Question

The rate of the reaction $2A + B \rightarrow C$ can be represented by which of the following?

• A. $-\dfrac{1}{2}\,\dfrac{d[A]}{dt}$
• B. $-\dfrac{d[B]}{dt}$
• C. $+\dfrac{d[C]}{dt}$
• D. All of these

Hint:

Always divide the disappearance/appearance rate by the stoichiometric coefficient to get the unique rate.

Answer 1

The Correct Option is D

Step 1: Use stoichiometry in rate definition.
For $aA+bB\rightarrow$ products, rate $= -\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt} = +\dfrac{d[\text{product}]}{dt}$.
Step 2: Apply to $2A + B \rightarrow C$.
Rate $= -\dfrac{1}{2}\dfrac{d[A]}{dt} = -\dfrac{d[B]}{dt} = +\dfrac{d[C]}{dt}$.
Step 3: Conclusion.
All three expressions are valid $\Rightarrow$ (D) All of these.