A common rule of thumb in organic chemistry is that increasing the temperature of a reaction at room temperature by 10°C doubles the rate.Calculate E_a for a reaction that follows this rule of thumb Assume room temperature is 25°C.

Question

Quizplus · Accepted Answer

The equation for calculating the activation energy (Ea) using the Arrhenius equation is:

k = Ae^(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

If we assume that increasing the temperature by 10°C doubles the rate, we can use this information to calculate the activation energy:

2k = Ae^(-Ea/(R*298 K))     // At room temperature (25°C or 298 K)
k =    Ae^(-Ea/((R*308 K))

Dividing the two equations to eliminate the pre-exponential factor A, we get:

2 = e^(Ea/(R*10))

Taking natural logarithms of both sides gives:

ln(2) = Ea/(R*10)

Rearranging this equation gives:

Ea = -R*10*ln(1/2) = 52.9 kJ

Therefore, the answer is D, 52.9 kJ.

A Common Rule of Thumb in Organic Chemistry Is That