In a study of the alcohol dehydrogenase catalysed oxidation of of ethanol at 25.0 C, the molar concentration of ethanol decreased in a first-order reaction from 220.0 mmol/L to 56.0 mmol/L in 1.22 x 104s. What is the rate constant of the reaction at 25.0 C?

To determine the rate constant of a first-order reaction, you can use the following equation:

k = -ln(A/A₀) / t

where:
k is the rate constant
A is the final concentration of the reactant
A₀ is the initial concentration of the reactant
t is the time elapsed during the reaction

In this case, the molar concentration of ethanol decreased from 220.0 mmol/L to 56.0 mmol/L in a time of 1.22 x 10^4 s.

Plugging in the values:

k = -ln(56.0/220.0) / (1.22 x 10^4)

Simplifying, we get:

k = -ln(0.254545) / (1.22 x 10^4)

Now you can use a scientific calculator or software that has a natural logarithm function (ln) to calculate: ln(0.254545). The result will be a negative value.

Finally, substitute the value into the equation to find k.

To find the rate constant of the reaction, we can use the first-order reaction equation:

ln([A]t/[A]0) = -kt

Where:
[A]t = final concentration of ethanol (56.0 mmol/L)
[A]0 = initial concentration of ethanol (220.0 mmol/L)
t = time (1.22 x 10^4 s)
k = rate constant

Plugging in the given values:

ln(56.0 mmol/L / 220.0 mmol/L) = -k(1.22 x 10^4 s)

Now we can solve for the rate constant, k.