I have no idea where to start with this problem:
A certain reaction has the following general form: aA -> bB
At a particular temperature and (A)o = 2.00(10^-2)M, concentration versus time data were collected for this reaction, and a plot of In(A) versus time resulted in a straight line with a slope value of -2.97(10^-2)min ^-1.
a. Determine the rate law, the integrated law, and the value of the rate constant for this reaction.
b. Calculate the half-life for this reaction.
c. How much time is required for the concentration of A to decrease to 2.50(10^-3)M?
To solve this problem, we need to use the integrated rate law for a first-order reaction. The integrated rate law for a first-order reaction is:
ln(A) = -kt + ln(Ao)
Where A is the concentration at a given time, A0 is the initial concentration, t is the time, k is the rate constant, and ln is the natural logarithm.
a. Determine the rate law, the integrated law, and the value of the rate constant for this reaction:
Given that the plot of ln(A) versus time resulted in a straight line with a slope value of -2.97(10^-2) min^-1, we can use this information to determine the rate constant (k).
From the integrated rate law, we can see that the slope of the straight line is equal to -k. So, the value of k is 2.97(10^-2) min^-1.
Since the reaction has the general form aA -> bB, we can deduce that the rate of the reaction is directly proportional to the concentration of A, which means the rate law can be written as:
Rate = k[A]^1, or simply Rate = k[A]
b. Calculate the half-life for this reaction:
The half-life of a first-order reaction can be calculated using the formula:
t(1/2) = (ln(2)) / k
The value of k is already known to be 2.97(10^-2) min^-1. Plugging this value into the formula, we have:
t(1/2) = (ln(2)) / (2.97(10^-2) min^-1)
Calculating this expression will give you the half-life of the reaction.
c. How much time is required for the concentration of A to decrease to 2.50(10^-3) M:
To calculate the time required for the concentration of A to decrease to a specific value, we can rearrange the integrated rate law equation:
ln(A) = -kt + ln(A0)
t = (ln(A) - ln(A0)) / -k
We know that A0 is given as 2.00(10^-2) M and A is given as 2.50(10^-3) M. Plugging these values into the equation, as well as the value of k, you can calculate the time required for the concentration of A to decrease to 2.50(10^-3) M.