The thermal decomposition of HCOOH is a first-order reaction with a rate constant of 2.4 × 10⁻⁷ s⁻¹ at a certain temperature. How long will it take for three-fourths of the initial quantity of HCOOH to decompose?

Half-life for a first-order reaction is given by t₁/₂ = 0.693/k.

t₁/₂ = 0.693 / (2.4 × 10⁻⁷ s⁻¹) = 288.75 sec

For three-fourths of the reactant to decompose, it takes two half-lives.

Time for three-fourths decomposition = 2 × t₁/₂ = 2 × 288.75 sec = 577.50 sec ≈ 578 sec

Hence, option C is correct.