The decomposition of formic acid follows first-order kinetics. HCO₂H(g) → CO₂(g) + H₂(g)
The half-life for the reaction at 550 °C is 24 seconds.How many seconds does it take for the formic acid concentration to decrease by 87.5%?

Question

Quizplus · Accepted Answer

Since the reaction follows first-order kinetics, we can use the equation:

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

where [A]t is the concentration of formic acid at time t, [A]0 is the initial concentration, k is the rate constant, and t is time.

To find the time it takes for the concentration of formic acid to decrease by 87.5%, we need to find when [A]t is 0.125[A]0:

ln(0.125[A]0/[A]0) = -k( t )

ln(0.125) = -k( t )

t = ln(0.125)/(-k)

To solve for k, we can use the half-life given:

ln(0.5[A]0/[A]0) = -k(24 s)

ln(0.5) = -k(24 s)

k = ln(2) / (24 s)

Substituting k into the first equation:

t = ln(0.125) / (-ln(2)/(24 s))

t = 72 s

Therefore, the answer is (D) 72 s.

The Decomposition of Formic Acid Follows First-Order Kinetics