Question

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E = 5.0 kJ/mol. If the rate constant of this reaction is 1.9 × 107 M¹-s Round your answer to 2 significant digits. -1 at 89.0 °C, what will the rate constant be at 121.0 °C?​

Answer 1

The Arrhenius equation relates the rate constant of a reaction to the activation energy, the temperature, and a constant known as the pre-exponential factor or frequency factor. The equation is given by:

k = A * exp(-Ea/RT)

where:

k = rate constant

A = pre-exponential factor or frequency factor

Ea = activation energy (in Joules/mol)

R = gas constant (8.314 J/mol-K)

T = temperature (in Kelvin)

We are given that the rate constant at 89.0°C (362.15 K) is 1.9 × 10^7 M^-1s^-1. We want to find the rate constant at 121.0°C (394.15 K).

First, we need to calculate the pre-exponential factor, A. We can do this by rearranging the Arrhenius equation and solving for A:

A = k * exp(Ea/RT)

We can plug in the values we know:

A = (1.9 × 10^7 M^-1s^-1) * exp((5.0 kJ/mol) / (8.314 J/mol-K * 362.15 K))

A = 6.46 × 10^11 M^-1s^-1

Now we can use the Arrhenius equation to calculate the rate constant at 121.0°C:

k = A * exp(-Ea/RT)

k = (6.46 × 10^11 M^-1s^-1) * exp((5.0 kJ/mol) / (8.314 J/mol-K * 394.15 K))

k = 1.9 × 10^9 M^-1s^-1

Therefore, the rate constant at 121.0°C is approximately 1.9 × 10^9 M^-1s^-1.