For the first order thermal decomposition reaction, the following data were obtained:
C2H5Cl(g) + hv → C2H4(g) + HCl(g)
Time (sec) Total pressure (atm)
0 0.30
300 0.50
Calculate the rate constant. (Given: log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)

C2H5Cl(g) + hν → C2H4(g) + HCl(g)
At t = 0, P₀ 0 0
At t = t, P₀ - p p p
After time t, total pressure, Pt = (P₀ - p) + p + p ⇒ Pt = (P₀ + p) ⇒ p = Pt - P₀
Therefore, P₀ - p = P₀ - Pt + P₀ = 2P₀ - Pt
For a first order reaction,
k = (2.303/t)log(P₀/(P₀ - p)) = (2.303/t)log(P₀/(2P₀ - Pt))
At t = 300, Pt = 0.5, P₀ = 0.3
So, k = (2.303/300)log(0.3/(2(0.3) - 0.5)) = (2.303/300)log(0.3/0.1) = (2.303/300)log(3) = (2.303/300)(0.4771) = 0.00366 s⁻¹ ≈ 3.66 x 10⁻³ s⁻¹