In a study of the effect of alcohol dehydrogenase on alcohol at 25.0 °C, the concentration of ethanol in a first-order reaction decreased from 220.0 mmol/L to 56.0 mmol/L in 1.22 x 104s. What is the rate constant for the reaction at 25.0 °C?
To determine the rate constant (k) for the first-order reaction, we can use the formula for a first-order reaction:
ln(Vf/Vi) = -kt
Where:
- Vf is the final concentration of ethanol (56.0 mmol/L)
- Vi is the initial concentration of ethanol (220.0 mmol/L)
- k is the rate constant we want to find
- t is the time it took for the concentration of ethanol to decrease (1.22 x 104 s)
First, we'll plug in the values into the formula:
ln(56.0 mmol/L / 220.0 mmol/L) = -k * (1.22 x 104 s)
Next, we can simplify the equation:
ln(0.2545) = -k * (1.22 x 104 s)
Now, we isolate the rate constant (k):
-k * (1.22 x 104 s) = ln(0.2545)
Divide both sides by -(1.22 x 104 s):
k = ln(0.2545) / -(1.22 x 104 s)
Using a calculator, we can evaluate the right side to find the rate constant:
k ≈ -3.802 x 10^-4 s^-1
Therefore, the rate constant for the reaction at 25.0 °C is approximately -3.802 x 10^-4 s^-1.