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?

k = 2,45x10⁻⁵ s⁻¹

Explanation:

The first order integrated rate law is:

ln [A] = -kt + ln [A]₀ (1)

The initial concentration of pyruvate ions is 3,23 mM

Using ideal gas law, the molar concentration of CO₂ in 522s is:

M = P/RT

Where P is pressure: 100 Pa; R is gas constant 8314,5 PaL/molK; T is temperature: 293 k.

Thus, molarity is:

M = 0,041mM

That means concentration of pyruvate after 522s is:

3,23mM - 0,041mM = 3,189mM

Replacing in (1):

ln [3,189] = -kt + ln [3,23]

ln (3,189/3,23) = -522s×k

k = 2,45x10⁻⁵ s⁻¹

I hope it helps!