Question

Reaction \( 2A \rightarrow B + 3C \) is a zero-order reaction. What will be the rate of production for "C"? 

Hint:

For a zero-order reaction, the rate is independent of reactant concentration and remains constant over time.

Answer 1

Step 1: Understanding Rate of Reaction
For a general reaction: \[ aA + bB \rightarrow cC + dD \] The rate of reaction is given by: \[ {Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt} \] Step 2: Given Reaction and Rate Expression
For the reaction: \[ 2A \rightarrow B + 3C \] The rate of reaction is: \[ {Rate} = -\frac{1}{2} \frac{d[A]}{dt} = \frac{1}{3} \frac{d[C]}{dt} \] Since it is a zero-order reaction, the rate is constant: \[ {Rate} = k \] Step 3: Finding the Rate of Production for "C"
Rearranging for \( C \): \[ \frac{d[C]}{dt} = 3 \times k \] Given \( k = 3.5 \times 10^{-4} \) mol L\(^{-1}\) s\(^{-1}\): \[ \frac{d[C]}{dt} = 3 \times (3.5 \times 10^{-4}) \] \[ = 10.5 \times 10^{-4} { mol L}^{-1} { s}^{-1} \] Step 4: Conclusion
Thus, the rate of production of C is: \[ 10.5 \times 10^{-4} { mol L}^{-1} { s}^{-1} \]