write an equation relating the concentration of a reactant A at t=0 to that at t= t for a first order reaction.
To write an equation relating the concentration of reactant A at t=0 to that at t=t for a first-order reaction, we need to use the mathematical expression of a first-order reaction.
The rate law for a first-order reaction is given by the equation:
rate = k[A]
Where:
- rate is the reaction rate
- k is the rate constant
- [A] is the concentration of reactant A
For a first-order reaction, the integrated rate law is:
ln([A]t/[A]0) = -kt
Where:
- [A]t is the concentration of reactant A at time t
- [A]0 is the initial concentration of reactant A at t=0
- k is the rate constant
- t is the time
To relate the concentration of reactant A at t=0 to that at t=t, we rearrange the equation:
ln([A]t/[A]0) = -kt
First, we isolate [A]t by multiplying both sides of the equation by [A]0:
[A]t = [A]0 * e^-kt
Where e represents Euler's number (approximately equal to 2.71828).
Therefore, the equation relating the concentration of reactant A at t=0 to that at t=t for a first-order reaction can be expressed as:
[A]t = [A]0 * e^-kt
For a first-order reaction, the rate of the reaction is proportional to the concentration of the reactant A. The general form of the rate equation for a first-order reaction is:
Rate = k[A]
Where:
- Rate is the rate of the reaction,
- k is the rate constant,
- [A] is the concentration of reactant A.
To relate the concentration of reactant A at the initial time (t=0) to the concentration at a later time (t=t), we can use the integrated form of the first-order rate equation, which is given by:
[A]t = [A]0 * e^(-kt)
Where:
- [A]t is the concentration of reactant A at time t,
- [A]0 is the initial concentration of reactant A,
- k is the rate constant,
- t is the time.
This equation relates the concentration of reactant A at time t=0 ([A]0) to the concentration at time t= t ([A]t) for a first-order reaction.