From a plot of the concentration–time data in Worked Example 14.9, estimate: (b) the initial rate of decomposition of NO₂.

Verified step by step guidance

1. Identify the reaction involved in the decomposition of NO_2, which is typically 2NO_2 \rightarrow 2NO + O_2.
2. Understand that the initial rate of reaction refers to the rate at which the reactant concentration changes at the very beginning of the reaction.
3. Use the concentration-time data provided in the plot to determine the initial concentration of NO_2.
4. Find the slope of the tangent to the concentration-time curve at time t = 0 to estimate the initial rate of decomposition.
5. Express the initial rate of decomposition in terms of the change in concentration of NO_2 over time, \text{Rate} = -\frac{\Delta [NO_2]}{\Delta t}, where \Delta [NO_2] is the change in concentration and \Delta t is the change in time.

Key Concepts

Rate of Reaction

The rate of reaction refers to the speed at which reactants are converted into products in a chemical reaction. It can be expressed in terms of the change in concentration of a reactant or product over time. Understanding how to calculate and interpret reaction rates is essential for analyzing concentration-time data.

Concentration-Time Graphs

Concentration-time graphs visually represent how the concentration of a reactant or product changes over time during a chemical reaction. The slope of the curve at any point indicates the rate of reaction at that time. By analyzing these graphs, one can estimate initial rates and understand the kinetics of the reaction.

Initial Rate

The initial rate of a reaction is the rate measured at the very beginning of the reaction, typically when the reactants are at their highest concentration. It is crucial for determining the kinetics of the reaction and can be estimated from the slope of the concentration-time graph at time zero. This concept helps in understanding how quickly a reaction proceeds under specific conditions.