The data shown here were collected for the first-order reaction: N₂O(g) → N₂(g) + O(g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
800 3.24⨉10^{- 5}
900 0.00214
1000 0.0614
1100 0.955

Verified step by step guidance

1. First, understand that an Arrhenius plot graphs the natural logarithm of the rate constant (ln(k)) against the reciprocal of the temperature in Kelvin (1/T). This plot helps determine the activation energy and the frequency factor of a reaction.
2. Next, convert the given temperatures into their reciprocal form (1/T) where T is the temperature in Kelvin. This will be the x-axis of your Arrhenius plot.
3. Then, take the natural logarithm of each rate constant (ln(k)). These values will form the y-axis of your Arrhenius plot.
4. Plot the points with the reciprocal of the temperature on the x-axis and the natural logarithm of the rate constant on the y-axis. Draw the best fit line through these points.
5. Finally, the slope of the line from the Arrhenius plot will give you the negative activation energy divided by the gas constant (R), and the y-intercept will give you the natural logarithm of the frequency factor (ln(A)).

Key Concepts

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that if the concentration of the reactant doubles, the reaction rate also doubles. Understanding this concept is crucial for analyzing the provided rate constants at different temperatures, as it allows for the application of the integrated rate law to determine the relationship between concentration and time.

Arrhenius Equation

The Arrhenius equation describes how the rate constant of a reaction depends on temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation is fundamental for constructing an Arrhenius plot, which is a graph of ln(k) versus 1/T, allowing for the determination of both the activation energy and frequency factor from the slope and intercept.

Activation Energy

Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. In the context of the Arrhenius equation, a higher activation energy results in a lower rate constant at a given temperature, indicating that the reaction is slower. Understanding activation energy is essential for interpreting the results from the Arrhenius plot and assessing the feasibility of the reaction under different thermal conditions.