2 NO2(g) <-> N2O4(g) (dark brown to colorless) The dimerization of NO2(g), an exothermic process, is — Equilibrium Chemistry Question

STEPS:

1. Analyze the chemical equation and physical properties of the species:
The dimerization reaction of nitrogen dioxide is represented as $2\ \text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g)$. Crucially, the reactant $\text{NO}_2(g)$ is a dark brown gas, whereas the product $\text{N}_2\text{O}_4(g)$ is a colorless gas.
2. Relate physical properties to light absorption:
Because $\text{NO}_2(g)$ is a colored substance and $\text{N}_2\text{O}_4(g)$ is colorless, only the $\text{NO}_2(g)$ reactant molecules will absorb visible electromagnetic radiation.
3. Understand the concept of spectrophotometry:
Spectrophotometry is an analytical technique where the light absorbance of a chemical species in a sample is measured. According to the Beer^-Lambert Law, absorbance ($A$) is directly proportional to concentration ($c$) via the relationship:
$$A = abc$$
where $a$ is the molar absorptivity coefficient of the species and $b$ is the path length of the sample cell.
4. Determine concentration at equilibrium:
By measuring the absorbance of the dynamic equilibrium mixture in a closed optical cell, a student can determine the exact concentration of the colored gas, $\text{NO}_2(g)$, at equilibrium. Because spectrophotometry is a non-destructive method that does not physically or chemically alter the molecules, the system remains completely undisturbed at dynamic equilibrium during measurement. This identifies Option D as the correct choice.

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WHY_OTHERS_WRONG:

• Option A is incorrect: Paper chromatography is a physical separation method used to separate the components of liquid mixtures based on their differing polarities and differential affinities for a stationary phase (paper) and a mobile phase (solvent). It cannot be used to measure gas-phase concentrations or study gas-phase dynamic equilibria.
• Option B is incorrect: Gravimetric analysis involves determining concentration by measuring the mass of a solid precipitate (such as filtering, drying, and weighing an insoluble salt like copper phosphate). Because both $\text{NO}_2$ and $\text{N}_2\text{O}_4$ are gases in a closed reaction vessel, gravimetric analysis is not a viable technique here.
• Option C is incorrect: Titration is a volumetric technique where a sample is chemically reacted with a standard solution (such as titrating an acid with a base to an endpoint). Titrating this mixture would chemically consume and remove the reactant or product molecules, driving the dynamic equilibrium to shift (according to Le Chatelier's principle) to replace them, thereby disrupting the system and preventing an accurate measurement of the original equilibrium concentrations.