Understanding Activation Energy and Temperature Dependence in Chemical Reactions
The Arrhenius equation is used for calculating the rate of reaction. It is a crucial part in chemical kinetics. It helps to understand the impact of temperature on the rate of reaction. This equation was first introduced by Svente Arrhenius in 1889.
In the equation, A = Frequency factor
K = Rate constant
R = Gas constant
Ea = Activation energy
T = Kelvin temperature
The collision theory is the foundation for the Arrhenius equation. As per this theory, the reaction is essentially a collision involving two molecules ( of same or different substances) to form the intermediate. This intermediate that is formed is unstable, and itt exists for a short duration of time. The intermediate breaks down thereby giving out two molecules of product. The energy that is used for forming this intermediate is called the activation energy.
If we look at log on both sides of the equation, the equation becomes
Ln is the natural algorithm, and these values can be picked up from a logarithmic table.
For the graphical representation,
When we compare this equation with the straight-line equation, we get
X = \[\frac {1} {T}\]
Y = ln k
M = \[\frac {-Ea} {R}\]
C = ln A
This provides the straight-line graph but has a negative slope.
Plotting the k v/s \[(\frac {1} {T})\].
Impact of Temperature
With the help of the graph, we can conclude that the rate of reactions and temperature are proportional. As temperature increases, the rate of reaction also tends to increase. There is an increase in kinetic energy with temperature. So when the temperature is increased, the number of molecules having kinetic energy higher than activation energy also increases. This leads to a rise in the rate of overall reaction as the activation energy decreases.
For the 10K shift in temperature, the rate is almost doubled.
Let us consider the Arrhenius equation at times T1 and T2 where the rates of reaction are denoted by K1 and K2 respectively.
In K1 = \[\frac {-Ea} {RT_1}\] + In A —--- (1)
In K2 = \[\frac {-Ea} {RT_2}\] + In A —--- (2)
Now we subtract 1 from 2
In K2 - In K1 equals to \[\frac {Ea} {RT_1}\] - \[\frac {Ea} {RT_2}\]
In \[\frac {K_2} {K_1}\] = \[(\frac {Ea} {R})\] \[\frac {1} {T_1}\] - \[\frac {1} {T_2}\]
Converting to log,
Log \[(\frac {Ea} {2.303R})\] \[\frac {T_2-T_1} {T_1T_2}\]
The Arrhenius equation also suggests that uncatalyzed reaction is more impacted by temperature in comparison to the catalyzed reaction.
Real-Life Examples of This Theory:
Milk gets sour faster when it is kept at room temperature instead of being kept in the refrigerator.
Eggs tend to hard boil faster when they are at sea level in comparison to mountains or elevated levels.
The butter tends to become rancid at a faster rate in summer than it does in winter
Cold-blooded animals or species like reptiles and insects become more lethargic during colder days.
Significance of Arrhenius Equation
This equation enables the accounting of factors that have an effect on the rate of reaction and which is not possible to be determined by the rate law.
It helps in finding the impact of energy barrier, frequency, temperature, the orientation of collisions, and presence of catalyst using the equation.
FAQs on Arrhenius Equation: Rate Constant and Temperature Explained
1. What is the Arrhenius equation and what fundamental relationship does it explain?
The Arrhenius equation is a fundamental formula in chemical kinetics that describes the relationship between the rate of a chemical reaction and the temperature. It is expressed as k = Ae-Ea/RT. This equation quantitatively shows how the rate constant (k) of a reaction increases exponentially as the absolute temperature (T) increases.
2. What is the significance of each component in the Arrhenius equation, k = Ae-Ea/RT?
Each component in the Arrhenius equation has a specific physical meaning:
- k is the rate constant, which quantifies the speed of the reaction.
- A is the pre-exponential factor or Arrhenius constant. It is related to the frequency of collisions between reactant molecules in the correct orientation.
- Ea is the activation energy, which is the minimum energy required for reactants to transform into products. It is measured in Joules/mole.
- R is the universal gas constant (8.314 J K-1 mol-1).
- T is the absolute temperature in Kelvin.
3. How does an increase in temperature affect the rate constant (k) of a reaction?
According to the Arrhenius equation, an increase in temperature (T) causes the negative exponent (-Ea/RT) to become smaller (less negative). This results in a larger value for the term e-Ea/RT, which in turn leads to an exponential increase in the rate constant (k). Consequently, the overall rate of the reaction increases significantly with a rise in temperature.
4. Why does even a small rise in temperature often lead to a large increase in the reaction rate?
A small temperature rise causes a large increase in the reaction rate primarily because it significantly increases the number of molecules possessing energy equal to or greater than the activation energy (Ea). The relationship is exponential, not linear. As temperature rises, the fraction of effective collisions (those with sufficient energy) increases dramatically, leading to a much faster reaction rate. A common rule of thumb is that for many reactions, a 10°C rise in temperature nearly doubles the reaction rate.
5. What is the physical meaning of activation energy (Ea) and how does it act as a barrier?
Activation energy (Ea) represents the minimum amount of energy that reactant molecules must possess to overcome the energy barrier and form an activated complex before they can be converted into products. It can be visualised as a 'hill' that reactants must climb. A higher activation energy means a higher barrier, resulting in fewer molecules having enough energy to react at a given temperature, thus leading to a slower reaction. Conversely, a lower Ea results in a faster reaction.
6. How can you graphically determine the activation energy (Ea) of a reaction?
The activation energy can be determined graphically by rearranging the Arrhenius equation into its linear form: ln k = - (Ea/R)(1/T) + ln A. This equation is in the form of a straight line (y = mx + c). By plotting ln k (natural log of the rate constant) on the y-axis against 1/T (inverse of absolute temperature) on the x-axis, you will get a straight line with a negative slope. The slope of this line is equal to -Ea/R. Therefore, the activation energy can be calculated as Ea = - (slope × R), where R is the gas constant.
7. Is the pre-exponential factor 'A' a universal constant for all reactions?
No, the pre-exponential factor 'A' is not a universal constant. It is specific to each individual reaction and depends on factors like the frequency of collisions and the steric factor (the orientation of molecules during collision). While it is considered constant for a particular reaction over a narrow temperature range, it is incorrect to assume it has the same value for different chemical reactions. Therefore, 'A' is a reaction-specific constant, not a universal one.
