Decomposition of $X$ exhibits a rate constant for $0.05 \mu$g/year. How many years are required for the decomposition of $5 \mu$g of X into $2.5 \mu$g?

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Chemical Kinetics

Decomposition of

X

exhibits a rate constant for

0.05 μ

g/year. How many years are required for the decomposition of

5 μ

g of X into

2.5 μ

(A)50✓ Correct
(B)25
(C)20
(D)40

Answer: (A)

Solution

A rate constant quoted in

μ g/year

, a rate independent of concentration, is the signature of a zero-order decomposition. For zero order the amount falls linearly with time at the constant rate

k

, so the time to consume a given mass is simply that mass divided by

k

. Going from

5 μ g

2.5 μ g

removes

2.5 μ g

, which at

0.05 μ g/year

takes

\frac{2.5}{0.05} = 50

years.

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option

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