In a study of the gas phase decomposition of nitrosyl chloride at 400 K NOCl(g-N

Question

In a study of the gas phase decomposition of nitrosyl chloride at 400 K NOCl(g-NO(g) + ½ Cl2(g) the following data were obtained: seconds 2.81-104 3.40-104 .96-10s Hint: It is not necessary to graph these data. The observed half life for this reaction when the starting concentration is 7.10x102 Mis The average (1 [NOCI]) / tfrom t-0sto t-2.81×104 s is s and when the starting concentration is 3.55x102Mis r1 The average (1 [NOCIDAt from t = 2.81-104 s to t = 8.40-104 s is Ms Based on these data, the rate constant for thisorder reaction is 1

Explanation / Answer

half life is the time required for the concentration to drop to 50% of the initial value.

hence when the initial concentration is 7.1*10-2M, the time required to drop to 7.1*10-2/2= 3.55*10-2 is as per the table given is 2.81*104 sec

2. when the initial concentration is 3.55*10-2M, the concentration at half life is 1.78*10-2M, the time required ( half life)= 8.4*104-(2.41*104)=5.99*104 seconds

3. The average of d[NOCl]/dt= (3.55-7.51)*10-2/ 2.81*104=-1.41*10-6 /M.sec

4. The average of d[NOCl]/dt= (1.78*10-2 - 3.55*10-2) /(8.4-2.81)*104 =-3.16*10-7/M.sec

5. for second order reaction 1/CA= 1/CAO+ Kt

for CA=0.5CO, 1/CAO= K*t1/2, t/2 is half life

for second order reaction, the product of CAO* t1/2 is constant which was the scenario in the present case. This is shown below.

K= 1/CAO*t1/2=1/(3.55*10-2* 2.81*104 ) =0.00100 /M.sec for the second change of d[NOCl]/dt = 1/(1.78*10-2* 5.99*104) =0.001 M/sec

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