Consider the following reaction:

CH3X + Y --> CH3Y + X
At 25 degrees Celcius the following two experiments were run, yielding the following data:

Experiment 1: [Y]0 = 3.0 M
[CH3X] (mol/L) Time (hours)
7.08*10^-3 1.0
4.52*10^-3 1.5
2.23*10^-3 2.3
4.76*10^-4 4.0
8.44*10^-5 5.7
2.75*10^-5 7.0

Experiment 2: [Y]0 = 4.5 M
[CH3X] (mol/L) Time (hours)
4.50*10^-3 0
1.70*10^-3 1.0
4.19*10^-4 2.5
1.11*10^-4 4.0
2.81*10^-5 5.5

Experiments were also run at 85 degrees Celcius. The value of the rate constant at 85 degrees Celcius was found to be 7.88*10^8 (with the time in units of hours), where [CH3X]0=1.0*10^-2 M and [Y]0= 3.0 M.
a) Determine the rate law and the value of k for the reaction at 25 degrees Celcius.
b) Determine the half-life at 85 degrees Celcius.
c) Determine the activation energy (Ea) for the reaction.
d) Given that C-X bond energy is known to be about 320 kJ/mol, suggest a mechanism that explains the results in parts a and c.

Nice try

To determine the rate law and the value of k for the reaction at 25 degrees Celsius, we need to use the rate data from the experiments. The rate law can be determined by finding the order of the reaction with respect to each reactant, and the value of k can be calculated using the rate law.

a) Determining the rate law and the value of k:
1. Start by selecting two experiments that have different initial concentrations of one reactant and keep the other reactant concentration constant. For example, in Experiment 1, the initial concentration of Y is 3.0 M, and in Experiment 2, the initial concentration of Y is 4.5 M.
2. Calculate the initial rate of the reaction (R) for each experiment using the data provided. The initial rate is the change in concentration of a reactant divided by the corresponding time interval.
For Experiment 1: R1 = (4.52 * 10^-3 - 7.08 * 10^-3) mol/(L * hour) / (1.5 - 1.0) hour
For Experiment 2: R2 = (1.70 * 10^-3 - 4.50 * 10^-3) mol/(L * hour) / (1.0 - 0) hour
3. Calculate the ratio of the initial rates from the two experiments to determine the order of the reaction with respect to Y.
R1 / R2 = (4.52 * 10^-3 - 7.08 * 10^-3) mol/(L * hour) / (1.5 - 1.0) hour / (1.70 * 10^-3 - 4.50 * 10^-3) mol/(L * hour) / (1.0 - 0) hour
This ratio should be constant, indicating a first-order reaction with respect to Y.
4. Repeat steps 2 and 3 using experiments with different initial concentrations of CH3X to determine the order of the reaction with respect to CH3X. In this case, since the rate appears to decrease linearly with time, the reaction is likely first-order with respect to CH3X.
5. Therefore, the overall rate law for the reaction is rate = k[CH3X][Y], with the reaction being first-order in both CH3X and Y.
6. To find the value of k, choose one set of experimental conditions where all concentrations are known and calculate k. For example, using Experiment 1:
k = (4.52 * 10^-3 - 7.08 * 10^-3) mol/(L * hour) / [CH3X] * [Y]
Plug in the values from Experiment 1 to calculate k. Repeat for Experiment 2 to ensure consistency.

b) To determine the half-life of the reaction at 85 degrees Celsius, we need to use the rate constant obtained for that temperature.

1. In a first-order reaction, the half-life (t1/2) is defined as the time it takes for the reactant concentration to decrease to half of its initial value.
2. The equation for the first-order reaction rate is ln([A]0/[A]) = kt.
Using the given rate constant k = 7.88 * 10^8 hours^-1, [A]0 = 1.0 * 10^-2 M, and [A]/[A]0 = 1/2, solve for t.
ln(1) - ln(1/2) = (7.88 * 10^8 hours^-1) * t
Simplify the equation to find t.

c) To determine the activation energy (Ea) for the reaction, we can use the Arrhenius equation, which relates the rate constant (k) to the temperature (T) and the activation energy (Ea).

1. The Arrhenius equation is given by k = A * exp(-Ea/RT), where A is the pre-exponential factor, R is the ideal gas constant, and T is the temperature in Kelvin.
2. Rearrange the equation to solve for Ea: Ea = -ln(k/A) * RT
Plug in the given values for k, A, and T to calculate Ea.

d) To suggest a mechanism that explains the results in parts a and c, we need to consider the nature of the reactants and products, as well as any intermediates and transition states involved in the reaction. Without additional information about the reactants and the possible steps involved, it is difficult to suggest a specific mechanism. However, based on the known results, a likely mechanism could involve a nucleophilic substitution reaction, where Y acts as the nucleophile and attacks the carbon atom in CH3X, resulting in a displacement of X, forming the product CH3Y. An energy diagram or more detailed information about the reaction is necessary to provide a more specific suggestion.