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A first order reaction has the rate constant, $K = 4.6 \times 10^{- 3} s^{- 1} .$ The number of correct statements from the following $(\log 3 = 0.48)$
(A) Reaction complete is 1000 s
(B) The reaction has half-life of 500 s
(C) The time required for 10% completion is 25 times the time required for 90% completion.
(D) The degree of dissociation is equal to $(1 - e^{- K t})$
(E) The rate and the rate constant have the same unit.

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answer is 2.

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Detailed Solution

$t_{10 %} = \frac{1}{k} l n (\frac{a}{a - n}) t_{10 %} = \frac{1}{k} l n (\frac{100}{90}) t_{10 %} = \frac{2.303}{k} (\log 10 - \log 9) t_{10 %} = \frac{2.303}{k} (0.04)$

$s i m i l a r l y$

$t_{90 %} = \frac{1}{k} l n (\frac{100}{10})$

$t_{90 %} = \frac{2.303}{k}$

$\frac{t_{90 %}}{t_{10 %}} = \frac{1}{0.04} = 25$

$e^{k t} = \frac{a}{a - x} \frac{a - x}{a} = e^{- k t}$

$1 - \frac{x}{a} = e^{- k t}$

$x = a (1 - e^{- k t})$

$α = \frac{x}{a} = (1 - e^{- k t})$

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