Question

The elimination of carbon dioxide from pyruvate ions by a decarboxylase enzyme was monitored by measuring the partial pressure of the gas as it was formed in a 250 mL flask at 293.

In one experiment, the partial pressure increased from zero to 100 Pa in 522 s in a first-order reaction when the initial concentration of pyruvate ions in 100 mL of solution was 3.23 mmol L^-1.

What is the rate constant of the reaction?

Answer 1

The rate constant of a reaction can be determined using the first-order reaction equation. In this case, the partial pressure of carbon dioxide in the flask at time t can be related to the concentration of pyruvate ions using the ideal gas law. By rearranging the equation and substituting into the first-order reaction equation, the rate constant can be calculated.

Step-by-step explanation:

The rate constant of a reaction can be determined using the first-order reaction equation:

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

Where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time.

In this case, the partial pressure of carbon dioxide in the flask at time t can be related to the concentration of pyruvate ions using the ideal gas law:

PV = nRT

Where P is the partial pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

By rearranging the equation, we can get the concentration of pyruvate ions at time t, [A]t:

[A]t = (P / (RT / V))

Substituting this expression into the first-order reaction equation, we can solve for the rate constant k:

ln((P / (RT / V)) / (P0 / (RT / V))) = -kt

Where P0 is the initial partial pressure.

Using the given values for the partial pressure, volume, time, and initial concentration, we can calculate the rate constant of the reaction.