Suppose 100 moles of a chemical is spilled into a lake. After 15.0 days, the total amount of the chemical in the lake 3.50 moles. Assuming that the reaction followed first order kinetics and no chemical was lost due to advection or volatilization, then what is the rate constant for the degradation reaction? The units are 1/days.

Question

Suppose 100 moles of a chemical is spilled into a lake. After 15.0 days, the total amount of the chemical in the lake 3.50 moles. Assuming that the reaction followed first order kinetics and no chemical was lost due to advection or volatilization, then what is the rate constant for the degradation reaction? The units are 1/days.

Answer 1

100/2^n = 3.50

Solve for n = number of half lives.

half life = 15.0 days/n = ?

k = 0.693/t_1/2

Answer 2

To determine the rate constant for the degradation reaction, we can use the first-order kinetics equation:

ln(A₀/A) = -kt

Where:
A₀ is the initial amount of the chemical (100 moles)
A is the final amount of the chemical (3.50 moles)
t is the time elapsed (15.0 days)
k is the rate constant we want to find

First, let's rearrange the equation to solve for k:

k = -ln(A/A₀) / t

Now, substitute the given values:

k = -ln(3.50/100) / 15.0

Using a calculator or software that supports natural logarithm (ln) function, calculate the right side of the equation and divide by 15.0 to find the rate constant (k) in units of 1/days.