A popular chemical demonstration is the “magic genie” procedure, in which hydrog

Question

A popular chemical demonstration is the “magic genie” procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is 70.0 kJ/mol. When the catalyst is added, the activation energy (at 20.ºC) is 42.0 kJ/mol. Theoretically, to what temperature (ºC) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at 20.ºC? Assume the frequency factor A is constant, and assume the initial concentrations are the same. Temperature = __ºC

Explanation / Answer

Reaction rate,
K = A* e^ (-Ea/RT)

for uncatalysed reaction:
K1 = A*e^(-70000/(8.314*T))

for catalysed reaction:
K2 = A*e^(-42000/(8.314*293)) {Because T = 20 oC +293 K}

for K1= K2
A*e^(-70000/(8.314*T)) = A*e^(-42000/(8.314*293))
70000/(8.314*T) = 42000/(8.314*293)
70000/(T) = 42000/(293)
T= 488 K
   = (488-273) oC
   = 215 oC
Answer: 215 oC

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