Relationship between ln k and 1/t using different formula

In summary, the conversation discusses two equations, the first referring to the equilibrium constant and the heat of reaction, while the second refers to the reaction rate constant and the activation energy. The conversation highlights a contradiction between the two equations and raises questions about the values of K and k.
  • #1
Ethan Cheng
1
0
Hi, I'm currently taking Chemistry 101 and came across this equation that seems to contradict what I've learned before. I don't know the name of it, but here is the equation and its implication.
Chem 1.PNG
Chem 2.PNG

Now another equation we have learned is the Arrhenius equation, which is as follows:
arrhenius%20plot1.jpg


If I understood the equations correctly, they are referring to the same k (equilibrium constant) and the same t (temperature), which gave rise to something that seems to be wrong.

Take the example of combustion, where the activation energy is above 0 and is an exothermic reaction. The graph produced by the first equation will be one with a positive slope, but the one produced by the second equation is one with a negative slope, even though they have the same axis. To illustrate this further, if we somehow experimentally determined the ln k and 1/t (appears very often in our homework), we usually start by graphing them. The linear regression is seen (using Arrhenius equation) as -Ea/R, and we can, therefore, use it to find activation energy. But this same slope should also be -H / R, and therefore will lead to Ea = H, which is also obviously wrong.

What am I missing here? Are the K referring to different values?
 

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  • #2
The equation in your first figures refers to the equilibrium constant and the heat of reaction. The equation in your 2nd figure refers to the reaction rate constant and the activation energy for the reaction.
 
  • #3
Ethan Cheng said:
Are the K referring to different values?

Yes. One is often written as k (for kinetics), the other as K (for equilibrium).
 

1. What is the relationship between ln k and 1/t using different formula?

The relationship between ln k and 1/t can be described by the Arrhenius equation, which states that ln k is directly proportional to 1/t. This means that as the temperature (t) increases, the natural logarithm of the rate constant (ln k) also increases. This relationship can be seen in various formulae, such as the Van 't Hoff equation and the Eyring equation.

2. How do different formulae represent the relationship between ln k and 1/t?

Different formulae represent the relationship between ln k and 1/t in different ways. For example, the Van 't Hoff equation uses the ratio of rate constants at two different temperatures to calculate the change in ln k with respect to temperature. The Eyring equation, on the other hand, uses the activation energy and temperature to calculate ln k. However, both of these equations ultimately show that ln k is directly proportional to 1/t.

3. Can the relationship between ln k and 1/t be used to predict reaction rates?

Yes, the relationship between ln k and 1/t can be used to predict reaction rates. By knowing the temperature and rate constant at one temperature, the Van 't Hoff equation can be used to calculate the rate constant at a different temperature. This information can then be used to predict the rate of the reaction at the new temperature.

4. How does the relationship between ln k and 1/t relate to the activation energy of a reaction?

The relationship between ln k and 1/t is directly related to the activation energy of a reaction. As the temperature increases, the rate constant (k) also increases, meaning that the activation energy barrier is easier to overcome. This is reflected in the Eyring equation, where the activation energy is used to calculate the rate constant at a specific temperature.

5. Are there any limitations to using the relationship between ln k and 1/t to predict reaction rates?

While the relationship between ln k and 1/t can be useful in predicting reaction rates, there are some limitations. This relationship assumes that the reaction follows the Arrhenius equation and that the rate constant is only affected by temperature. In reality, other factors such as catalysts and concentration can also affect the rate of a reaction. Additionally, this relationship may not be accurate for reactions with very high or very low temperatures.

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