Activation energy, abbreviated Ea, can best be described as the minimum energy required before a chemical reaction can proceed. It is like a barrier that has to be overcome in order for your chemical reaction to take place. Activation energy can be calculated in two ways: by using the rates of reaction at two different temperatures or by using the Arrhenius equation.
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Things you need
- Graphing calculator
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."
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).
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 reaction rate at two different temperatures method
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).
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.
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.
Divide the calculated slope by the universal gas constant to isolate the value (- Ea) from (- Ea/R).
Multiply (- Ea) by -1 to get Ea, the activation energy of your reaction. This forms the basis of the experimental determination of activation energy.
By experimental method using the Arrhenius equation
Tips and warnings
- Always cross-reference your answer/final result with published values in laboratory data log books, chemistry textbooks or on online databases for accuracy and correct units.
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