*Concentration of Reactant at Equilibrium*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))

Backward Reaction Rate Constant of First Order Opposed by First Order Reaction

Go Backward Reaction Rate Constant = (ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))/Time taken for Backward Reaction)-Forward Reaction Rate Constant

Product Conc of First Order Opposed by First Order Reaction given Initial Conc of Reactant

Go Concentration of Product at Time t = Concentration of Reactant at Equilibrium*(1-exp(-Forward Reaction Rate Constant*Time*(Initial Concentration of Reactant A/Concentration of Reactant at Equilibrium)))

Forward Reaction Rate Constant of First Order Opposed by First Order Reaction

Go Forward Reaction Rate Constant = (ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))/Time)-Backward Reaction Rate Constant

Time taken for 1st Order Opposed by 1st Order Reaction

Go Time = ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))/(Forward Reaction Rate Constant+Backward Reaction Rate Constant)

Equilibrium Reactant Concentration of First Order Opposed by First Order Reaction at given Time t

Go Concentration of Reactant at Equilibrium = Concentration of Product at Time t/(1-exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time))

Product Concentration of 1st Order Opposed by 1st Order Reaction at given Time t

Go Concentration of Product at Time t = Concentration of Reactant at Equilibrium*(1-exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time))

Time taken for Completion of Reaction given Product Concentration Formula

What is an Opposing Reaction?

Opposing reactions or reversible reactions are those in which both forward and backward reaction takes place simultaneously. To start with, the rate of forward reaction is very large and it decreases as reactant concentration decreases with time. Similarly, initially the rate of backward reaction is slow and it increases as product concentration increases with time.
The state at which the rate of forward reaction equals the rate of backward reaction is called the equilibrium state. Thus, equilibrium is a dynamic equilibrium where all the participants of a reaction are being formed as fast as they are being destroyed and hence no further change in the various concentrations is observed.

What are the classifications of Opposing Reactions?

A reversible reaction may be classified on the basis of orders of elementary forward and backward reactions. We describe below a few reversible reactions classified accordingly:
1. First Order Opposed by First Order Reaction
2. First Order Opposed by Second Order Reaction
3. Second Order Opposed by First Order Reaction
4. Second Order Opposed by Second Order Reaction.

How to Calculate Time taken for Completion of Reaction given Product Concentration?

Time taken for Completion of Reaction given Product Concentration calculator uses Time = (1/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*ln(Initial Concentration of Reactant A*Forward Reaction Rate Constant/(Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of B)-Backward Reaction Rate Constant*Concentration of B)) to calculate the Time, The Time taken for Completion of Reaction given Product Concentration formula is defined as the time interval required to convert a particular concentration reactant to a certain concentration of product in a First Order Opposed by First Order Reaction. Time is denoted by t symbol.

How to calculate Time taken for Completion of Reaction given Product Concentration using this online calculator? To use this online calculator for Time taken for Completion of Reaction given Product Concentration, enter Forward Reaction Rate Constant (k_f), Backward Reaction Rate Constant (k_b), Initial Concentration of Reactant A (A₀) & Concentration of B (B) and hit the calculate button. Here is how the Time taken for Completion of Reaction given Product Concentration calculation can be explained with given input values -> 1107.896 = (1/(9.74E-05+4.18E-05))*ln(100000*9.74E-05/(9.74E-05*(100000-10000)-4.18E-05*10000)).

FAQ

What is Time taken for Completion of Reaction given Product Concentration?

The Time taken for Completion of Reaction given Product Concentration formula is defined as the time interval required to convert a particular concentration reactant to a certain concentration of product in a First Order Opposed by First Order Reaction and is represented as t = (1/(k_f+k_b))*ln(A₀*k_f/(k_f*(A₀-B)-k_b*B)) or Time = (1/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*ln(Initial Concentration of Reactant A*Forward Reaction Rate Constant/(Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of B)-Backward Reaction Rate Constant*Concentration of B)). Forward Reaction Rate Constant is used to define the relationship between the molar concentration of the reactants and the rate of the chemical reaction in forward direction, Backward Reaction Rate Constant is defined as the relationship between the molar concentration of the reactants and the rate of the chemical reaction in backward direction, Initial Concentration of Reactant A is defined as the concentration of the reactant A at time t=0 & Concentration of B is defined as the amount of substance B present after reacting for a given interval of time t.

How to calculate Time taken for Completion of Reaction given Product Concentration?

The Time taken for Completion of Reaction given Product Concentration formula is defined as the time interval required to convert a particular concentration reactant to a certain concentration of product in a First Order Opposed by First Order Reaction is calculated using Time = (1/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*ln(Initial Concentration of Reactant A*Forward Reaction Rate Constant/(Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of B)-Backward Reaction Rate Constant*Concentration of B)). To calculate Time taken for Completion of Reaction given Product Concentration, you need Forward Reaction Rate Constant (k_f), Backward Reaction Rate Constant (k_b), Initial Concentration of Reactant A (A₀) & Concentration of B (B). With our tool, you need to enter the respective value for Forward Reaction Rate Constant, Backward Reaction Rate Constant, Initial Concentration of Reactant A & Concentration of B 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 Time?

In this formula, Time uses Forward Reaction Rate Constant, Backward Reaction Rate Constant, Initial Concentration of Reactant A & Concentration of B. We can use 3 other way(s) to calculate the same, which is/are as follows -

Time = ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))/(Forward Reaction Rate Constant+Backward Reaction Rate Constant)
Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/Initial Concentration of Reactant A)*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))
Time = 1/Forward Reaction Rate Constant*ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))*((Initial Concentration of Reactant B+Concentration of Reactant at Equilibrium)/(Initial Concentration of Reactant A+Initial Concentration of Reactant B))

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