Hi! I am stuck with this question and I would like to know what I did wrong:
Given that the initial rate constant is 0.0160 s-1 at an initial temperature of 25 degrees C, what would the rate constant be at a temperature of 130 degrees C for the same reaction described in Part A?
I solved for the Ea, and I got 32,900 J.
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
ln(k2/0.0160) = (32,900/8.314)(1/298.15 - 1/314.55)
ln(k2/0.0160) = (3,957.180)(0.00174871)
ln(k2/0.0160) = (0.6919986)
(k2/0.0160) = e^(0.6919986)
(k2/0.0160) = 1.997704
k2 = 0.03196
The answer above is not correct.
Thanks!
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
The equation is OK
ln(k2/0.0160) = (32,900/8.314)(1/298.15 - 1/314.55)
All of the substitutions look ok except for T2. 273.15 + 130 C = 403.15 and not 314.15.
ln(k2/0.0160) = (3,957.180)(0.00174871)
ln(k2/0.0160) = (0.6919986)
(k2/0.0160) = e^(0.6919986)
(k2/0.0160) = 1.997704
k2 = 0.03196
With the corrected T2 I obtained k2 = 0.5074.
This is the same problem I did yesterday, I think, EXCEPT the problem then was to calculate T2 when k was doubled. This is just the reverse, so of course, you obtained 0.032 for k2 which is just double k1 when you substituted the T2 we calculated. If this k2 (0.5074 to the right number of significant figures) is not right, the problem may be the Ea. Since that came from another problem (at least it appears that way from your presentation) that could be the culprit. Hope this helps.
To find the rate constant at a temperature of 130 degrees Celsius, you used the Arrhenius equation, which is a common approach for determining the rate constant at different temperatures. However, it seems there was an error in your calculations.
Let's go through the steps again:
1. Begin with the Arrhenius equation:
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
Here, k1 is the initial rate constant at the initial temperature (25 degrees Celsius), T1 is the initial temperature in Kelvin (25 + 273.15), k2 is the rate constant at the desired temperature (130 degrees Celsius), and T2 is the desired temperature in Kelvin (130 + 273.15).
2. Substitute the values into the equation:
ln(k2/0.0160) = (32,900/8.314)(1/(25 + 273.15) - 1/(130 + 273.15))
3. Evaluate the natural logarithm:
ln(k2/0.0160) = (32,900/8.314)(0.00357 - 0.00142)
ln(k2/0.0160) = 14.4901
4. Solve for (k2/0.0160):
(k2/0.0160) = e^14.4901
(k2/0.0160) = 171212.448
5. Solve for k2:
k2 = 0.0160 * 171212.448
k2 = 2,739.399 s-1
Thus, the rate constant at a temperature of 130 degrees Celsius for the same reaction would be approximately 2,739.399 s-1.