Question

What is the rate of appearance of Z in following reaction? $3\text{x} \rightarrow 2\text{y} + \text{z}$, if rate of disappearance of x is $0.072\text{ mol s}^{-1}$?

• A. $0.072\text{ mol s}^{-1}$
• B. $0.048\text{ mol s}^{-1}$
• C. $0.024\text{ mol s}^{-1}$
• D. $0.096\text{ mol s}^{-1}$

Hint:

To avoid confusion, remember that "Rate of disappearance/appearance" is just $\frac{d[C]}{dt}$ (without the stoichiometric fraction). The fraction is only used when setting them equal to each other!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given a balanced chemical equation and the rate of disappearance of the reactant (x). We need to find the rate of appearance of one of the products (z).

Step 2: Key Formula or Approach:
For a general reaction $aA + bB \rightarrow cC + dD$, the overall rate of reaction is related to the rates of individual components by their stoichiometric coefficients:
$$\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$$

Step 3: Detailed Explanation:
Applying the rate law relationship to the given reaction $3\text{x} \rightarrow 2\text{y} + \text{z}$:
$$-\frac{1}{3}\frac{d[\text{x}]}{dt} = +\frac{1}{2}\frac{d[\text{y}]}{dt} = +\frac{d[\text{z}]}{dt}$$
We are given the rate of disappearance of x:
$$-\frac{d[\text{x}]}{dt} = 0.072\text{ mol s}^{-1}$$
Now, equate the terms for x and z:
$$+\frac{d[\text{z}]}{dt} = \frac{1}{3} \times \left(-\frac{d[\text{x}]}{dt}\right)$$
$$+\frac{d[\text{z}]}{dt} = \frac{1}{3} \times 0.072$$
$$+\frac{d[\text{z}]}{dt} = 0.024\text{ mol s}^{-1}$$

Step 4: Final Answer:
The rate of appearance of z is $0.024\text{ mol s}^{-1}$, which matches option (C).