I believe that you are correct because you have more experience in G-chem then I have. But how does doubling the reaction rate double the k value? Isn't k just a constant for a particular reaction?
Yes and no. What I said, or should have said, is that changing the temperature by 10 C (approximately) doubles the rate. The question asked for the temperature at which the rate was doubled. So yes, the reaction rate is constant but ONLY for that particular temperature. At any other temperature the rate will be different. The "rule of thumb" is that we double the rate for 10 C change. So increasing T from 20 to 70 we increase rate by approximately 25/sup> = 32 times faster.
Okay, I think I get what you are saying. So, let's say that I keep the concentration of reactants constant, but I increase the temperature or decrease the temperature for a reaction. Since I played around with the temperature (i.e., varying it) I changed the reaction rate, that I calculated for the reaction for the same reaction before I varied the temperature, therefore I changed the constant k, since I used the same concentration to determine k. Is there a specific equation that shows how the relationship works, or did you learn this in course work or while doing research?
So increasing T from 20 to 70 we increase rate by approximately 25/sup> = 32 times faster.
This part here is why I am asking about an equation.
Yes, it's the Arrhenius equation.
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). This give you a specific equation to determine what the new k will be at the new T. The 2^5 thing I quoted is a "rule of thumb" that is approximate. Try the equation giving values for k1 and T1 and Ea (R is 8.314 here) and use T2 that's 10+T1. Calculate k. It should be close to double k1. Or use ln (k2/k1) = ln 2 and solve for T2 for some given value of T1 and Ea. T2 should be close to 10 C.
Got it. I had to reread the original problem to see what went on. I haven't had use for some of these calculations and years, so some concepts are fuzzier than others.
You are correct that the rate constant, k, is a constant for a specific reaction at a particular temperature. However, there is a misconception in your understanding about how doubling the reaction rate relates to the value of k.
Doubling the reaction rate does not directly double the rate constant, k. The rate constant is determined by several factors, such as the temperature and the activation energy of the reaction. It provides information about the overall speed of the reaction.
If we want to double the reaction rate, there are different ways to achieve this. One possibility is by increasing the concentration of reactants, which would increase the number of collisions and, consequently, the rate of the reaction. Another way is to increase the temperature, which would increase the average kinetic energy of the molecules, leading to more frequent and energetic collisions.
Doubling the reaction rate does not alter the value of k itself. The rate constant remains the same, as it represents the intrinsic behavior of the reaction. However, increasing the rate of the reaction can impact the observed rate at a given time, as it is determined by the product of the concentrations of reactants and the rate constant.
In summary, doubling the reaction rate does not double the value of k, as k is a constant specific to a reaction. It is crucial to differentiate between the rate constant and the rate of the reaction, which can be manipulated by adjusting factors such as concentration or temperature.