⇒Chemical Kinetics

Correct Option is (A)

In the rate expression, always make sure to express the rates with the correct sign: Negative for the reactants and positive for the products.

Correct Option is (D)

$\begin{array}{rl}\text{ Rate of reaction }& =-\frac{1}{2}\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}=\frac{1}{3}\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}\\ \text{ Rate of reaction }& =\frac{1}{3}\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}\\ & =\frac{1}{3}\times 1.3\times {10}^{-4}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\\ & =0.433\times {10}^{-4}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\end{array}$

$\therefore$ Rate of disappearance of $\mathrm{A}$

$\begin{array}{rl}& =2\times 0.433\times {10}^{-4}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\\ & =0.866\times {10}^{-4}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\\ & =8.66\times {10}^{-5}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\end{array}$

Correct Option is (C)

$\begin{array}{rl}& \frac{-\mathrm{\Delta }\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{\Delta }\mathrm{t}}=x\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}\\ & 2{\mathrm{N}}_2{\mathrm{O}}_{5(\mathrm{g})}\to 4{\mathrm{NO}}_{2(\mathrm{g})}+{\mathrm{O}}_{2(\mathrm{g})}\end{array}$

Average rate of reaction

$\begin{array}{rl}& =-\frac{1}{2}\frac{\mathrm{\Delta }\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{\Delta }\mathrm{t}}=\frac{1}{4}\frac{\mathrm{\Delta }\left[{\mathrm{NO}}_2\right]}{\mathrm{\Delta }\mathrm{t}}=\frac{\mathrm{\Delta }\left[{\mathrm{O}}_2\right]}{\mathrm{\Delta }\mathrm{t}}\\ \therefore & \frac{\mathrm{\Delta }\left[{\mathrm{NO}}_2\right]}{\mathrm{\Delta }\mathrm{t}}=-\frac{4}{2}\frac{\mathrm{\Delta }\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{\Delta }\mathrm{t}}=\frac{4}{2}\times x\\ & =2x\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}\end{array}$

$\therefore$ Average rate of formation of ${\mathrm{NO}}_{2(\mathrm{g})}=2x\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}$

[Note: In the question, $\frac{\mathrm{\Delta }\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{\Delta }\mathrm{t}}$ is changed to $\frac{-\mathrm{\Delta }\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{\Delta }\mathrm{t}}$ to apply appropriate textual concepts.]

Correct Option is (B)

$\begin{array}{rl}& 3\mathrm{\Gamma }+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}\to {\mathrm{I}}_3^{-}+2{\mathrm{SO}}_4^{2-}\\ & \text{ Rate of reaction }=-\frac{1}{3}\frac{\mathrm{d}\left[{\mathrm{I}}^{-}\right]}{\mathrm{dt}}=+\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{SO}}_4^{2-}\right]}{\mathrm{dt}}\\ & \begin{array}{rl}-\frac{\mathrm{d}\left[{\mathrm{I}}^{-}\right]}{\mathrm{dt}}& =\frac{3\mathrm{d}\left[{\mathrm{SO}}_4^{2-}\right]}{2}=\frac{3}{2}\times 2.2\times {10}^{-2}\\ & =3.3\times {10}^{-2}\mathrm{mol}\mathrm{dm}{\mathrm{s}}^{-3}\end{array}\end{array}$

[Note: In the question, $\frac{\mathrm{d}[{\mathrm{I}}^{-}]}{\mathrm{dt}}$ is changed to $-\frac{d\left[{\mathrm{I}}^{-}\right]}{\mathrm{dt}}$ to apply appropriate textual concepts.]

Correct Option is (A)

Average rate of reaction

$=-\frac{1}{2}\frac{\mathrm{\Delta }\left[{\mathrm{NO}}_2\right]}{\mathrm{\Delta }t}=\frac{1}{2}\frac{\mathrm{\Delta }\left[{\mathrm{NO}}_2\right]}{\mathrm{\Delta }t}=\frac{\mathrm{\Delta }\left[{\mathrm{O}}_2\right]}{\mathrm{\Delta }t}$

Rate of formation of ${\mathrm{O}}_2=\frac{\mathrm{\Delta }\left[{\mathrm{O}}_2\right]}{\mathrm{\Delta }\mathrm{t}}$

$\begin{array}{rl}& =\frac{1}{2}\frac{-\mathrm{\Delta }\left[{\mathrm{NO}}_2\right]}{\mathrm{\Delta }t}\\ & =\frac{1}{2}\times x=\frac{x}{2}\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}\end{array}$