E a is 14.0 kJ/mol, for the uncatalyzed reaction: E a for the same reaction, whe
ID: 1002899 • Letter: E
Question
Ea is 14.0 kJ/mol, for the uncatalyzed reaction:
Ea for the same reaction, when catalyzed as above, is 11.9 kJ/mol.
At 7°C, what is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction?
(Assume the frequency factor A is the same for each reaction.)
One of the concerns about the use of freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the reaction
Chlorine atoms can also act as a catalyst for the destruction of ozone.
The activation energy for the reaction
is 2.1 kJ/mol.
Cl is regenerated by the fast reaction
If the frequency factors are the same and both catalysts are in equal concentration, how many times faster, at -32°C, does the Cl catalysed reaction proceed compared to the reaction catalysed as described in the previous question.
Explanation / Answer
First one) Since k = A e^(-Ea / RT), when comparing two rates with the same frequency factor, A, we get:
k(cat) / k(uncat) = e^(-Ea(cat) / RT1) / e^(-Ea(uncat) / RT) = e^[(Ea(uncat) / RT) - (Ea(cat) / RT)]
we have T = 7 °C = 280 K, Ea(cat)=14kJ/mol=14000J/mol, Ea(uncat)=11.9kJ/mol=11900J/mol, R=8.314J/K/mol
So, k(cat) / k(uncat) = e^[(Ea(uncat) - Ea(cat)) / RT]
(Ea(uncat) - Ea(cat)) / RT = (14 000 J mol¹ - 11 900 J mol¹) / (8.314 J K¹ mol¹ * 280 K)=0.902
So, k(cat) / k(uncat) = e^[(Ea(uncat) - Ea(cat)) / RT] = e^0.902 = 2.4647.
Thus, the catalysed reaction occurs almost 2.5 times as fast as the uncatalysed at the same temperature
Second One)
k(catalyzed by Cl) / k(catalyzed by O) = e^(Ea (O catalyzed) - Ea (Cl catalyzed) / RT)
Give Ea (Cl catalysed)=2.1kJ/mol=2100J/mol, Ea (O catalysed)=11.9kJ/mol=11900J/mol, T=-32 oC=241K and R=8.314J/K/mol
Ea (O Catalyzed) - Ea (Cl catalyzed) / RT =11,900 J mol - 2,100 J mol / 8.3145 J/ K mol x 241 K = 4.891.
k (Cl catalyzed) / k (O Catalyzed) = e (Ea(O Catalyzed) - Ea (Cl catalyzed) / RT = e^4.89101 = 133.088
Thus, the reaction catalysed by Cl occurs almost 133 times as fast as the catalysed by O at the same temperature
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