Which reaction is faster, one with E_act = +10 kcal/mol(+41.8 kJ/mol) or one with E_act = +5 kcal/mol(+20.9 kJ/mol)? Explain.

Verified step by step guidance

1. Step 1: Understand the concept of activation energy (E_act). Activation energy is the minimum energy required for a chemical reaction to occur. A lower activation energy means that the reaction is more likely to occur at a given temperature, making it faster.
2. Step 2: Compare the given activation energies. The problem provides two activation energies: E_act = +10 kcal/mol (+41.8 kJ/mol) and E_act = +5 kcal/mol (+20.9 kJ/mol). Note that the second value is lower than the first.
3. Step 3: Recall the relationship between activation energy and reaction rate. According to the Arrhenius equation, the rate constant (k) of a reaction is inversely related to the activation energy. A lower activation energy results in a higher rate constant, meaning the reaction proceeds faster.
4. Step 4: Conclude which reaction is faster. Since the reaction with E_act = +5 kcal/mol (+20.9 kJ/mol) has a lower activation energy compared to E_act = +10 kcal/mol (+41.8 kJ/mol), it will be faster.
5. Step 5: Explain the reasoning. The reaction with the lower activation energy requires less energy for the reactants to reach the transition state, leading to a higher probability of successful collisions and a faster reaction rate.

Key Concepts

Activation Energy (E_act)

Activation energy (E_act) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. A lower activation energy indicates that a reaction can proceed more easily and quickly, as fewer energy inputs are needed to initiate the reaction.

Reaction Rate

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It is influenced by several factors, including temperature, concentration, and the presence of catalysts. Generally, reactions with lower activation energies have higher rates because they require less energy to reach the transition state.

Arrhenius Equation

The Arrhenius equation describes the relationship between the rate constant of a reaction and its activation energy, temperature, and a pre-exponential factor. It is mathematically expressed as k = A * e^(-E_act/RT), where k is the rate constant, A is the frequency factor, R is the gas constant, and T is the temperature in Kelvin. This equation illustrates that as activation energy decreases, the rate constant increases, leading to faster reactions.