i already posted this but i tried to solve it on my own can you check at the end of this paragraph?

The study of kinetics

group 1:
Temp: 12.6 C
T(K): 12.6+273= 285.6
1/T(K): 3.50X10^-3 this one is the x value
Time: 816 sec
Rate ®: 7.66 x10^-6
LnR: -11.8 this is the y value

group 2:
Temp: 45C
T(K): 45+273= 318
1/T(K): 3.14X10^-3 this one is the x value
Time: 495 sec
Rate ®: 1.26 x10^-6
LnR: -11.3

group 3:
Temp: 12.6 C
T(K): 34.8+273= 285.6
1/T(K): 3.28X10^-3 this one is the x value
Time: 107 sec
Rate ®: 5.84 x10^-5
LnR: -9.75

now I need to find the

group 1:
Temp: 12.6 C
T(K): 12.6+273= 285.6
1/T(K): 3.50X10^-3 this one is the x value
Time: 816 sec
Rate ®: 7.66 x10^-6
LnR: -11.8

1. the teacher said our k from last week was strong, and to use LnR instead.
so my ANSWER:
(-11.8)-(9.75)
_____________________________
(3.50 X 10^-3)-(3.28 X 10^-3)

= -2.05/0.22 X 10^-3
= -9.32 X 10^3

2. also ANSWER for Ea:
9.32 x 10^3 x gas constant 8.3144125 j/mole

= 77.5 x 10^3 j/mole
=77.5 kj/mol

Based on the information provided, it seems that you are trying to calculate the activation energy (Ea) based on the given data for different temperatures (in Celsius) and corresponding reaction rates (Rate) in different groups. Let's go through the steps to verify your calculations:

1. Find the difference in LnR values:
For group 1, the LnR value is -11.8, and for group 3, it is -9.75. So, the difference in LnR values is -11.8 - (-9.75) = -2.05.

2. Find the difference in 1/T(K) values:
For group 1, the 1/T(K) value is 3.50 x 10^-3, and for group 3, it is 3.28 x 10^-3. So, the difference in 1/T(K) values is 3.50 x 10^-3 - 3.28 x 10^-3 = 0.22 x 10^-3 = 0.22 x 10^-6 = 2.2 x 10^-7.

3. Calculate the ratio:
Divide the difference in LnR values by the difference in 1/T(K) values:
-2.05 / (2.2 x 10^-7) = -9.32 x 10^6

4. Calculate the activation energy (Ea):
Multiply the ratio by the gas constant (R = 8.3144125 J/mol·K):
-9.32 x 10^6 x 8.3144125 = -77.5 x 10^6 J/mol = -77.5 kJ/mol

Therefore, based on your calculations, the activation energy (Ea) is indeed -77.5 kJ/mol.