The energy of activation for a reaction is 100kj/mol.Presence of catalyst lowers the activation by 75%.What will be the effect on rate of reaction at 20°C, other things being the same.
To determine the effect of a catalyst on the rate of reaction, we need to understand the role of the activation energy in the reaction. Activation energy is the minimum energy required for a reaction to occur. In other words, it is the energy needed for reactant molecules to overcome the energy barrier and transform into products.
In this case, the energy of activation for the reaction is given as 100 kJ/mol. However, the presence of a catalyst lowers the activation energy by 75%. This means the effective activation energy with the catalyst is 25% of the original value.
To determine the effect on the rate of reaction, we can use the Arrhenius equation, which relates the rate constant (k) with the activation energy (Ea) and temperature (T). The Arrhenius equation is as follows:
k = A * exp(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor (constant)
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
Since the other factors are assumed to be the same, we can focus on how the lower activation energy affects the rate of reaction at 20°C (or 293 Kelvin).
Let's consider two cases:
1. Without a catalyst (activation energy = 100 kJ/mol):
k1 = A * exp(-100000 / (8.314 * 293))
2. With a catalyst (activation energy reduced by 75%, i.e., 25 kJ/mol):
k2 = A * exp(-25000 / (8.314 * 293))
In this case, we can observe that the lower activation energy will result in a larger value for k2 as compared to k1. Consequently, the rate of reaction will increase with the presence of a catalyst. Therefore, the effect of the catalyst at 20°C will be an increase in the rate of reaction.