# Problem: Consider the following reaction: 2O3(g) → 3O2(g). The rate law for this reaction is as follows: Rate = k[O3]2/[O2]Suppose that a 1.0-L reaction vessel initially contains 1.0 mol of O3 and 1.0 mol of O2. What fraction of the O3 will have reacted when the rate falls to one-half of its initial value?

###### FREE Expert Solution

We are asked to determine what fraction of the O3 will have reacted when the rate falls to one-half of its initial value.

Recall that the rate law only focuses on the reactant concentrations and has a general form of:

k = rate constant
A & B = reactants
x & y = reactant orders

Given:

$\overline{){\mathbf{Rate}}{\mathbf{=}}{\mathbf{k}}\frac{{\mathbf{\left[}{\mathbf{O}}_{\mathbf{3}}\mathbf{\right]}}^{{\mathbf{2}}}}{\mathbf{\left[}{\mathbf{O}}_{\mathbf{2}}\mathbf{\right]}}}$

[O3] = 1.0 mol

[O2] = 1.0 mol

Volume of Container = 1 L

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###### Problem Details
Consider the following reaction: 2O3(g) → 3O2(g). The rate law for this reaction is as follows: Rate = k[O3]2/[O2]

Suppose that a 1.0-L reaction vessel initially contains 1.0 mol of O3 and 1.0 mol of O2. What fraction of the O3 will have reacted when the rate falls to one-half of its initial value?