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denis23 [38]
3 years ago
10

The thermal decomposition of N2O5 obeys first-order kinetics. At 45°C, a plot of ln[N2O5] versus t gives a slope of −6.40 × 10−4

min−1. What is the half-life of the reaction?
Chemistry
1 answer:
finlep [7]3 years ago
5 0

Answer:

  • <u>1,080 min</u>

<u></u>

Explanation:

A <em>first order reaction</em> follows the law:

     rate=k[A]  , where [A] is the concentraion of the reactant A.

Equivalently:

       \dfrac{d[A]}{dt}=-k[A]

Integrating:

    \dfrac{d[A]}{[A]}=-kdt

   \ln \dfrac{[A]}{[A_o]}=-kt

Half-life means [A]/[A₀] = 1/2, t = t½:

  •    t½ = ln (2) / k

That means that the half-life is constant.

The slope of the plot of ln [N₂O₅]  is -k. Then k is equal to 6.40 × 10⁻⁴ min⁻¹.

Thus, you can calculate t½:

   t½ = ln(2) / 6.40 × 10⁻⁴ min⁻¹

   t½ = 1,083 min.

Rounding to 3 significant figures, that is 1,080 min.

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