Textbook Question
The activation energy of a reaction is 44.2 kJ/mol and the frequency factor is 1.9⨉1011/ s. Calculate the rate constant of the reaction at 25 °C.
Ch.15 - Chemical Kinetics
Chapter 15, Problem 72
The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
300 0.0134
310 0.0407
320 0.114
330 0.303
340 0.757
Verified step by step guidance1
insert step 1> Convert the given temperatures from Kelvin to the reciprocal of temperature in Kelvin (1/T) for each data point. This will be used for the x-axis of the Arrhenius plot.
insert step 2> Take the natural logarithm of each rate constant (k) to obtain ln(k) for each data point. This will be used for the y-axis of the Arrhenius plot.
insert step 3> Plot ln(k) versus 1/T. The resulting graph should be a straight line if the reaction follows the Arrhenius equation.
insert step 4> Determine the slope of the line from the plot. The slope is equal to -Ea/R, where Ea is the activation energy and R is the universal gas constant (8.314 J/mol·K).
insert step 5> Calculate the activation energy (Ea) using the slope from the plot. Then, use the y-intercept of the line to find the frequency factor (A) by rearranging the Arrhenius equation: ln(A) = y-intercept.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arrhenius Equation
The Arrhenius equation relates the rate constant of a chemical reaction to 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 universal gas constant, and T is the temperature in Kelvin. This equation highlights how temperature influences reaction rates and allows for the determination of activation energy from experimental data.
Recommended video:
Guided course
01:20
Arrhenius Equation
Activation Energy (Ea)
Activation energy 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 plot, the slope of the linear relationship between the natural logarithm of the rate constant and the inverse of temperature can be used to calculate the activation energy, providing insight into the reaction's kinetics.
Recommended video:
Guided course
02:02Activity Series Chart
Frequency Factor (A)
The frequency factor, also known as the pre-exponential factor, is a constant in the Arrhenius equation that reflects the frequency of collisions and the orientation of reactants during a reaction. It indicates how often reactants collide with the correct orientation to form products. The frequency factor is crucial for understanding the overall rate of a reaction, especially when combined with the activation energy to predict how changes in temperature affect reaction rates.
Recommended video:
Guided course
00:31Frequency-Wavelength Relationship
Related Practice
Textbook Question
The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1/T (in K) is linear and has a slope of -7012 K. Calculate the activation energy for the reaction.
Textbook Question
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
Textbook Question
A reaction has a rate constant of 0.0117/s at 400.0 K and 0.689/s at 450.0 K. a. Determine the activation barrier for the reaction.
1
views