TOPIC 16 KINETICS 16.3 Activation Energy

ESSENTIAL IDEA NATURE OF SCIENCE (2.5) The activation energy of a reaction can be determined from the effect of temperature on reaction rate. NATURE OF SCIENCE (2.5) Theories can be supported or falsified and replaced by new theories – changing the temperature of a reaction has a much greater effect on the rate of reaction than can be explained by its effect on collision rates. This resulted in the development of the Arrhenius equation which proposes a quantitative model to explain the effect of temperature change on reaction rate.

UNDERSTANDING/KEY IDEA 16.2.A The Arrhenius equation uses the temperature dependence of the rate constant to determine the activation energy.

RATE CONSTANT (k) AND TEMPERATURE There is a rule of thumb (which means that it may not always be true) that for every 10˚C increase in temperature, the rate doubles. From the rate expression, we know that the rate of the rxn depends upon both the rate constant (k) and the concentrations of reactants raised to some power. Since raising the temperature does not change the concentration, its effect must be on the rate constant (k).

ACTIVATION ENERGY AND RATE CONSTANT (k) If the Ea is large, a temperature increase will cause a significant amount of particles that can react at higher temperatures. If Ea is low, the same temperature increase will have a proportionally smaller effect on the reaction rate. This means that the temperature dependence of (k) depends on the value of the activation energy. This leads us to explore a mathematical relationship among the 3 variables.

APPLICATION/SKILLS Be able to use the Arrhenius equation k = Ae-Ea/RT

UNDERSTANDING/KEY IDEA 16.2.B A graph of ln k against 1/T is a linear plot with gradient (slope) –Ea/RT and intercept ln A.

APPLICATION/SKILLS Be able to analyze graphical representations of the Arrhenius equation in its linear form ln k = -Ea/RT + ln A

ARRHENIUS EQUATION The Arrhenius equation relates k, Ea, and T. k = Ae-Ea/RT Where A = Arrhenius constant(also called the frequency factor) k = rate constant Ea = activation energy T = temperature in Kelvin R = gas constant 8.31 J K-1 mol-1 The frequency factor (A) takes into account the frequency with which successful collisions occur based on energy requirements and collision geometry.

The frequency factor or Arrhenius constant is a constant for the reaction and has the same units as k so the units vary depending upon the order of the reaction. Manipulating the equation by taking the natural log of both sides gives: The equation is now in the form y = mx + c which gives a straight line. A graph of ln k (y axis) vs 1/T (x axis) will give a straight line with slope of -Ea/R. This is known as the Arrhenius plot. You can then derive the activation energy from the slope.

APPLICATION/SKILLS Be able to determine and evaluate values of activation energy and frequency factors from data.

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Pay particular attention to the data you are given. Many times you are given a series of k’s at different Celsius temperatures. To make the graph to solve for Ea, you have to take the natural log of each of the k’s for the y-axis and convert Celsius temp to Kelvin temp by adding 273. The inverse of the Kelvin temp (1/T) is the x-axis.

GUIDANCE Be able to use the following equation which is found in the data booklet. ln k1/k2 = Ea/R(1/T2 – 1/T1)

Integrated form This equation which is found in your data booklet is used to solve for activation energy when you are given two temperatures and the “k’s” at each temperature.

The above equation, shows temperature's effect on multiple rate constants. This allows easy inference of the rate constants' sensitivity to activation energy and temperature changes. If the activation energy is high for a given temperature range, then the rate constant is highly sensitive; changes in temperature have a significant effect on the rate constant. f the activation energy is low for a given temperature range, then the rate constant is less sensitive, and changes in temperature have little effect on the rate constant.

The plot with the steeper slope has a higher activation energy and the plot with the flatter slope has a smaller activation energy.  the same temperature range, a reaction with a higher activation energy changes more rapidly than a reaction with a lower activation energy.

Ea=1.026×105 J/mol

UNDERSTANDING/KEY IDEA 16.2.C The frequency factor (A) takes into account the frequency of collisions with proper orientation.

The frequency factor (A) has the same units as k.

APPLICATION/SKILLS Be able to describe the relationships between temperature and rate constant; frequency factor and complexity of molecules colliding.

As temperature increases, k increases. The odds of three or more reactant molecules colliding with sufficient energy and the correct orientation are extremely low.

Using table 1 in data booklet find the activation energy for the reaction. 1.6x102 kJ/mol

Citations International Baccalaureate Organization. Chemistry Guide, First assessment 2016. Updated 2015. Brown, Catrin, and Mike Ford. Higher Level Chemistry. 2nd ed. N.p.: Pearson Baccalaureate, 2014. Print. Most of the information found in this power point comes directly from this textbook. The power point has been made to directly complement the Higher Level Chemistry textbook by Catrin and Brown and is used for direct instructional purposes only.