consider the following reactions
O+N2->NO+N Ea=315kj/mol
Cl+H2->HCl+H Ea=23kj/mol
Why is the activation energy for one much lower that the other.
The frequency factor is very close in value for the two. Assume they are the same compute the ratio of the reaction constants for these to reactions at 25'c
1. Because a N2 bond takes much more energy to break because it is a triple bond whereas H2 bond is relatively easy to break
2. use the Arhenius equation to obtain a ratio of 0.3078
To understand why the activation energy for one reaction is much lower than the other, we need to consider the factors that influence the activation energy.
Activation energy (Ea) is the minimum amount of energy required for a chemical reaction to occur. It represents the energy barrier that reactant molecules must overcome in order to transform into product molecules.
In general, the factors that affect activation energy include the complexity of the reaction mechanism, the stability of the transition state, and the strength of chemical bonds involved.
In the first reaction O + N2 -> NO + N (Ea = 315 kJ/mol), the activation energy is relatively high. This could be due to the complexity of the reaction mechanism, involving multiple steps or intermediates. Additionally, the formation of NO and N from O and N2 requires breaking strong chemical bonds, which requires a higher amount of energy.
In the second reaction Cl + H2 -> HCl + H (Ea = 23 kJ/mol), the activation energy is much lower. This can be attributed to the simplicity of the reaction mechanism, possibly involving a direct collision between Cl and H2 molecules. Furthermore, the formation of HCl and H involves the formation of relatively weaker bonds compared to the first reaction, leading to a lower energy requirement.
Now, let's compute the ratio of the reaction constants for these two reactions at 25°C, assuming the frequency factor (pre-exponential factor) is the same for both reactions.
The general equation relating the rate constant (k) and the activation energy (Ea) is given by the Arrhenius equation:
k = A * e^(-Ea/RT)
Where:
k is the rate constant
A is the frequency factor
Ea is the activation energy
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Since we assume the frequency factor (A) is the same for both reactions, we can cancel it out when calculating the ratio of the rate constants.
The ratio of the rate constants (k1/k2) is given by:
k1/k2 = (e^(-Ea1/RT)) / (e^(-Ea2/RT))
To compute this ratio, we need the specific values of the activation energies (Ea1 = 315 kJ/mol and Ea2 = 23 kJ/mol) and the temperature (25°C = 298 K).
k1/k2 = (e^(-315000/(8.314*298))) / (e^(-23000/(8.314*298)))
Simplifying and calculating this expression will give you the ratio of the reaction constants for the two reactions at 25°C.