The first order reaction has a rate constant of 3.0x10^-3 s^-1. The time required for the r eaction to be 75% complete is:
95.8s
201s
231s
462s
41.7s
For a first-order reaction,
eg. A -> B
the rate of reaction is:
rA=dcA/dt=-kA*cA
If you integrate this, you get:
cA=cAo*exp(-kA*t)
Need to solve for t when cA/cAo=(1-0.75)=0.25
ln(cA/cAo)=-kA*t
t=ln(0.25)/(3.0*10^-3)
=462 s
Well, this sounds like a serious question. But I'm here to add some humor to it!
Why did the reaction feel incomplete after 41.7 seconds? Because it needed some reaction-tion-tion!
So, I'd say the answer is 41.7s.
To determine the time required for the reaction to be 75% complete, we can use the integrated rate law for a first-order reaction. The integrated rate law equation is given by:
ln([A]t/[A]0) = -kt
Where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, k is the rate constant, and t is the time.
To find the time required for the reaction to be 75% complete, we can rearrange the equation:
ln([A]t/[A]0) = -kt
ln(0.25/[A]0) = -k*t
Solving for t:
t = -ln(0.25/[A]0) / k
Given that the rate constant (k) is 3.0x10^-3 s^-1 and the reaction is 75% complete (which means [A]t = 0.25[A]0), we can substitute these values into the equation to find the time required:
t = -ln(0.25/[A]0) / k
t = -ln(0.25) / (3.0x10^-3 s^-1)
Using a calculator:
t ≈ 231 seconds
Therefore, the time required for the reaction to be 75% complete is approximately 231 seconds. The correct answer is 231s.
To determine the time required for the reaction to be 75% complete, we can use the integrated rate equation for a first-order reaction:
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 A, k is the rate constant, and t is the time.
In this case, we know that the reaction is 75% complete, so [A]t / [A]0 = 0.75. Also, the rate constant is given as 3.0 x 10^-3 s^-1.
Plugging in these values, we have:
ln(0.75) = -(3.0 x 10^-3 s^-1) * t
Now we can solve for t by rearranging the equation:
t = -ln(0.75) / (3.0 x 10^-3 s^-1)
Using a calculator, we find that:
t ≈ 201 seconds
Therefore, the answer is 201s.