b
Rate of disappearance of reactant \(=\) rate of appearance of product

\(=-\frac{1}{\text { stoichiometric coefficient of reactant }} \frac{\text {d[reactant]}}{\mathrm{d} t}\)

\(=+\frac{1}{\text { stoichiometric coefficient of product }} \frac{\text {d[product]}}{\mathrm{dt}}\)

For the reaction

\(\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})\)

\(-\frac{\mathrm{d}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]}{\mathrm{dt}}=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{dt}}\)

\(=+\frac{2 \mathrm{d}\left[O_{2}\right]}{\mathrm{dt}}\)

therefore, \(\frac{\mathrm{d}\left[ \mathrm{NO}_{2}\right]}{\mathrm{dt}}=-2 \frac{\mathrm{d}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]}{\mathrm{dt}}\)

\(=2 \times 6.25 \times 10^{-3}\, \mathrm{mol} \,L^{-1}\, \mathrm{s}^{-1}\)

\(=12.5 \times 10^{-3} \,\mathrm{mol} \,\mathrm{L}^{-1}\, \mathrm{s}^{-1}\)

\(=1.25 \times 10^{-2}\, \mathrm{mol} \,\mathrm{L}^{-1}\, \mathrm{s}^{-1}\)

\(\frac{\mathrm{d}\left[O_{2}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]}{\mathrm{d} t} \times \frac{1}{2}\)

\(\frac{6.25 \times 10^{-3} \,\mathrm{mol} \,\mathrm{L}^{-1} \,\mathrm{s}^{-1}}{2}\)

\(=3.125 \times 10^{-3} \,\mathrm{mol}\, \mathrm{L}^{-1}\, \mathrm{s}^{-1}\)