## Time taken for First Order Opposed by First Order Reaction Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
t = ln(xeqm/(xeqm-x))/(Kf+Kb)
This formula uses 1 Functions, 5 Variables
Functions Used
ln - Natural logarithm function (base e), 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.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Concentration of Reactant at Equilibrium: 70 Mole per Liter --> 70000 Mole per Cubic Meter (Check conversion here)
Concentration of Product at Time t: 20 Mole per Liter --> 20000 Mole per Cubic Meter (Check conversion here)
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = ln(xeqm/(xeqm-x))/(Kf+Kb) --> ln(70000/(70000-20000))/(9.74E-05+4.18E-05)
Evaluating ... ...
t = 2417.18560791101
STEP 3: Convert Result to Output's Unit
2417.18560791101 Second --> No Conversion Required
2417.18560791101 Second <-- Time
(Calculation completed in 00.031 seconds)
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## < 10+ Reversible Reaction Calculators

Initial Conc. of Reactant for 1st Order Opposed by 1st Order Rxn. given Conc. of Product

## Initial Conc. of Reactant for 1st Order Opposed by 1st Order Rxn. given Conc. of Product

Formula
"A"_{"0"} = "B"*(("K"_{"f"}+"K"_{"b"})/"K"_{"f"})*(1/(1-exp(-("K"_{"f"}+"K"_{"b"})*"t")))

Example
"36.2594mol/L"="10mol/L"*(("0.0000974s⁻¹"+"0.0000418s⁻¹")/"0.0000974s⁻¹")*(1/(1-exp(-("0.0000974s⁻¹"+"0.0000418s⁻¹")*"3600s")))

Calculator
LaTeX
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)))
Time taken for First Order Opposed by First Order Reaction given Initial Concentration of Reactant

## Time taken for First Order Opposed by First Order Reaction given Initial Concentration of Reactant

Formula
"t" = (1/"K"_{"f"})*("x"_{"eqm"}/"A"_{"0"})*ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))

Example
"2418.178s"=(1/"0.0000974s⁻¹")*("70mol/L"/"100mol/L")*ln("70mol/L"/("70mol/L"-"20mol/L"))

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

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

Formula
"K"_{"f"} = (1/"t")*("x"_{"eqm"}/"A"_{"0"})*ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))

Example
"6.5E^-5s⁻¹"=(1/"3600s")*("70mol/L"/"100mol/L")*ln("70mol/L"/("70mol/L"-"20mol/L"))

Calculator
LaTeX
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))
Initial Concentration of Reactant for First Order Opposed by First Order Reaction

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

Formula
"A"_{"0"} = (1/("t"*"K"_{"f"}))*"x"_{"eqm"}*ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))

Example
"67.17162mol/L"=(1/("3600s"*"0.0000974s⁻¹"))*"70mol/L"*ln("70mol/L"/("70mol/L"-"20mol/L"))

Calculator
LaTeX
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))
Product Conc. of First Order Opposed by First Order Reaction given Initial Conc. of Reactant

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

Formula
"x" = "x"_{"eqm"}*(1-exp(-"K"_{"f"}*"t"*("A"_{"0"}/"x"_{"eqm"})))

Example
"27.58165mol/L"="70mol/L"*(1-exp(-"0.0000974s⁻¹"*"3600s"*("100mol/L"/"70mol/L")))

Calculator
LaTeX
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)))
Backward Reaction Rate Constant of First Order Opposed by First Order Reaction

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

Formula
"K"_{"b"} = (ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))/"t")-"K"_{"f"}

Example
"-3.9E^-6s⁻¹"=(ln("70mol/L"/("70mol/L"-"20mol/L"))/"3600s")-"0.0000974s⁻¹"

Calculator
LaTeX
Backward Reaction Rate Constant = (ln(Concentration of Reactant at Equilibrium/(Concentration of Reactant at Equilibrium-Concentration of Product at Time t))/Time)-Forward Reaction Rate Constant
Forward Reaction Rate Constant of First Order Opposed by First Order Reaction

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

Formula
"K"_{"f"} = (ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))/"t")-"K"_{"b"}

Example
"5.2E^-5s⁻¹"=(ln("70mol/L"/("70mol/L"-"20mol/L"))/"3600s")-"0.0000418s⁻¹"

Calculator
LaTeX
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 First Order Opposed by First Order Reaction

## Time taken for First Order Opposed by First Order Reaction

Formula
"t" = ln("x"_{"eqm"}/("x"_{"eqm"}-"x"))/("K"_{"f"}+"K"_{"b"})

Example
"2417.186s"=ln("70mol/L"/("70mol/L"-"20mol/L"))/("0.0000974s⁻¹"+"0.0000418s⁻¹")

Calculator
LaTeX
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

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

Formula
"x"_{"eqm"} = "x"/(1-exp(-("K"_{"f"}+"K"_{"b"})*"t"))

Example
"50.74233mol/L"="20mol/L"/(1-exp(-("0.0000974s⁻¹"+"0.0000418s⁻¹")*"3600s"))

Calculator
LaTeX
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 First Order Opposed by First Order Reaction at given Time t

## Product Concentration of First Order Opposed by First Order Reaction at given Time t

Formula
"x" = "x"_{"eqm"}*(1-exp(-("K"_{"f"}+"K"_{"b"})*"t"))

Example
"27.59038mol/L"="70mol/L"*(1-exp(-("0.0000974s⁻¹"+"0.0000418s⁻¹")*"3600s"))

Calculator
LaTeX
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 First Order Opposed by First Order Reaction Formula

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)
t = ln(xeqm/(xeqm-x))/(Kf+Kb)

## 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.

## How to Calculate Time taken for First Order Opposed by First Order Reaction?

Time taken for First Order Opposed by First Order Reaction calculator uses 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) to calculate the Time, Time taken for First Order Opposed by First Order 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 First Order Reaction. Time is denoted by t symbol.

How to calculate Time taken for First Order Opposed by First Order Reaction using this online calculator? To use this online calculator for Time taken for First Order Opposed by First Order Reaction, enter Concentration of Reactant at Equilibrium (xeqm), Concentration of Product at Time t (x), Forward Reaction Rate Constant (Kf) & Backward Reaction Rate Constant (Kb) and hit the calculate button. Here is how the Time taken for First Order Opposed by First Order Reaction calculation can be explained with given input values -> 2417.186 = ln(70000/(70000-20000))/(9.74E-05+4.18E-05).

### FAQ

What is Time taken for First Order Opposed by First Order Reaction?
Time taken for First Order Opposed by First Order 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 First Order Reaction and is represented as t = ln(xeqm/(xeqm-x))/(Kf+Kb) or 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). Concentration of Reactant at Equilibrium is defined as the amount of reactant present when the reaction is at equilibrium condition, 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, 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.
How to calculate Time taken for First Order Opposed by First Order Reaction?
Time taken for First Order Opposed by First Order 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 First Order Reaction is calculated using 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). To calculate Time taken for First Order Opposed by First Order Reaction, you need Concentration of Reactant at Equilibrium (xeqm), Concentration of Product at Time t (x), Forward Reaction Rate Constant (Kf) & Backward Reaction Rate Constant (Kb). With our tool, you need to enter the respective value for Concentration of Reactant at Equilibrium, Concentration of Product at Time t, Forward Reaction Rate Constant & Backward Reaction Rate Constant 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 Concentration of Reactant at Equilibrium, Concentration of Product at Time t, Forward Reaction Rate Constant & Backward Reaction Rate Constant. We can use 3 other way(s) to calculate the same, which is/are as follows -
• 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+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))
• 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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