Consider an elementary gas-phase reaction with a measured rate constant of k1=1.2×10−3s−1 at 500 K and an activation energy of 160 kJ mol⁻¹.
(a) Derive a linearized form that allows lnk to be expressed as a function of reciprocal temperature, and state the slope and intercept in terms of physical constants.
(b) Using the expression from part (a), calculate the rate constant k2 at 510 K.
(c) Determine the percentage increase in rate constant when the temperature is raised from 500 K to 510 K.
(d) Suppose the initial concentration of reactant is 0.020 mol L⁻¹. Calculate the time required for the concentration to decrease to 0.010 mol L⁻¹ at 500 K and at 510 K, assuming first-order kinetics. Express each time to three significant figures.
(e) Discuss whether a further temperature increase of 10 K (to 520 K) would continue to result in an equal percentage increase in rate constant. Support your argument with mathematical reasoning based on the form of the temperature dependence.
a. Part (a)
b. Part (b)
c. Part (c)
d. Part (d)
e. Part (e)