An important reaction in the formation of photochemical smog is the reaction bet

Question

An important reaction in the formation of photochemical smog is the reaction between ozone and NO The reaction is first order in NO and 03-The rate constant of the reaction is 80.0 M-1s-1 at 25°C and 3.000 x 103 M-1s-1 at 75 1st attempt Part1 (1 point) d See Periodic Table f this reaction were to occur in a single step, would the rate law be consistent with the observed order of the reaction for NO and O3? Choose one: A. yes B. no Part2 (1point) What is the value of the activation energy of the reaction? J/mol Part 3 (1 point)

Explanation / Answer

NO(g)+ O3(g) ------->NO2(g)+ O2(g)

the rate of this elementary reaction is -dNO/dt= -dO3/dt= K[NO]m[O3]n, where the powers m and n indicate the order of reaction with respect to NO and O3 respectively. Hence the overall order is sum of the orders of individual reaction is m+n. Since the m=1 and n=1, the rate is -dO3/dt= K[NO][O3] which is also true as per the stoichiometry of the reaction. Hence the above reaction can be considered as elementary reaction.

2. Arhenius equation will be used to determine the activation energy of this reaction. The equation is

K= Ko*e(-E/RT), taking ln, the equation becomes lnK= lnK0-Ea/RT (1)

where Ko is frequency factor, T is temperature in K, Ea= activation energy and R= gas constant= 8.314 J/mole.K

at T= 25 deg,, T= 25+273=298K, K= 80/M.sec

with these values equation -1becomes ln(80)= lnK0-Ea/R*298 (2)

T=75 deg.c= 75+273=348K, K=3*1000, ln(3000)= lnKo- Ea/R*348 (3)

Eq.3-Eq.2 gives ln (3000/80)= (Ea/R)*(1/298-1/348)

Ea= activation energy = 62498 J/mole

2. The rate of reaction is -r = K[ NO][O3]=80*4*10-6*5.4*10-9=1.728*10-12M/sec

at two different temperatures T1 and T2 ( T2= 25 deg.c= 298K), The Arhenius equation becomes

ln(K2/K1)= (Ea/R)*(1/T1-1/T2)

K2= rate constant at 25 deg.c =80 /M.sec , K1 is rate constant at T1= 10 deg.c= 10+273=283K

ln(80/K1)=(62498/8.314)*(1/283-1/298)

K1= 21/M.sec

at T1= 35 deg.c= 35+273= 308K,

ln(80/K1)= (62498/8.314)*(1/308-1/298)

K1= 181.5/M.sec

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