JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Chemical Kinetics

For the first order reaction

2 N_{2} O_{5} (g) \to 4 NO_{2} (g) + O_{2} (g)

(A) the concentration of the reactant decreases exponentially with time.
(B) the half-life of the reaction decreases with increasing temperature.
(C) the half-life of the reaction depends on the initial concentration of the reactant.
(D) the reaction proceeds to 99.6% completion in eight half-life duration.

(A)A✓ Correct
(B)B✓ Correct
(C)C
(D)D✓ Correct

Answer: (A), (B), (D)

Solution

For a first-order reaction:

(A) The integrated rate law is

[A] = [A]_{0} e^{- k t}

, showing exponential decrease. TRUE

(B) Half-life

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

. Since rate constant

k

increases with temperature (Arrhenius equation),

t_{1/2}

decreases with increasing temperature. TRUE

(C) For first-order reactions,

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

is independent of initial concentration. FALSE

(D) After

n

half-lives, fraction remaining =

(1/2)^{n}

. After 8 half-lives:

(1/2)^{8} = 1/256 \approx 0.004

or 0.4% remaining, meaning 99.6% completion. TRUE

Therefore, options (A), (B), and (D) are correct.

JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · One or more correct options

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JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Chemical Kinetics

Solution

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