Question

For the reaction $2\text{NO} + \text{Cl}_2 \rightarrow 2\text{NOCl}$, what is the relation between $\frac{d[\text{NO}]}{dt}$ and $\frac{d[\text{NOCl}]}{dt}$?

• A. $\frac{d[\text{NO}]}{dt} = 2\frac{d[\text{NOCl}]}{dt}$
• B. $\frac{d[\text{NO}]}{dt} = \frac{d[\text{NOCl}]}{dt}$
• C. $\frac{1}{4}\frac{d[\text{NO}]}{dt} = \frac{d[\text{NOCl}]}{dt}$
• D. $4\frac{d[\text{NO}]}{dt} = \frac{d[\text{NOCl}]}{dt}$

Hint:

If the stoichiometric coefficients of two species in a balanced chemical equation are identical (here, both NO and NOCl have a coefficient of 2), their respective rates of change of concentration will always be equal in magnitude.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the mathematical relationship linking the rate of consumption of a reactant (NO) to the rate of formation of a product (NOCl) based on the stoichiometry of the chemical reaction.

Step 2: Key Formula or Approach:
For any generalized chemical reaction:
$$ a\text{A} + b\text{B} \rightarrow c\text{C} + d\text{D} $$ The unified rate of reaction is expressed by dividing the individual rates of concentration change by their respective stoichiometric coefficients:
$$ \text{Rate} = -\frac{1}{a}\frac{d[\text{A}]}{dt} = -\frac{1}{b}\frac{d[\text{B}]}{dt} = +\frac{1}{c}\frac{d[\text{C}]}{dt} = +\frac{1}{d}\frac{d[\text{D}]}{dt} $$

Step 3: Detailed Explanation: Given the chemical equation:
$$ 2\text{NO} + \text{Cl}_2 \rightarrow 2\text{NOCl} $$ Applying the rate expression rules to the reactant NO and the product NOCl:
$$ \text{Rate} = -\frac{1}{2}\frac{d[\text{NO}]}{dt} = +\frac{1}{2}\frac{d[\text{NOCl}]}{dt} $$ By equating the individual terms and focusing purely on the absolute magnitudes of their operational rates:
$$ \frac{1}{2}\frac{d[\text{NO}]}{dt} = \frac{1}{2}\frac{d[\text{NOCl}]}{dt} $$ Multiplying both sides of the equation by 2 gives a direct relation:
$$ \frac{d[\text{NO}]}{dt} = \frac{d[\text{NOCl}]}{dt} $$

Step 4: Final Answer: The operational rate magnitudes are completely equal, which corresponds to option (B).