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For the reaction :
$2A + B \rightarrow 3C + D$
Which of the following does not express the reaction rate :-
$2A + B \rightarrow 3C + D$
Which of the following does not express the reaction rate :-
A
$-\dfrac{d[C]}{3\,dt}$
B
$-\dfrac{d[B]}{dt}$
C
$\dfrac{d[D]}{dt}$
D
$-\dfrac{d[A]}{2\,dt}$
Detailed Solution
For the reaction $2A + B \rightarrow 3C + D$, the rate is expressed as:
Rate $= -\dfrac{1}{2}\dfrac{d[A]}{dt} = -\dfrac{d[B]}{dt} = +\dfrac{1}{3}\dfrac{d[C]}{dt} = +\dfrac{d[D]}{dt}$
The concentration of a reactant decreases with time, so a negative sign is used to make the rate positive.
The concentration of a product increases with time, so a positive sign is used.
C is a product, so the correct expression for it is $+\dfrac{d[C]}{3\,dt}$.
$-\dfrac{d[C]}{3\,dt}$ would be a negative quantity, so it does not express the reaction rate.
Rate $= -\dfrac{1}{2}\dfrac{d[A]}{dt} = -\dfrac{d[B]}{dt} = +\dfrac{1}{3}\dfrac{d[C]}{dt} = +\dfrac{d[D]}{dt}$
The concentration of a reactant decreases with time, so a negative sign is used to make the rate positive.
The concentration of a product increases with time, so a positive sign is used.
C is a product, so the correct expression for it is $+\dfrac{d[C]}{3\,dt}$.
$-\dfrac{d[C]}{3\,dt}$ would be a negative quantity, so it does not express the reaction rate.