Question

Which from following is a correct representation of reaction rate for reaction stated below?
\( \text{N}_{2(\text{g}) + 3\text{H}_{2(\text{g})} \rightleftharpoons 2\text{NH}_{3(\text{g})} \)}

• A. \( \frac{\text{d}[\text{N}_2]}{\text{dt}} = -3\frac{\text{d}[\text{H}_2]}{\text{dt}} = 2\frac{\text{d}[\text{NH}_3]}{\text{dt}} \)
• B. \( \frac{\text{d}[\text{N}_2]}{\text{dt}} = -\frac{1}{3}\frac{\text{d}[\text{H}_2]}{\text{dt}} = \frac{1}{2}\frac{\text{d}[\text{NH}_3]}{\text{dt}} \)
• C. \( -\frac{\text{d}[\text{N}_2]}{\text{dt}} = -\frac{1}{3}\frac{\text{d}[\text{H}_2]}{\text{dt}} = \frac{1}{2}\frac{\text{d}[\text{NH}_3]}{\text{dt}} \)
• D. \( \frac{\text{d}[\text{N}_2]}{\text{dt}} = \frac{1}{3}\frac{\text{d}[\text{H}_2]}{\text{dt}} = -\frac{1}{2}\frac{\text{d}[\text{NH}_3]}{\text{dt}} \)

Hint:

Rate = $\frac{1}{coefficient} \times \frac{d[Concentration]}{dt}$. Use $(-)$ for reactants.

Answer 1

The Correct Option is C

Step 1: Concept
The rate of reaction is expressed as the decrease in concentration of reactants or increase in concentration of products, divided by their stoichiometric coefficients.

Step 2: Meaning
Negative signs indicate disappearance (reactants); positive signs indicate appearance (products).

Step 3: Analysis
For the given reaction: Rate $= -\frac{1}{1}\frac{\text{d}[\text{N}_2]}{\text{dt}} = -\frac{1}{3}\frac{\text{d}[\text{H}_2]}{\text{dt}} = +\frac{1}{2}\frac{\text{d}[\text{NH}_3]}{\text{dt}}$.

Step 4: Conclusion
Option (C) matches the stoichiometry and correct sign convention. Final Answer: (C)