Question

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy =21.0ea/kjmol. if the rate constant of this reaction is 2.0 × 10⁶·m⁻¹ s⁻¹ at 23.0°c, what will the rate constant be at 60.0°c?

a. 1.546×10⁶ m⁻¹ s⁻¹
b. 2.0×10⁶ m⁻¹ s⁻¹
c. 3.432×10 ⁶ m⁻¹ s⁻¹
d. 5.002×10 ⁶ m⁻¹ s⁻¹

Answer 1

The rate constant at a different temperature can be calculated using the two-point form of the Arrhenius equation and given data on activation energy and initial rate constant.

Step-by-step explanation:

To calculate the rate constant of a reaction at a new temperature using the Arrhenius equation, we utilize the fact that the logarithm of the rate constant is linearly related to the inverse of the temperature (in Kelvin). We can rearrange this to a two-point form for easy calculation when we know the activation energy and rate constant at a certain temperature. Here, we use the given activation energy (Ea) and rate constant (k1) at temperature T1 to find the rate constant (k2) at a different temperature T2.

The two-point form of the Arrhenius equation is given by:

ln(k2/k1) = -Ea/R(1/T2 - 1/T1)

where:

• k1 and k2 are the rate constants at temperatures T1 and T2, respectively
• Ea is the activation energy
• R is the ideal gas constant (8.314 J/mol·K)
• T1 and T2 are the temperatures in Kelvin

Convert the temperatures from Celsius to Kelvin (K = °C + 273.15), then solve for k2 using the rearranged Arrhenius equation.