Eduprobe
Question:
For a first-order gas-phase reaction: A(g) → 2B(g) + C(g). P₀ be the initial pressure of A and Pt the total pressure at time 't'. Integrated rate equation is:
2.303tlog(P₀/(2P₀−Pt))
2.303tlog(P₀/(P₀−Pt))
2.303tlog(2P₀/(3P₀−Pt))
2.303tlog(2P₀/(2P₀−Pt))
Solution:
The given reaction is : A(g) → 2B(g) + C(g)
Initial A B C
Pressure P₀ 0 0
Final A B C
Pressure P₀−P 2P P
Total pressure at time(t) = P₀−P + 2P + P = Pt
→ Pt = P₀ + 2P
Pt − P₀ = 2P
→ P = (Pt − P₀)/2
k = (2.303/t)log[P₀/(P₀−P)] = (2.303/t)log[P₀/(P₀−(Pt−P₀)/2)]
= (2.303/t)log[P₀/(2P₀−Pt+P₀)/2]
= (2.303/t)log[2P₀/(3P₀−Pt)]
Hence, option C is correct.