High School

The activation energy of a reaction is 46.5 kJ/mol, and the frequency factor is \(1.9 \times 10^{11}\, s^{-1}\).

Calculate the rate constant of the reaction at \(24^\circ \text{C}\).

Answer :

Final answer:

The rate constant for the reaction at 24° C can be calculated using the Arrhenius equation.

Explanation:

The rate constant can be calculated using the Arrhenius equation:

k = A * e-Ea / (R * T)

where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.

Given that the activation energy is 46.5 kJ/mol and the frequency factor is 1.9 x 10^11/s, we can convert these values to the appropriate units and calculate the rate constant at 24° C:

  1. Convert activation energy to J/mol: (46.5 kJ/mol) * (1000 J/1 kJ) = 46,500 J/mol
  2. Convert temperature to Kelvin: 24°C + 273 = 297 K
  3. Plug the values into the Arrhenius equation: k = (1.9 x 10^11/s) * e-46,500 J/mol / (8.314 J/(mol·K) * 297 K)
  4. Calculate the rate constant using a scientific calculator or software.

Learn more about Rate constant here:

https://brainly.com/question/20305871

#SPJ11

Final Answer

The rate constant (k) for the reaction at 24°C is approximately 1.54 x 10^9 1/s.

Explanation

To calculate the rate constant (k) for a reaction at a given temperature (T), you can use the Arrhenius equation:

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

Where:

k = rate constant

A = frequency factor (pre-exponential factor)

Ea = activation energy

R = gas constant (8.314 J/(mol·K))

T = temperature in Kelvin (K)

First, we need to convert the temperature from Celsius to Kelvin:

T(K) = 24°C + 273.15 = 297.15 K

Now, plug the values into the Arrhenius equation:

k = (1.9 x 10^11 1/s) * e^(-46.5 kJ/mol / (8.314 J/(mol·K) * 297.15 K))

k = (1.9 x 10^11 1/s) * e^(-46.5 * 1000 J / (8.314 J/(mol·K) * 297.15 K))

k ≈ 1.54 x 10^9 1/s

So, the rate constant (k) for the reaction at 24°C is approximately 1.54 x 10^9 1/s.

The Arrhenius equation describes the temperature dependence of reaction rates and is essential in chemical kinetics. It illustrates how temperature impacts reaction rates by considering the activation energy and the frequency factor.

Activation energy represents the energy barrier that reactant molecules must overcome for a reaction to occur, while the frequency factor accounts for the frequency of successful collisions between reactants. Increasing the temperature leads to a higher rate constant, indicating that reactions occur more rapidly at higher temperatures due to increased kinetic energy and more effective collisions between molecules.

Learn more about constant

brainly.com/question/31730278

#SPJ11