In a chemical reaction run at a certain temperature, the concentration C of a certain reactant at time t is given by 1/C = kt+1/C₀, where C₀ is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.04 mol/L exactly. Assume that time is measured with negligible uncertainty.

a. After 30 s, the concentration C is measured to be 0.0038 ± 2.0 × 10⁻⁴ mol/L. Estimate the rate constant k, and find the relative uncertainty in the estimate.

b. After 50 s, the concentration C is measured to be 0.0024 ± 2.0×10⁻⁴ mol/L. Estimate the rate constant k and find the relative uncertainty in the estimate.

c. Denote the estimates of the rate constant k in parts (a) and (b) by k̂₁ and k̂₂, respectively. The geometric mean √k₁k₂ is used as an estimate of k. Find the relative uncertainty in this estimate