N 2 is obtained by the decomposition of benzene diazonium chloride at constant temperature. It is a first-order reaction the various volumes obtained at different time intervals are as Time ( min) 0 20 50 50 ∞ N2(mL) 0 10 25 32 162 The rate constant of the reaction is

Question

N 2 is obtained by the decomposition of benzene diazonium chloride at constant temperature. It is a first-order reaction the various volumes obtained at different time intervals are as Time ( min) 0 20 50 50 ∞ N2(mL) 0 10 25 32 162 The rate constant of the reaction is (A) 3.54 × 10-2 min -1 (B) 3.2 × 10-3 min -1 (C) 3.89 × 10-3 min -1 (D) 3.1 × 10-5 min -1

Tardigrade Admin · Accepted Answer

Decomposition of benzene diazonium chloride occur the following manner.

C_{6} H_{5} N = NCl ⟶ C_{6} H_{5} Cl + N_{2}

The volume of nitrogen obtained shows the extent of decomposition of benzene diazonium chloride so

a \propto V_{\infty} = 162 m L

(a - x) \propto (V_{\infty} - V_{t}) m L

For first order reaction,

k = \frac{2.303}{t} lo g_{10} \frac{V _{\infty} - V _{0}}{V _{\infty} - V _{t}}

or

k = \frac{2.303}{t} lo g_{10} \frac{V _{\infty}}{V _{\infty} - V _{t}}

(∵ V_{0} = 0)

At

20 min

k = \frac{2.303}{20} lo g_{10} \frac{162}{162 - 10}

= \frac{2.303}{20} lo g_{10} \frac{162}{152}

= 3.18 \times 1 0^{- 3} min^{- 1}

\approx 3.2 \times 1 0^{- 3} min^{- 1}

Time $(min)$	$0$	$20$	$50$	$50$	$\infty$
$N_{2} (m L)$	$0$	$10$	$25$	$32$	$162$

$3.54 \times 1 0^{- 2} min^{- 1}$

$3.2 \times 1 0^{- 3} min^{- 1}$

$3.89 \times 1 0^{- 3} min^{- 1}$

$3.1 \times 1 0^{- 5} min^{- 1}$

Q. N2​ is obtained by the decomposition of benzene diazonium chloride at constant temperature. It is a first-order reaction the various volumes obtained at different time intervals are as Time (min) 0 20 50 50 ∞ N2​(mL) 0 10 25 32 162 The rate constant of the reaction is

3.54×10−2min−1

3.2×10−3min−1

3.89×10−3min−1

3.1×10−5min−1

$3.54 \times 1 0^{- 2} min^{- 1}$

$3.2 \times 1 0^{- 3} min^{- 1}$

$3.89 \times 1 0^{- 3} min^{- 1}$

$3.1 \times 1 0^{- 5} min^{- 1}$