A reaction is 50% complete in 34.0 min.
1.) How long after its start will the reaction be 75% complete if it is first order?
2.)How long after its start will the reaction be 75% complete if it is zero order?
steps would be helpful
For 1 use ln(No/N) = kt
Use the 34 min and 50% complete to determine k, then use that k and the same equation to use the conditions in problem 1.
So its Ln ( 50/100) = k (34 min)?
for the second part do i subtract 100-75 = 25 = -(the constant)(time)
To answer these questions, we need to understand the concepts of first order and zero order reactions. In a first order reaction, the rate of the reaction is directly proportional to the concentration of the reactant. In a zero order reaction, the rate of the reaction is independent of the concentration of the reactant.
Let's tackle each question step by step:
1. How long after its start will the reaction be 75% complete if it is first order?
To determine the time at which the reaction is 75% complete for a first-order reaction, we can use the integrated rate law equation for a first-order reaction:
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.
Given that the reaction is 50% complete in 34.0 min, we can assume that [A]t/[A]0 = 0.5. Substituting these values into the equation, we have:
ln(0.5) = -k * 34.0 min
To solve for k, we rearrange the equation:
k = -ln(0.5) / 34.0 min
Now, to find the time required for the reaction to be 75% complete, we need to solve for t when [A]t/[A]0 = 0.75. Plugging in the known values:
ln(0.75) = -k * t
Now we can solve for t by rearranging the equation:
t = -ln(0.75) / k
Substitute the value of k we calculated earlier into the equation to find the time required for the reaction to be 75% complete.
2. How long after its start will the reaction be 75% complete if it is zero order?
In a zero order reaction, the rate of the reaction is independent of the concentration of the reactant. Therefore, the half-life of the reaction will remain constant.
Given that the reaction is 50% complete in 34.0 min, we can assume that the half-life of the reaction is 34.0 min. The half-life is the time taken for the concentration of the reactant to decrease by half.
To find the time required for the reaction to be 75% complete, we need to find how many half-lives are needed. By dividing the natural logarithm of 0.75 by the natural logarithm of 0.5 (since we know that the concentration decreases by half in each half-life), we can determine the number of half-lives required.
t = (ln(0.75) / ln(0.5)) * half-life
Substitute the given half-life value into the equation to find the time required for the reaction to be 75% complete.
Remember to always double-check your calculations and units throughout the process.