Question

For the reaction \(\text{N}_{2}(g)+3\text{H}_{2}(g)\rightarrow 2\text{NH}_{3}(g)\), the rate of reaction is equal to

• A. the rate of consumption of \(\text{N}_{2}\).
• B. three times the rate of consumption of \(\text{H}_{2}\).
• C. two times the rate of consumption of \(\text{NH}_{3}\).
• D. two times the rate of consumption of \(\text{N}_{2}\).

Hint:

Divide each rate of change by its stoichiometric coefficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For \(a\text{A} + b\text{B}\rightarrow c\text{C}\), the rate of reaction is
\(-\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt} = \dfrac{1}{c}\dfrac{d[C]}{dt}\).

Step 2: Apply to the reaction
For \(\text{N}_{2}+3\text{H}_{2}\rightarrow 2\text{NH}_{3}\):
Rate \(= -\dfrac{d[\text{N}_{2}]}{dt} = -\dfrac{1}{3}\dfrac{d[\text{H}_{2}]}{dt} = \dfrac{1}{2}\dfrac{d[\text{NH}_{3}]}{dt}\).

Step 3: Compare the options
The rate of reaction equals the rate of consumption of \(\text{N}_{2}\), the first option.
The other options use wrong multiples.

Final Answer:
The rate of reaction equals the rate of consumption of N2. \[ \boxed{\text{(A) }\text{the rate of consumption of N}_{2}} \]