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Q.

For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are P0 and Pt, respectively. Initially, only A is present with concentration [A]0, and t1/3 is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) :-(Assume that all these gases behave as ideal gases)

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a

b

c

d

answer is A.

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Detailed Solution

A→2B+Ct=0P0 − −t=t P0−P2PPP0+2P=Pt K=1tln⁡P0P0−P=1tln⁡P0P0−Pt−P02K=1tln⁡2P03P0−Pt⇒−Kt+ln⁡2P0=ln⁡3P0−Pt and t13=1Kln⁡P0P0/3=1Kln⁡3=con⁡stan⁡tRate constant does not depends on concentration. As rate constant is a constant quantity and independent of initial concentration. So Graph (D) is correct.
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