The concentration of N₂O₄ in the vessel 130 seconds later is approximately 0.086 M.
Chemical Kinetics and the N₂O₄ System
This problem explores the concept of first-order decay, a fundamental principle in chemical kinetics. It involves the analysis of how the concentration of a reactant decreases over time due to its transformation into products.
The scenario presented deals with the decomposition of nitrogen tetroxide (N₂O₄) into its constituent nitrogen dioxide (NO₂) molecules, as shown by the equation:
2 N₂O₄ (g) ⇌ 4 NO₂ (g)
The rate of this reaction can be described by the first-order decay equation:
A₀ = Ae^(-kt)
where:
A₀ is the initial concentration of N₂O₄
A is the concentration of N₂O₄ at any time t
k is the rate constant for the reaction
t is the time elapsed
Understanding the Problem:
The problem provides us with the following information:
A₀ (initial concentration of N₂O₄) = 0.190 M
k (rate constant) = 0.00555 s⁻¹
t (time) = 130 s
The objective is to determine the final concentration of N₂O₄ (A) after 130 seconds.
Solution:
Substitute the given values into the first-order decay equation:
0.190 M = A * e^(-0.00555 s⁻¹ * 130 s)
Solve for A:
Divide both sides by e^(-0.00555 s⁻¹ * 130 s)
A ≈ 0.086 M .