The following data show the rate constant of a reaction measured at several different temperatures.

Temperature (K) | Rate Constant (1/s) |

310 | 0.190 |

320 | 0.544 |

330 | 1.46 |

340 | 3.70 |

350 | 8.89 |

Use an Arrhenius plot to determine the activation barrier for the reaction.

We’re being asked to **determine the activation energy (E _{a})** of a reaction given the temperature and rate constant values.

We’re given the temperature (K) and rate constant (1/s) values.

This means that we need to use the ** two-point form of the Arrhenius Equation**:

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{k}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}{\mathbf{}}\left(\frac{\mathbf{1}}{\mathbf{T}}\right){\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{}}{\mathbf{A}}}$

where:

**k** = rate constant

**E _{a}** = activation energy (in J/mol)

**R** = gas constant (8.314 J/mol • K)

**T** = temperature (in K)

**A** = Arrhenius constant or frequency factor