Problem: The following data were obtained for the gas‑phase decomposition of dinitrogen pentoxide,2 N2O5 (g) → 4 NO2 (g) + O2 (g)Defining the rate as -Δ[N2O5] / Δt, write the rate law and calculate the value of the rate constant.

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FREE Expert Solution

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

Step 1. Calculate the order of the reaction with respect to N2O5.

Use experimental data 1 and 2 (you can use any):

x = order

(Larger concentration should be on the numerator)

Solve for x:

$\frac{\mathbf{2}\mathbf{.}\mathbf{26}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}}{\mathbf{8}\mathbf{.}\mathbf{90}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{4}}}\mathbf{=}\frac{{\left[\mathbf{0}\mathbf{.}\mathbf{190}\right]}^{\mathbf{x}}}{{\left[\mathbf{0}\mathbf{.}\mathbf{0750}\right]}^{\mathbf{x}}}$

since the numerator and the denominator are raised to the same power, you can simplify the equation to:

$\frac{\mathbf{2}\mathbf{.}\mathbf{26}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}}{\mathbf{8}\mathbf{.}\mathbf{90}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{4}}}\mathbf{=}{\left[\frac{\mathbf{0}\mathbf{.}\mathbf{190}}{\mathbf{0}\mathbf{.}\mathbf{0750}}\right]}^{\mathbf{x}}\phantom{\rule{0ex}{0ex}}\mathbf{2}\mathbf{.}\mathbf{53}\mathbf{=}{\left[\mathbf{2}\mathbf{.}\mathbf{53}\right]}^{\mathbf{x}}$

2.53 raised to the power of 1 = 2.53

x = 1 → 1st order with respect to N2O5

Step 2. Determine the rate law of the reaction

Substitute N2O5 and O2 and their orders:

rate law = k[N2O5]1

or simply

rate = k[N2O5]

Step 3. Calculate the value of the rate constant

Problem Details

The following data were obtained for the gas‑phase decomposition of dinitrogen pentoxide,

2 N2O(g) → 4 NO2 (g) + O(g)

Defining the rate as -Δ[N2O5] / Δt, write the rate law and calculate the value of the rate constant.