Which of the following is an example of first order reaction?

Reaction order is an experimentally determined quantity describing how rate depends on reactant concentrations. A first-order reaction exhibits a rate linearly dependent on a single reactant concentration, or one where the sum of concentration exponents in the rate law equals one.

Considering each option:

A) $\mathrm{CH}_3\mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$: Acetaldehyde decomposition may follow first-order kinetics at high temperatures but exhibits complex behavior and is not universally first-order.

B) $2\mathrm{NO}_{2(\mathrm{~g})}+\mathrm{F}_{2(\mathrm{~g})} \rightarrow 2\mathrm{NO}_2\mathrm{~F}_{(\mathrm{g})}$: The rate law is Rate $= k[\mathrm{NO}_2][\mathrm{F}_2]$, with exponent sum $1+1=2$, indicating second-order kinetics.

C) $2\mathrm{NO}_{(\mathrm{g})}+2\mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{N}_{2(\mathrm{~g})}+2\mathrm{H}_2\mathrm{O}_{(\mathrm{g})}$: The rate law is Rate $= k[\mathrm{NO}]^2[\mathrm{H}_2]$, with exponent sum $2+1=3$, making it third-order.

D) $2\mathrm{H}_2\mathrm{O}_{2(\ell)} \rightarrow 2\mathrm{H}_2\mathrm{O}_{(\ell)}+\mathrm{O}_{2(\mathrm{~g})}$: Hydrogen peroxide decomposition has the rate law Rate $= k[\mathrm{H}_2\mathrm{O}_2]$, with exponent 1, confirming it as a first-order reaction.

Option D is the unambiguous example of first-order kinetics.