CBSE Class 12 · 2008 · Chemical KineticsLong Answer

a) Derive the general form of the expression for the half-life of a first order reaction.
b) The decomposition of NH

_{3}

on a platinum surface is a zero order reaction. What are the rates of production of N

_{2}

and H

_{2}

if k = 2.5 × 10

^{- 4}

mol L

^{- 1}

^{- 1}

Answer: (a) t₁/₂ = 0.693/k. (b) d[N₂]/dt = 2.5 × 10⁻⁴ M s⁻¹; d[H₂]/dt = 7.5 × 10⁻⁴ M s⁻¹.

Solution

(a) For first order,

k = \frac{2.303}{t} lo g \frac{[ R ] _{0}}{[ R ]}

.
At

t = t_{1/2}

[R] = [R]_{0} /2

k = \frac{2.303}{t _{1/2}} lo g 2 = \frac{2.303 \times 0.3010}{t _{1/2}}

t_{1/2} = \frac{0.693}{k}

— independent of the initial concentration.
(b)

2 N H_{3} \to N_{2} + 3 H_{2}

; for zero order the rate of reaction

= k

\frac{d [ N _{2} ]}{d t} = k = 2.5 \times 1 0^{- 4} M s^{- 1}

\frac{d [ H _{2} ]}{d t} = 3 k = 7.5 \times 1 0^{- 4} M s^{- 1}

CBSE Class 12 Board · 2008 · Subjective