The reaction between ethyl iodide and hydroxide ion in ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 ¡ C2H5OH1l2 + I - 1alc2, has an activation energy of 86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s-1. (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature (50 °C).
2. Use the Arrhenius equation: \( k = A \cdot e^{-\frac{E_a}{RT}} \), where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin.
3. Substitute the given values into the Arrhenius equation: \( A = 2.10 \times 10^{11} \text{ M}^{-1} \text{ s}^{-1} \), \( E_a = 86.8 \text{ kJ/mol} \) (convert this to J/mol by multiplying by 1000), and \( T \) is the temperature in Kelvin calculated in step 1.
4. Calculate the exponent \( -\frac{E_a}{RT} \) using the values from step 3.
5. Compute the rate constant \( k \) by evaluating the Arrhenius equation with the calculated exponent and the given frequency factor.

Key Concepts

Arrhenius Equation

The Arrhenius equation relates the rate constant of a chemical reaction to temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation shows how an increase in temperature can lead to an increase in the rate constant, thereby accelerating the reaction.

Activation Energy

Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. In the context of the Arrhenius equation, a higher activation energy results in a lower rate constant at a given temperature, indicating that the reaction proceeds more slowly. Understanding activation energy is crucial for predicting reaction rates and mechanisms.

Temperature Conversion

Temperature must be expressed in Kelvin when using the Arrhenius equation. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. For example, 50°C is equivalent to 323.15 K. Accurate temperature conversion is essential for correctly calculating the rate constant, as the rate constant is temperature-dependent and influences the overall reaction kinetics.