By reaction rate at two different temperatures method

• 1). Write down the equation for finding activation energy.
  
  Activation energy, Ea = ((T1 x T2 x R) / (T2 - T1)) x In(k2 / k1)
  
  "T1" is the first temperature and "T2" is the second temperature. R is the universal gas constant, which equals 8.314 J (K mol). "k1" is the rate of reaction at "T1" and "k2" is the rate of reaction at "T2."
  
  
• 2). Plug in the values for the temperatures, reaction rates and universal gas constant. As an instance, take a reaction that has a reaction rate of 0.0139 at 285K and a rate of reaction of 0.0493 at 350K. The resulting equation is:
  
  Ea = (((285K x 350K x 8.314 J/(K mol)) / (350K - 285K))) x In(0.0493 / 0.00139).
  
  
• 3). Use your calculator to solve the equation and obtain the activation energy. In this case:
  
  Ea = (829321 / 65) * In(35.47) = 45532.11 J/mol = 45.53 kJ/mol.
  
  

By experimental method using the Arrhenius equation

• 1). Take the natural logarithm of both sides of the Arrhenius equation. The Arrhenius equation is:
  
  k = A e ^ -Ea/RT.
  
  "k" is the rate of reaction constant, A is the pre-exponential factor which is assumed to be independent of temperature change, Ea is the activation energy itself, R is the universal gas constant and T the temperature in Kelvin (K).
  
  This gives ln k = ln A - Ea/(RT).
  
  
• 2). Rearrange the equation into the formula of a straight line in the form y = mx + c. This yields:
  
  ln k = -Ea/(RT) + constant or ln k = -(Ea/R)(1/T) + constant.
  
  
• 3). Use the second option to plot a graph of In k vs. 1/T with a graphing calculator to get (- Ea/R) as your slope as the second option is already in the form y = mx + c.
  
  
• 4). Divide the calculated slope by the universal gas constant to isolate the value (- Ea) from (- Ea/R).
  
  
• 5). Multiply (- Ea) by -1 to get Ea, the activation energy of your reaction. This forms the basis of the experimental determination of activation energy.