Time Taken for Completion of Reaction 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%
✖Concentration of Reactant at Equilibrium is defined as the amount of reactant present when the reaction is at equilibrium condition.ⓘ Concentration of Reactant at Equilibrium [x_eq]			+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 Product at Time t is defined as the amount of reactant that has been converted into product in a time interval of t.ⓘ Concentration of Product at Time t [x]			+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 [t]

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Formula

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Time Taken for Completion of Reaction

Formula

`"t" = (1/"k"_{"f"})*("x"_{"eq"}/(2*"A"_{"0"}-"x"_{"eq"}))*ln(("A"_{"0"}*"x"_{"eq"}+"x"*("A"_{"0"}-"x"_{"eq"}))/("A"_{"0"}*("x"_{"eq"}-"x")))`

Example

`"3374.533s"=(1/"0.0000974s⁻¹")*("70mol/L"/(2*"100mol/L"-"70mol/L"))*ln(("100mol/L"*"70mol/L"+"27.5mol/L"*("100mol/L"-"70mol/L"))/("100mol/L"*("70mol/L"-"27.5mol/L")))`

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Time Taken for Completion of Reaction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))
t = (1/k_f)*(x_eq/(2*A₀-x_eq))*ln((A₀*x_eq+x*(A₀-x_eq))/(A₀*(x_eq-x)))
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.
Concentration of Reactant at Equilibrium - (Measured in Mole per Cubic Meter) - Concentration of Reactant at Equilibrium is defined as the amount of reactant present when the reaction is at equilibrium condition.
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 Product at Time t - (Measured in Mole per Cubic Meter) - Concentration of Product at Time t is defined as the amount of reactant that has been converted into product in a time interval of 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
Concentration of Reactant at Equilibrium: 70 Mole per Liter --> 70000 Mole per Cubic Meter (Check conversion here)
Initial Concentration of Reactant A: 100 Mole per Liter --> 100000 Mole per Cubic Meter (Check conversion here)
Concentration of Product at Time t: 27.5 Mole per Liter --> 27500 Mole per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t = (1/k_f)*(x_eq/(2*A₀-x_eq))*ln((A₀*x_eq+x*(A₀-x_eq))/(A₀*(x_eq-x))) --> (1/9.74E-05)*(70000/(2*100000-70000))*ln((100000*70000+27500*(100000-70000))/(100000*(70000-27500)))

Evaluating ... ...

t = 3374.53267606163

STEP 3: Convert Result to Output's Unit

3374.53267606163 Second --> No Conversion Required

FINAL ANSWER

3374.53267606163 ≈ 3374.533 Second <-- Time

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Chemical Kinetics » Complex Reactions » Reversible Reactions » First Order Opposed by Second Order Reactions » Time Taken for Completion of Reaction

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< 3 First Order Opposed by Second Order Reactions Calculators

Time Taken for Completion of Reaction

Go Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

Rate Constant for Forward Reaction

Go Forward Reaction Rate Constant = (1/Time)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

Rate Constant for Backward Reaction

Go Rate Constant of Backward Reaction = Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium)/Concentration of Reactant at Equilibrium^2

< 23 Important Formulas on Reversible Reaction Calculators

Time taken for 2nd Order Opposed by 2nd Order Reaction given Initial Conc of Reactant B

Go Time for 2nd Order = (1/Forward Reaction Rate Constant for 2nd Order)*(Concentration of Reactant at Equilibrium^2/(2*Initial Concentration of Reactant B*(Initial Concentration of Reactant B-Concentration of Reactant at Equilibrium)))*ln((Concentration of Product at Time t*(Initial Concentration of Reactant B-2*Concentration of Reactant at Equilibrium)+Initial Concentration of Reactant B*Concentration of Reactant at Equilibrium)/(Initial Concentration of Reactant B*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

Forward Rxn Rate Const for 2nd Order Opposed by 2nd Order Rxn given Ini Conc of Reactant A

Go Forward Reaction Rate Constant given A = (1/Time)*(Concentration of Reactant at Equilibrium^2/(2*Initial Concentration of Reactant A*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium)))*ln((Concentration of Product at Time t*(Initial Concentration of Reactant A-2*Concentration of Reactant at Equilibrium)+Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium)/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

Time Taken for Completion of Reaction

Rate Constant for Forward Reaction

Time taken for 2nd Order Opposed by 1st Order Reaction given Initial Conc of Reactant A

Go Time = (1/Forward Reaction Rate Constant for 2nd Order)*(Concentration of Reactant at Equilibrium/((Initial Concentration of Reactant A^2)-(Concentration of Reactant at Equilibrium^2)))*ln((Concentration of Reactant at Equilibrium*(Initial Concentration of Reactant A^2-Concentration of Product at Time t*Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A^2*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

Forward Rxn Rate Const for 2nd Order Opposed by 1st Order Rxn given Ini Conc of Reactant B

Go Forward Reaction Rate Constant given B = (1/Time)*(Concentration of Reactant at Equilibrium/(Initial Concentration of Reactant B^2-Concentration of Reactant at Equilibrium^2))*ln((Concentration of Reactant at Equilibrium*(Initial Concentration of Reactant B^2-Concentration of Product at Time t*Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant B^2*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

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))

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))

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))

Backward Reaction Rate Constant for 2nd Order Opposed by 2nd Order Reaction

Go Backward Reaction Rate Constant for 2nd Order = Forward Reaction Rate Constant for 2nd Order*((Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium)*(Initial Concentration of Reactant B-Concentration of Reactant at Equilibrium))/Concentration of Reactant at Equilibrium^2

