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For a given reaction A→ B, the rate constant is 1.2 × 10$^{–2}$ M s$^{–1}$. What is the concentration of B after 20 min., if we start with 10 M of A. It is zero order kinetics.

When I try to solve the question, the equation would be

$$x_i - x_f = kt$$ $$10 M - x_f = kt = (1.2×10^{–2}M s^{–1})(20 min)(60 s/min)$$

So, $$x_f=10M - 14.4 M$$ I do not understand how it can be negative.

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    $\begingroup$ Why am I getting negative votes ? $\endgroup$ Jan 5, 2017 at 15:05
  • $\begingroup$ How did you get 14.4 ? $\endgroup$
    – Shailesh
    Jan 5, 2017 at 16:11
  • $\begingroup$ @Shailesh I get it from kt = 1.2x10$^{-2}$ (20x60) $\endgroup$ Jan 5, 2017 at 16:59
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    $\begingroup$ Your math checks out. B cannot be negative, and indeed since the reaction forms B, it has to be zero. What's the highest it could go? Hint: first solve an alternate problem where you want to calculate the time $t$ it takes for A to be completely depleted. What is the concentration of B at that time, and at all times thereafter? $\endgroup$
    – Curt F.
    Jan 5, 2017 at 17:11

1 Answer 1

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It is negative because your reactant would be depleted before 20min. When the reaction is reaching the end, the mechanism is no longer 0th order.

Imagine a catalytic reaction mechanism where the rate is limited by the concentration of catalyst. You'd get a rate that is independent from the reactant concentration because the reaction rate is limited by the disassociation process of reactant-catalyst complex whose concentration is the same as the initial concentration of the catalyst.

However, when the reaction is ending, it would be limited by the interaction between the reactant and the catalyst instead, where the reactant would probably take a pseudo-first order mechanism.

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