Question

For the reaction 2A + B $\longrightarrow$ 2C + 3D, the rate of change in concentration of C is 1.0 mol L$^{-1$ s$^{-1}$. Find the rate of reaction and rate of change in concentration of A, B and D.}

Hint:

Use the stoichiometric coefficients in the rate equation to relate the rate of reaction with the rate of change of species.

Answer 1

Step 1: General rate expression.
For the reaction: \[ 2A + B \longrightarrow 2C + 3D \] The rate of reaction is given by: \[ \text{Rate} = -\frac{1}{2}\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{1}{2}\frac{d[C]}{dt} = \frac{1}{3}\frac{d[D]}{dt} \] Step 2: Given data.
\[ \frac{d[C]}{dt} = +1.0 \, \text{mol L}^{-1}\text{s}^{-1} \] Step 3: Calculate rate of reaction.
\[ \text{Rate} = \frac{1}{2}\frac{d[C]}{dt} = \frac{1}{2}(1.0) = 0.5 \, \text{mol L}^{-1}\text{s}^{-1} \] Step 4: Calculate rate of change of other species.
- For A: \[ -\frac{1}{2}\frac{d[A]}{dt} = 0.5 \quad \Rightarrow \quad \frac{d[A]}{dt} = -1.0 \, \text{mol L}^{-1}\text{s}^{-1} \] - For B: \[ -\frac{d[B]}{dt} = 0.5 \quad \Rightarrow \quad \frac{d[B]}{dt} = -0.5 \, \text{mol L}^{-1}\text{s}^{-1} \] - For D: \[ \frac{1}{3}\frac{d[D]}{dt} = 0.5 \quad \Rightarrow \quad \frac{d[D]}{dt} = +1.5 \, \text{mol L}^{-1}\text{s}^{-1} \] Conclusion:
- Rate of reaction = $0.5 \, \text{mol L}^{-1}\text{s}^{-1}$
- Rate of change: $d[A]/dt = -1.0$, $d[B]/dt = -0.5$, $d[C]/dt = +1.0$, $d[D]/dt = +1.5$ mol L$^{-1}$s$^{-1}$.