Question

For the reaction
\(2A + 3B + \frac{3}{2}C \to 3P\), which statement is correct ?

• A. \(\frac{dn_A}{dt} = \frac{dn_B}{dt} = \frac{dn_C}{dt}\)
• B. \(\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_B}{dt} = \frac{3}{4}\frac{dn_C}{dt}\)
• C. \(\frac{dn_A}{dt} = \frac{3}{2}\frac{dn_B}{dt} = \frac{3}{4}\frac{dn_C}{dt}\)
• D. \(\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_B}{dt} = \frac{4}{3}\frac{dn_C}{dt}\)

Hint:

The rate of reaction is the same for every species when each rate of change is divided by its stoichiometric coefficient.

Answer 1

The Correct Option is D

For \(2A + 3B + \frac{3}{2}C \to 3P\) the rate of reaction is
\(r = -\frac{1}{2}\frac{dn_A}{dt} = -\frac{1}{3}\frac{dn_B}{dt} = -\frac{2}{3}\frac{dn_C}{dt}\).
Equating the first two: \(\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_B}{dt}\).
Equating the first and third: \(\frac{1}{2}\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_C}{dt}\), so \(\frac{dn_A}{dt} = \frac{4}{3}\frac{dn_C}{dt}\).
Therefore \(\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_B}{dt} = \frac{4}{3}\frac{dn_C}{dt}\).
Answer: (4) \(\frac{dn_A}{dt} = \frac{2}{3}\frac{dn_B}{dt} = \frac{4}{3}\frac{dn_C}{dt}\)