An important reaction in the formation of photochemical smog is the reaction bet
ID: 814191 • Letter: A
Question
An important reaction in the formation of photochemical smog is the reaction between ozone and NO:
NO(g)+O3(g)--> NO2(g)+O2(g)
The reaction is first order in NO and O3. The rate constant of the reaction is 80 (1/M*s) at 25 C and 3.000 x 10^3 (1/M*s) at 75 C.
(a) If this reaction were to occur in single step, would the rate law be consistent with the observed order of the reaction for NO and O3? yes/no
(b) What is the value of the activation energy of the reaction?
(c) What is the rate of the reaction at 25 X when [NO]= 2.63 x 10^-6 M and [O3]=5.96 x 10^-9 M?
(d) Predict the values of the rate constant at the following temperatures:
10 C and 35 C
Explanation / Answer
For the given reaction,
(a) The rate law will be consistent even when the reaction occurs in a single step for the given reaction. The order with respect to both the reactants NO and O3 would remain first-order in all the cases.
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(b) Energy of activation (Ea)
using arrhenius relation,
ln(k2/k1) = Ea/R[1/T1 - 1/T2]
with,
k1 = 80 (1/M.s) at T1 = 25 + 273 = 298 K
k2 = 3 x 10^3 (1/M.s) at T2 = 75 + 273 = 348 K
R = gas constant
feeding the values,
ln(3 x 10^3/80) = Ea/8.314[1/298 - 1/348]
Ea = 62498 J/mol
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(c) Rate of reaction,
Rate = k[NO][O3]
with,
[NO] = 2.63 x 10^-6 M
[O3] = 5.96 x 10^-9 M
k = 80 (1/M.s)
we get,
Rate at 25 oC = 80 (2.63 x 10^-6) (5.96 x 10^-9)
= 1.254 x 10^-12 M/s
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(d) rate constant at,
T1 = 10 oC + 273 = 283 K
using arrhenius equation,
ln(k2/k1) = Ea/R[1/T1 - 1/T2]
with,
k1 = ? at 10 oC
k2 = 80 (1/M.s) at T1 = 25 + 273 = 298 K
Ea = 62498 J/mol
R = gas constant feeding the values,
feeding the values,
ln(80/k1) = 62498/8.314[1/283 - 1/298]
rate constant (k1) at 10 oC = 21.01 (1/M.s)
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rate constant at,
T1 = 35 oC + 273 = 308 K
using arrhenius equation,
ln(k2/k1) = Ea/R[1/T1 - 1/T2]
with,
k1 = ? at 35 oC
k2 = 3 x 10^3 (1/M.s) at T2 = 75 + 273 = 348 K
Ea = 62498 J/mol
R = gas constant feeding the values,
feeding the values,
ln(3 x 10^3/k1) = 62498/8.314[1/308 - 1/348]
rate constant (k1) at 35 oC = 181.46 (1/M.s)
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