Question

A definite volume of H₂O₂ undergoing spontaneous decomposition required 22.8 c.c. of standard permanganate solution for titration. After 10 and 20 minutes respectively the volumes of permanganate required were 13.8 and 8.25 c.c. The time required for the decomposition to be half completed is ______ min.

Options

• 11.24

• 13.71

• 15.62

• 18.75

Answer 1

A definite volume of H₂O₂ undergoing spontaneous decomposition required 22.8 c.c. of standard permanganate solution for titration. After 10 and 20 minutes respectively the volumes of permanganate required were 13.8 and 8.25 c.c. The time required for the decomposition to be half completed is 13.71 min.

Explanation:

(A) Given V₀ = 22.8 c.c.

t (min.)	Vt (c.c.)	k = `2.303/"t" log  "V"_0/"V"_"t"`
10	13.8	k1 = `2.303/"t" log  22.8/13.8`
		= `2.303/10 log 1.652`
		= 0.2303 × 0.2180
		= 0.0502054
20	8.25	k2 = `2.303/10 log  22.8/8.25`
		= 0.0508387

∵ k₁ = k₂

∴ Reaction is of the first order.

(B) t_1/2 = `0.693/"k"`

= `0.693/0.0505221`

= 13.71 min.