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A reaction $2 A P$ follows $- d [A] / d t = k [A]^{2}$ with $k = 0.040 L mo l^{- 1} s^{- 1}$ and $[A]_{0} = 0.50 mol L^{- 1}$ . Select the correct statement(s).

AThe half-life is $50 s$ .
BThe initial rate of disappearance of $A$ is $0.010 mol L^{- 1} s^{- 1}$ .
C $[A]$ at $t = 100 s$ is $0.25 mol L^{- 1}$ .
D $[A]$ falls to $0.10 mol L^{- 1}$ after $200 s$ .

Answer: A, B, D

Using

t_{1/2} = 1/ (k [A]_{0}) = 50 s

, initial rate

= k [A]_{0}^{2} = 0.010

, and

1/ [A] = 2 + 0.040 t

. At

t = 100

s this is 6.00, so

[A] = 0.167

M, not 0.25 M (0.25 M is the value at 50 s). For 0.10 M,

t = (10 - 2) /0.040 = 200 s

.

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