Time for Completion of First Order Reaction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A)
tcompletion = 2.303/kfirst*log10(CAO/ax)
This formula uses 1 Functions, 4 Variables
Functions Used
log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)
Variables Used
Time for completion - (Measured in Second) - The Time for completion is defined as the time required for a complete transformation of reactant into the product.
Rate Constant for First Order Reaction - (Measured in 1 Per Second) - The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.
Initial Reactant A Concentration - (Measured in Mole per Cubic Meter) - The Initial Reactant A Concentration refers to the amount of reactant A present in the solvent before the considered process.
Concentration at Time t of Reactant A - (Measured in Mole per Cubic Meter) - The Concentration at time t of reactant A is defined as the concentration of reactant A after a certain time interval.
STEP 1: Convert Input(s) to Base Unit
Rate Constant for First Order Reaction: 0.520001 1 Per Second --> 0.520001 1 Per Second No Conversion Required
Initial Reactant A Concentration: 10 Mole per Liter --> 10000 Mole per Cubic Meter (Check conversion here)
Concentration at Time t of Reactant A: 8 Mole per Liter --> 8000 Mole per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tcompletion = 2.303/kfirst*log10(CAO/ax) --> 2.303/0.520001*log10(10000/8000)
Evaluating ... ...
tcompletion = 0.429198712997771
STEP 3: Convert Result to Output's Unit
0.429198712997771 Second --> No Conversion Required
FINAL ANSWER
0.429198712997771 0.429199 Second <-- Time for completion
(Calculation completed in 00.004 seconds)

Credits

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K J Somaiya College of science (K J Somaiya), Mumbai
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18 First Order Reaction Calculators

Graphical Representation of Time for Completion
Go Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Concentration for First Order Reaction)-(2.303/Rate Constant for First Order Reaction)*log10(Concentration at Time t)
Temperature in Arrhenius Equation for First Order Reaction
Go Temperature in Arrhenius Eq for 1st Order Reaction = modulus(Activation Energy/[R]*(ln(Frequency Factor from Arrhenius Eqn for 1st Order/Rate Constant for First Order Reaction)))
Rate Constant for First Order Reaction from Arrhenius Equation
Go Rate Constant for First Order Reaction = Frequency Factor from Arrhenius Eqn for 1st Order*exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Arrhenius Constant for First Order Reaction
Go Frequency Factor from Arrhenius Eqn for 1st Order = Rate Constant for First Order Reaction/exp(-Activation Energy/([R]*Temperature for First Order Reaction))
Activation Energy for First Order Reaction
Go Energy of Activation = [R]*Temperature of Gas*(ln(Frequency Factor from Arrhenius Equation/Rate Constant for First Order Reaction))
Time for Completion for First Order given Rate Constant and Initial Concentration
Go Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Concentration for First Order Reaction/Concentration at Time t)
Rate Constant of First Order Reaction using Logarithm to base 10
Go Rate Constant for First Order Reaction = 2.303/Time for completion*log10(Initial Concentration for First Order Reaction/Concentration at Time t)
Time for Completion of First Order Reaction
Go Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A)
Time for Completion by Titration Method for First Order Reaction
Go Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Reactant Volume/Volume at Time t)
Rate Constant by Titration Method for First Order Reaction
Go Rate Constant for First Order Reaction = (2.303/Time for completion)*log10(Initial Reactant Volume/Volume at Time t)
Relaxation Time of Reversible First Order
Go Relaxation Time of Reversible First Order = 1/(Forward Rate Constant+Rate Constant of Backward First Order)
Quarter Life of First Order Reaction
Go Quarter Life of First Order Reaction = ln(4)/Rate Constant for First Order Reaction
Rate Constant at Half Time for First Order Reaction
Go Rate Constant for First Order Reaction = 0.693/Half Time
Half Time Completion of First Order Reaction
Go Half Time = 0.693/Rate Constant for First Order Reaction
Average Time of Completion for First Order Reaction
Go Average time = 1/Rate Constant for First Order Reaction
Rate constant given average time
Go Rate Constant for First Order Reaction = 1/Average time
Half Time for Completion given Average Time
Go Half Time = Average time/1.44
Average Time of Completion given Half Time
Go Average time = 1.44*Half Time

Time for Completion of First Order Reaction Formula

Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A)
tcompletion = 2.303/kfirst*log10(CAO/ax)

What is first order reaction?

In the first-order reaction, the rate of reaction is proportional to the first power of the concentration of the reactant. The concentration of the reactant in the first-order reaction decreases exponentially with time.

How to Calculate Time for Completion of First Order Reaction?

Time for Completion of First Order Reaction calculator uses Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A) to calculate the Time for completion, The Time for completion of first order reaction formula is defined as the total time required to convert the reactant completely into the product. The formula is the logarithm to the base 10 of initial concentration per concentration at the time t, the whole is divided by rate constant. Time for completion is denoted by tcompletion symbol.

How to calculate Time for Completion of First Order Reaction using this online calculator? To use this online calculator for Time for Completion of First Order Reaction, enter Rate Constant for First Order Reaction (kfirst), Initial Reactant A Concentration (CAO) & Concentration at Time t of Reactant A (ax) and hit the calculate button. Here is how the Time for Completion of First Order Reaction calculation can be explained with given input values -> 0.429199 = 2.303/0.520001*log10(10000/8000).

FAQ

What is Time for Completion of First Order Reaction?
The Time for completion of first order reaction formula is defined as the total time required to convert the reactant completely into the product. The formula is the logarithm to the base 10 of initial concentration per concentration at the time t, the whole is divided by rate constant and is represented as tcompletion = 2.303/kfirst*log10(CAO/ax) or Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A). The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant, The Initial Reactant A Concentration refers to the amount of reactant A present in the solvent before the considered process & The Concentration at time t of reactant A is defined as the concentration of reactant A after a certain time interval.
How to calculate Time for Completion of First Order Reaction?
The Time for completion of first order reaction formula is defined as the total time required to convert the reactant completely into the product. The formula is the logarithm to the base 10 of initial concentration per concentration at the time t, the whole is divided by rate constant is calculated using Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Reactant A Concentration/Concentration at Time t of Reactant A). To calculate Time for Completion of First Order Reaction, you need Rate Constant for First Order Reaction (kfirst), Initial Reactant A Concentration (CAO) & Concentration at Time t of Reactant A (ax). With our tool, you need to enter the respective value for Rate Constant for First Order Reaction, Initial Reactant A Concentration & Concentration at Time t of Reactant A 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 for completion?
In this formula, Time for completion uses Rate Constant for First Order Reaction, Initial Reactant A Concentration & Concentration at Time t of Reactant A. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Time for completion = 2.303/Rate Constant for First Order Reaction*log10(Initial Concentration for First Order Reaction/Concentration at Time t)
  • Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Reactant Volume/Volume at Time t)
  • Time for completion = (2.303/Rate Constant for First Order Reaction)*log10(Initial Concentration for First Order Reaction)-(2.303/Rate Constant for First Order Reaction)*log10(Concentration at Time t)
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