AT 373 K, a gaseous reaction A `rarr` 2B + C is found to be of first order. Starting with pure A, the total pressure at the end of 10 min. was 176 mm and after a long time when A was completely dissociated, it was 270 mm. The pressure of A at the end of 10 minutes was :

Explanation

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).`