The rate constants for a first order decay reaction are found to be:
To answer this question, we would need more information such as the initial concentration or amount of the substance undergoing decay and the rate of decay at a given time. With that information, we can calculate the rate constants for the first-order decay reaction.
The first-order decay reaction follows the exponential decay equation:
A = A₀ * e^(-kt)
Where:
A is the amount of substance remaining at a given time t
A₀ is the initial amount of the substance
k is the rate constant
t is the time
If we know the initial amount A₀ and the amount remaining A at a specific time t, we can rearrange the equation to solve for the rate constant k:
k = -(1/t) * ln(A/A₀)
To calculate the rate constant, substitute the values of A, A₀, and t into the equation and calculate the natural logarithm (ln) of the ratio (A/A₀). Multiply the result by (-1) and divide by the time t.
Repeat this calculation for each set of data you have, and you will obtain the rate constants for the first-order decay reaction.