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For first order parallel reactions k(1) ...

For first order parallel reactions `k_(1)` and `k_(2)` are 4 and 2 `min^(- 1)` respectively at 300 K.. If the activation energies for the formation of B and C are respectively 30,000 and 38,314 joule/mol respectively. The temperature at which B and C will be obtained in equimolar ratio is:

A

757.48 K

B

378.74 K

C

600 K

D

450 K

Text Solution

Verified by Experts

`ln""(k._(1))/(k_(1)) = (E_(1))/(R)[(1)/(T_(1)) - (1)/(T_(2))]` ……(i) `ln""(k._(2))/(k_(2)) = (E_(2))/(R)[(1)/(T_(1)) - (1)/(T_(2))]` ………(ii)
Solving we get (ii) - (i), `ln""(k._(2))/(k_(2)) - ln""(k._(1))/(k_(1)) = ((E_(2) - E_(1))/(R)) ((1)/(T_(1) - T_(2)))`
(for equimolar formation of B and C, `k._(2) = k._(1)`)
`ln((k_(1))/(k_(2))) = ((8314)/(8.314))((T_(2) - 300))/(300 xx T_(2)), ln 2 = (1000)((T_(2) - 300)/(300 xx T_(2))), T_(2) = 378.74 K`
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