Backward Reaction Rate Constant for 2nd Order Opposed by 1st Order Reaction

Go Rate Constant for Backward Reaction = Forward Reaction Rate Constant for 2nd Order*((Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium)*(Initial Concentration of Reactant B-Concentration of Reactant at Equilibrium))/Concentration of Reactant at Equilibrium

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))

Concentration of Reactant A given kf and kb

Go Concentration of Reactant A at Equilibrium = Backward Reaction Rate Constant for 2nd Order/Forward Reaction Rate Constant for 2nd Order*((Concentration of Product C at Equilibrium*Concentration of Product D at Equilibrium)/Concentration of Reactant B at Equilibrium)

Concentration of Reactant B given kf and kb

Go Concentration of Reactant B at Equilibrium = Backward Reaction Rate Constant for 2nd Order/Forward Reaction Rate Constant for 2nd Order*((Concentration of Product C at Equilibrium*Concentration of Product D at Equilibrium)/Concentration of Reactant A at Equilibrium)

Concentration of Product C given kf and kb

Go Concentration of Product C at Equilibrium = Forward Reaction Rate Constant for 2nd Order/Backward Reaction Rate Constant for 2nd Order*((Concentration of Reactant A at Equilibrium*Concentration of Reactant B at Equilibrium)/Concentration of Product D at Equilibrium)

Concentration of Product D given kf and kb

Go Concentration of Product D at Equilibrium = Forward Reaction Rate Constant for 2nd Order/Backward Reaction Rate Constant for 2nd Order*((Concentration of Reactant A at Equilibrium*Concentration of Reactant B at Equilibrium)/Concentration of Product C at Equilibrium)

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)))

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)

Rate Constant for Backward Reaction

Go Rate Constant of Backward Reaction = Forward Reaction Rate Constant*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium)/Concentration of Reactant at Equilibrium^2

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))

Forward Rate Constant given Keq and kb

Go Forward Reaction Rate Constant given kf and Keq = Equilibrium Constant for Second Order Reaction*Backward Reaction Rate Constant for 2nd Order

Backward Reaction Rate Constant given Keq and kf

Go Backward Reaction Rate Constant given kf and Keq = Equilibrium Constant*Forward Reaction Rate Constant for 2nd Order

Equilibrium Rate Constant given kf and kb

Go Equilibrium Constant = Forward Reaction Rate Constant for 2nd Order/Backward Reaction Rate Constant for 2nd Order

Time Taken for Completion of Reaction Formula

What is an Opposing Reaction?

Opposing reaction or reversible reaction 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?

Time Taken for Completion of Reaction calculator uses Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))) to calculate the Time, The Time Taken for Completion of Reaction 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 Second Order Reaction. Time is denoted by t symbol.

How to calculate Time Taken for Completion of Reaction using this online calculator? To use this online calculator for Time Taken for Completion of Reaction, enter Forward Reaction Rate Constant (k_f), Concentration of Reactant at Equilibrium (x_eq), Initial Concentration of Reactant A (A₀) & Concentration of Product at Time t (x) and hit the calculate button. Here is how the Time Taken for Completion of Reaction calculation can be explained with given input values -> 2314.778 = (1/9.74E-05)*(70000/(2*100000-70000))*ln((100000*70000+27500*(100000-70000))/(100000*(70000-27500))).

FAQ

What is Time Taken for Completion of Reaction?

The Time Taken for Completion of Reaction 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 Second Order Reaction and is represented as t = (1/k_f)*(x_eq/(2*A₀-x_eq))*ln((A₀*x_eq+x*(A₀-x_eq))/(A₀*(x_eq-x))) or Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))). 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, Concentration of Reactant at Equilibrium is defined as the amount of reactant present when the reaction is at equilibrium condition, Initial Concentration of Reactant A is defined as the concentration of the reactant A at time t=0 & Concentration of Product at Time t is defined as the amount of reactant that has been converted into product in a time interval of t.

How to calculate Time Taken for Completion of Reaction?

The Time Taken for Completion of Reaction 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 Second Order Reaction is calculated using Time = (1/Forward Reaction Rate Constant)*(Concentration of Reactant at Equilibrium/(2*Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))*ln((Initial Concentration of Reactant A*Concentration of Reactant at Equilibrium+Concentration of Product at Time t*(Initial Concentration of Reactant A-Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))). To calculate Time Taken for Completion of Reaction, you need Forward Reaction Rate Constant (k_f), Concentration of Reactant at Equilibrium (x_eq), Initial Concentration of Reactant A (A₀) & Concentration of Product at Time t (x). With our tool, you need to enter the respective value for Forward Reaction Rate Constant, Concentration of Reactant at Equilibrium, Initial Concentration of Reactant A & Concentration of Product at Time t 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, Concentration of Reactant at Equilibrium, Initial Concentration of Reactant A & Concentration of Product at Time t. We can use 4 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))
Time = (1/Forward Reaction Rate Constant for 2nd Order)*(Concentration of Reactant at Equilibrium/((Initial Concentration of Reactant A^2)-(Concentration of Reactant at Equilibrium^2)))*ln((Concentration of Reactant at Equilibrium*(Initial Concentration of Reactant A^2-Concentration of Product at Time t*Concentration of Reactant at Equilibrium))/(Initial Concentration of Reactant A^2*(Concentration of Reactant at Equilibrium-Concentration of Product at Time t)))

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