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JEE Main levelOne or more correct optionsDifficulty 2 of 3ck075

For the reaction $2 A P$ with $- d [A] / d t = k [A]^{2}$ , select the correct statement(s).

AThe half-life doubles when $[A]_{0}$ is doubled.
BA plot of $1/ [A]$ against time is a straight line of slope $k$ .
CThe time for 75% completion is three times the half-life.
DThe unit of $k$ is $s^{- 1}$ .

Answer: B, C

Integrated law:

1/ [A] = 1/ [A]_{0} + k t

, so the plot is linear with slope

k

. With

t_{1/2} = 1/ (k [A]_{0})

and

t_{75} = 3/ (k [A]_{0})

,

t_{75} = 3 t_{1/2}

. The half-life is inversely (not directly) proportional to

[A]_{0}

, and

k

has units

L mo l^{- 1} s^{- 1}

.

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