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Question:

The reaction 2X → B is a zeroth-order reaction. If the initial concentration of X is 0.2M, the half-life is 6h. When the initial concentration of X is 0.5M, the time required to reach its final concentration of 0.2M will be:

7.2

12.0h

18.0h

9.0h

Solution:

For zero-order reaction,
[A₀] − [Aₜ] = kt
For half-life, [A₀] = 0.2 M, [Aₜ] = 0.1 M, t = 6 h
0.2 M − 0.1 M = k × 6 h
k = 0.1 M / 6 h = 1/60 M/h
When [A₀] = 0.5 M and [Aₜ] = 0.2 M
0.5 M − 0.2 M = (1/60 M/h) × t
0.3 M = (1/60 M/h) × t
t = 0.3 M × 60 h/M = 18 h