At 373 K, a gaseous reaction Ato2B+C is observed to be of first order. On starting with pure A, it was found that at the end of 10 minutes, the total pressure of the system was 176 mm of mercury and after a long time, when dissociation of A was complete, it was 270 mm. From these data, calculate (i) the initial pressure of A (ii) the pressure of A at the end of 10 minutes. (iii) the rate constant.

At 373 K, a gaseous reaction Ato2B+C is observed to be of first order.

1.	At 373 K, a gaseous reaction Ato2B+C is observed to be of first order. On starting with pure A, it was found that at the end of 10 minutes, the total pressure of the system was 176 mm of mercury and after a long time, when dissociation of A was complete, it was 270 mm. From these data, calculate (i) the initial pressure of A (ii) the pressure of A at the end of 10 minutes. (iii) the rate constant.
Answer» <P> Solution :Suppose initial of A = P mm. Decrease in the pressure of A after time t = p mm. `{:(,,,A,,to,,2B,,+,,C,,,"TOTAL pressure"),("Initial pressure",,,P,,,,0,,,,0,,,P),("Pressures after time t",,,P-p,,,,2p,,,,p,,,P+2p),("Final pressures",,,0,,,,2P,,,,P,,,3P):}` (i) Final pressure = 270 mm (Given)` :.3P=270" or "P=90" mm"` (ii) Pressure after 10 minutes = 176 mm (Given) `:.P+2p=176" or "90+2p=176" or "p=43" mm"` `:." Pressure of A after 10 MIN"=P-p=90-43=47" mm"` `:.K=(2.303)/(t)log""(a)/(a-x)=(2.303)/(t)log""(P)/(P-p)` or `k=(2.303)/(10" min")log""(90)/(90-43)=(2.303)/(10" min")log""(90)/(47)=6.496xx10^(-2)" min"^(-1).`