Arrhenius Equation

Identify whether the question gives a graph slope or two rate constants. Convert all temperatures to kelvin. Choose ln form for graph and two-point log form for two temperatures. Use R with matching energy units, then convert J mol^-1 to kJ mol^-1 if required.

An Arrhenius plot of ln k against 1/T is essential. The line has negative slope, and the magnitude of slope gives activation energy.

Writing slope = Ea/R instead of -Ea/R, which gives the wrong sign for the Arrhenius plot.

The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy: k = Ae^(-Ea/RT), where A is the frequency factor, Ea is activation energy, R is the gas constant, and T is absolute temperature.

The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy: k = Ae^(-Ea/RT), where A is the frequency factor, Ea is activation energy, R is the gas constant, and T is absolute temperature. Arrhenius equation: k = Ae^(-Ea/RT). Log form: ln k = ln A - Ea/(RT). Two-temperature form: log(k2/k1) = Ea/(2.303R)[(T2 - T1)/(T1T2)]. Use T in K and Ea in J mol^-1 with R = 8.314 J mol^-1 K^-1. If a plot of ln k against 1/T has slope -5000 K, then -Ea/R = -5000, so Ea = 5000 x 8.314 = 41570 J mol^-1 = 41.57 kJ mol^-1.

The rate constant usually increases with temperature because a larger fraction of molecules has energy equal to or greater than activation energy. The logarithmic form of the Arrhenius equation gives a straight line for ln k versus 1/T, with slope -Ea/R. A high activation energy means the rate is more sensitive to temperature change. Arrhenius equation: k = Ae^(-Ea/RT). Log form: ln k = ln A - Ea/(RT). Two-temperature form: log(k2/k1) = Ea/(2.303R)[(T2 - T1)/(T1T2)]. Use T in K and Ea in J mol^-1 with R = 8.314 J mol^-1 K^-1. For k1 = 2.0 x 10^-3 s^-1 at 300 K and k2 = 8.0 x 10^-3 s^-1 at 320 K, log(k2/k1) = log4 = 0.6021. Ea = [2.303 x 8.314 x 0.6021 x 300 x 320]/20 = 55290 J mol^-1 approximately, or 55.3 kJ mol^-1. Interpretation: the reaction needs moderate activation energy to speed up over this temperature rise. Questions ask for activation energy from slope, comparison of rate constants at two temperatures, explanation of temperature effect, and interpretation of energy distribution or activation barrier diagrams. Writing slope = Ea/R instead of -Ea/R, which gives the wrong sign for the Arrhenius plot.