The activation energy, Ea, for a particular reaction is 19.4 kJ/mol. If the rate constant at 80 °C is 0.820 M⁻¹s⁻¹, then what is the value of the rate constant at 339 °C? (R = 8.314 J/mol • K)

Answer 1

The key to solving this problem is using the Arrhenius Equation:

k = rate constant

Z = geometric-related constant

E_a = activation energy

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

T = temperature (in Kelvins)

** remember that to convert from Celsius to Kelvin, add 273 K to your current temperature

Here we need to set up two Arrhenius equations, set them equal to each other, and then solve for the rate constant, k:

First equation (when temperature is 80 C):

0.820 = Ze^-Ea/RT = Ze^{(-19.4)/(8.314)(353)} = Z(0.993)

Z = 0.820/0.993 = 0.826

Second equation (when temperature is 339 C):

** here we plug in the value of Z we solved for during the first equation to get the new rate constant, k:

k = (0.826)e^-Ea/RT = (0.826)e^{(-19.4)/(8.314)(612)} = 0.823

Answer 2

Arrhenius equation:

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

T1 = 80C + 273 = 353K

T2 = 339C + 273 = 612K

Ea = 19.4 kJ/mol = 19,400 J/mol

R = 8.314 J/K-mol

k1 = 0.820 M^-1s^-2

ln (k2/k1) = -19,400/8.314 (1/612 - 1/353) = -2333 (-0.00120)

ln (k2/k1) = 2.7996

ln k2 - ln k1 = 2.7996

ln k2 = 2.7996 + 0.198

ln k2 = 2.9976

k2 = 20 M^-1s^-1

note: please be sure to check my math