⇒Chemical Kinetics

Correct Option is (A)

$\begin{array}{rl}2\mathrm{A}+\mathrm{B}& \to 3\mathrm{C}\\ \text{ Rate }& =-\frac{1}{2}\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}=\frac{1}{3}\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}\\ \therefore \frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}& =\frac{1}{3}\times 1.3\times {10}^{-4}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\\ & =4.33\times {10}^{-5}\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}\end{array}$

Correct Option is (C)

$3x\to 2y+z$

Rate of formation $=-\frac{1}{3}\frac{\mathrm{d}[\mathrm{x}]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}[\mathrm{y}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{z}]}{\mathrm{dt}}$

$\frac{\mathrm{d}[\mathrm{z}]}{\mathrm{dt}}=\frac{1}{3}(0.072)=0.024\mathrm{mol}{\mathrm{s}}^{-1}$

Correct Option is (B)

$\begin{array}{rl}2\mathrm{NO}+{\mathrm{Cl}}_2\to & 2\mathrm{NOCl}\\ \text{ Rate of reaction }=& -\frac{1}{2}\frac{\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[{\mathrm{Cl}}_2\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}[\mathrm{NOCl}]}{\mathrm{dt}}\\ & \therefore \frac{\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{NOCl}]}{\mathrm{dt}}\end{array}$

Correct Option is (C)

$\begin{array}{rl}& 3{\mathrm{I}}_{(\mathrm{aq})}^{-}+{\mathrm{S}}_2{\mathrm{O}}_{8(\mathrm{aq})}^{2-}⟶{\mathrm{I}}_{3(\mathrm{aq})}^{-}+2{\mathrm{SO}}_{4(\mathrm{aq})}^{2-}\\ & \therefore \frac{\mathrm{d}\left[{\mathrm{I}}_3^{-}\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{SO}}_4^{2-}\right]}{\mathrm{dt}}=\frac{1}{2}\times 0.022=0.011\mathrm{mol}{\mathrm{dm}}^{-3}{\sec }^{-1}\\ & \end{array}$

Correct Option is (B)

Given the relationships :

$-\frac{1}{2}\frac{d[x]}{dt}=-\frac{d[y]}{dt}=\frac{1}{2}\frac{d[z]}{dt}$

This expression can be understood as follows :

1. The rate of disappearance of x is half that of y.


2. The rate of appearance of z is half the rate of disappearance of y.

To translate this into stoichiometric coefficients of a balanced chemical equation, let's analyze each component individually :

For compound x :

The negative sign indicates the disappearance (or consumption) of x. Given its relationship to y, we can infer that for every 2 moles of x that react, 1 mole of y will react.

$2x\to$ (the stoichiometric coefficient of x is 2)

For compound y :

The negative sign indicates the disappearance (or consumption) of y. Given its relationship to x and z, 1 mole of y is reacting for every 2 moles of x consumed and 2 moles of z produced.

$\to y\to$ (the stoichiometric coefficient of y is 1)

For compound z :

The positive sign indicates the production or appearance of z. Since the rate of appearance of z is half the rate of disappearance of y, 2 moles of z are produced for every mole of y that reacts.

$\to 2z$ (the stoichiometric coefficient of z is 2)

Combining all the components together, the balanced chemical equation is :

$2x+y\to 2z$

This represents a reaction where for every 2 moles of x and 1 mole of y that react, 2 moles of z are produced.

Therefore, Option B : $2x+y\to 2z$ is indeed the correct choice based on the given rate relationships.