Calculate the activation energy for the reverse reaction

[ChelseaQ]

For the decomposition of one mole of nitrosyl chloride, Delta H = 38kJ. NOCl(g)-->NO(g)+Cl2(g). The activation energy of this reaction is 100kJ. Calculate the activation energy for the reverse reaction in kJ.


I attempted this question but cannot find the process or equation to finish the question. So far I have only been able to calculate the Delta H of the product and reaction.
(NO + Cl2) - (NOCl) = (90.29 + 0) - (211.59)

I cannot figure out where to go from here and do not even know if I am starting off right..HELP PLEASE!

 

[Ygggdrasil]

Perhaps it would be helpful to draw a picture of the energies of the reactants, transition state, and products, then label the relevant energy values.

 

[Blueshift5]

To calculate the activation energy for the reverse reaction, we can use the Arrhenius equation:

k = A * e^(-Ea/RT)

Where:
k = reaction rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/mol*K)
T = temperature (in Kelvin)

First, we need to determine the reaction rate constant for the reverse reaction. This can be done by using the equilibrium constant (K) and the forward rate constant (k1):

K = k1/k-1

Since the reaction is at equilibrium, K = 1. Therefore, k1 = k-1

Next, we can use the Eyring equation to relate the forward and reverse rate constants to the activation energies:

k1 = k * e^(-ΔH/RT)
k-1 = k * e^-(ΔH-ΔEa)/RT)

Where:
ΔH = enthalpy change (38 kJ/mol in this case)
ΔEa = activation energy for the reverse reaction (what we are trying to find)
R = gas constant (8.314 J/mol*K)
T = temperature (in Kelvin)

Since k1 = k-1, we can equate the two equations and solve for ΔEa:

k * e^(-ΔH/RT) = k * e^-(ΔH-ΔEa)/RT)

e^(-ΔH/RT) = e^-(ΔH-ΔEa)/RT)

-ΔH/RT = -(ΔH-ΔEa)/RT

ΔH/RT = (ΔH-ΔEa)/RT

ΔH = ΔH-ΔEa

ΔEa = ΔH - ΔH

ΔEa = 38 kJ/mol - 100 kJ/mol

ΔEa = -62 kJ/mol

Therefore, the activation energy for the reverse reaction is -62 kJ/mol. It is negative because the reverse reaction is exothermic, meaning it releases energy instead of requiring energy to proceed.