Example A reaction carried out at 25oC has a value of k = 3.3 × 10−3 mol-1 dm3 s −1 ln A = 17.1 The gas constant R = 8.31 J K−1 mol−1 Calculate a value for the activation energy in kJ mol-1 Using Equation ln k = ln A – EA/(RT) Rearrange to EA = (ln A - ln k) x RT = (17.1 - - 5.71) x 8.31 x 298 = 56486 J mol-1 = 56.5 kJ mol-1
Example A reaction carried out at 25oC has a value of k = 3.3 × 10−3 mol-1 dm3 s −1 ln A = 17.1 The gas constant R = 8.31 J K−1 mol−1 Calculate a value for the activation energy in kJ mol-1 Using Equation ln k = ln A – EA/(RT) Rearrange to EA = (ln A - ln k) x RT = (17.1 - - 5.71) x 8.31 x 298 = 56486 J mol-1 = 56.5 kJ mol-1
You only really need to know what a natural log is if you are doing A level maths.
Otherwise, know that it is a mathematical operation that you can find on your calculator and it is the inverse of the exponential function, e^x.
Your calculator should have a ln( ) button and if you type ln(3.3 x 10^-3), the calculator will give an answer of roughly -5.71. This number is what you use in the rearranged equation.