In which of the following cases, rate of disappearance of any reactant at a given instant equals to rate of appearance of any product.

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$H_{2} + \frac{1}{2} O_{2} \to H_{2} O$

${PCl}_{5} \to {PCl}_{3} + {Cl}_{2}$

$N_{2} + 3 H_{2} \to 2 {NH}_{3}$

$H_{2} + F_{2} \to 2 HF$

answer is C.

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Detailed Solution

For the reaction to have rate of disappearance of any reactant at a given instant equals to rate of appearance of any product, the number of moles of the reactant and the product must be the same.
From the options given in the question, the reaction given in (C) has equal number of moles for each compound in the reaction.

The reaction and its rate of the reaction are given below:

$PC l_{5} \to PC l_{3} + {Cl}_{2} - \frac{d}{dt} ({PCl}_{5}) = \frac{d}{dt} ({PCl}_{3}) = \frac{d}{dt} ({Cl}_{2})$