If the initial concentration of NO2(g) is 0.050 M, what is the half-life of the reaction at 300°C given that the rate constant k is 0.54 M⁻¹s⁻¹?

• A. 74 seconds
• B. 37 seconds
• C. 27 seconds
• D. 18 seconds

Answer: (B)

Verified step by step guidance

1. Identify the order of the reaction. Since the rate constant k is given in units of M⁻¹s⁻¹, this indicates a second-order reaction.
2. For a second-order reaction, the half-life (t₁/₂) is given by the formula: $\frac{1}{kC{o}_2}$, where k is the rate constant and C₀ is the initial concentration.
3. Substitute the given values into the formula: k = 0.54 M⁻¹s⁻¹ and C₀ = 0.050 M.
4. Calculate the half-life using the formula: $\frac{1}{0.540.050}$.
5. Simplify the expression to find the half-life of the reaction at 300°C.