Question

For the reaction \[ 2A+B\rightarrow3C+D \] Which of the following does not express the reaction rate?

• A. \(-\dfrac{d[B]}{dt}\)
• B. \(\dfrac{d[D]}{dt}\)
• C. \(-\dfrac12\dfrac{d[A]}{dt}\)
• D. \(\dfrac13\dfrac{d[C]}{dt}\)

Hint:

For a reaction: \[ aA+bB\rightarrow cC+dD \] Reaction rate: \[ -\frac1a\frac{d[A]}{dt} = -\frac1b\frac{d[B]}{dt} = \frac1c\frac{d[C]}{dt} = \frac1d\frac{d[D]}{dt} \]

Answer 1

The Correct Option is A

Step 1: Write the rate expression.
For the reaction: \[ 2A+B\rightarrow3C+D \] Rate of reaction is: \[ \text{Rate} = -\frac12\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac13\frac{d[C]}{dt} = \frac{d[D]}{dt} \]

Step 2: Compare with given options.
Option (2): \[ \frac{d[D]}{dt} \] is correct. Option (3): \[ -\frac12\frac{d[A]}{dt} \] is correct. Option (4): \[ \frac13\frac{d[C]}{dt} \] is correct. Option (1): \[ -\frac{d[B]}{dt} \] should actually be: \[ -\frac1{1}\frac{d[B]}{dt} \] Thus it is not properly normalized according to stoichiometric coefficient form.

Step 3: Identify the incorrect expression.
Therefore: \[ \boxed{ \mathrm{(A)\ -\dfrac{d[B]}{dt} } } \]