Question

Compound MN decomposes to form M and N in a reaction that is first-order with respect to MN and first order overall. The half-life for the reaction is 2.3 × 10^4 s. What is the rate constant of this reaction at 25°C? MN → M + N a) 3.0 × 10^3 s
b) 1.6 × 10^(–4) s^(–1)
c) 3.0 × 10^(–5) s^(–1)
d) 3.3 × 10^(–4) s^(–1)

Answer 1

Answer:

• Option c) 3.0 × 10 ⁻⁵ s⁻¹

Explanation:

The reaction given follows this pattern:

1) Decomposition reaction:

• MN → M + N

2) First-order kinetic with respect to MN and first-order overall:

• Rate: r = - d{MN]/ dt = k [MN]

• Integration: -d[MN] / [MN] = kdt

• Solution:

                     

                       $ln\frac{[MN]}{[MN]_0}=-kt$

• Half-life time: [MN]/[MN]o= 1/2

                               t = τ

 ∴ τ =  ln(2) / k ⇒ k = ln (2) / τ =  ln(2) / 2.3 × 10⁴ s / ln(2) = 3.0 × 10⁻⁵ s⁻¹