Question

The rate constant for the first-order decomposition at 45 °C of dinitrogen pentoxide, N₂O₅, dissolved in chloroform, \({\bf{CHC}}{{\bf{l}}_3}\), is 6.2 × 10⁻⁴ min⁻¹.

\({\bf{2}}{{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{5}}} \to {\bf{4N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\)

What is the rate of the reaction when \({{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{5}}}{\bf{\; = 0}}{\bf{.40 M}}\)

Short answer

The value of rate of reactionis\({\bf{2}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}{\bf{mol}}{{\bf{L}}^{{\bf{ - 1}}}}{\bf{mi}}{{\bf{n}}^{{\bf{ - 1}}}}\)

Step-by-step solution

Definitions

The order of reaction refers to the power dependence of the rate on the concentration of each reactant.

The rate constant is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and concentration of reacting substances.

First order of reaction in \({\bf{N}}{}_{\bf{2}}{\bf{O}}{}_{\bf{5}}\)

A chemical reaction in which the rate of reaction is directly proportional to the concentration of reacting substance is called first order reaction

Rate of reaction\({\bf{ = K}}\left( {{\bf{N}}{}_{\bf{2}}{\bf{O}}{}_{\bf{5}}} \right)\)

Where k is the rate constant. Given value of k for the reaction is

Rate constant =\({\bf{6}}{\bf{.2 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}{\bf{mi}}{{\bf{n}}^{{\bf{ - 1}}}}\)

Rate of reaction

The rate law for a chemical reaction is an expression that provides a relationship between the rate of the reaction and the concentration of the reactants participating in it.

Rate of reaction can be calculated as

\(\begin{align}Rate &= 6.2 \times {10^{ - 4}}{\min ^{ - 1}}(0.40)\\ &= 2.5 \times {10^{ - 4}}mol{L^{ - 1}}{\min ^{ - 1}}\end{align}\)