In a study of die decomposition of ammonia on a platinum surface at 856 degree C

Question

In a study of die decomposition of ammonia on a platinum surface at 856 degree C NH_3 rightarrow 1/2 N_2 + 3/2 H_2 the following data were obtained The observed half life for this reaction when the starting concentration is 8.52 times 10^-3 M is and when the starting concentration is 4.26 times 10^-3 M is The average rate of disappearance of NH_3 from t = 0 s to t = 1000 s is M s^-1. The average rate of disappearance of NH_3 from t = 1000 s to t = 1.50 times 10^3 s is M s^-1 Based on these data, the rate constant for tins order reaction is M s^-1.

Explanation / Answer

for   a zero order reaction, -dCA/dt= K, K is rate constant

or -dCA= Kdt

CA =CAO- Kt, CAO= initial concentration of A, CA= concentration of A at any time.

So a plot of CA vs t if gives straight line, the zero order equation is satisfied.

The plotted data is in accordance with zero order and is shown below

So the reaction order iz zero with a slope of 4*10-6 M/sec

For CA= CAO- Kt

half life(t1/2) is achieved for CA= CAO/2

CAO/2= CAO- Kt1/2

ot Kt1/2= CAO/2

t1/2 = 8.52*10-3/ 4*10-6 =2130 seconds

for CAO= 4.26*10-3

t1/2= 4.26*10-3/(4*10-6)= 1062.5 seconds

for zero order reaction , the average rate between 0 and 1000 sec is = (8.52-4.26)*10-3/1000 =4.26*10-6 M/sec ( actually the rate is independent of concentration)

between 1000 to 1500 sec, the rate = (4.26-2.13)*10-3/(1500-1000) = 4.26*10-6 M/sec

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