Question

What is the rate of disappearance of B in following reaction? $2 \text{A} + \text{B} \rightarrow 3 \text{C}$, if rate of appearance of C is $1.3 \times 10^{-4}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$.

• A. $4.33 \times 10^{-5}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$
• B. $8.6 \times 10^{-5}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$
• C. $2.6 \times 10^{-4}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$
• D. $5.2 \times 10^{-5}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$

Hint:

To quickly relate rates of reactions, use the shortcut: $\text{Rate of Required Species} = \frac{\text{Coefficient of Required}}{\text{Coefficient of Given}} \times \text{Rate of Given Species}$.
Here, $\text{Rate of B} = \frac{1}{3} \times \text{Rate of C}$. Dividing $1.3 \times 10^{-4}$ by 3 quickly yields $4.33 \times 10^{-5}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem presents a balanced chemical equation and provides the rate of appearance of product C.
We need to determine the corresponding rate of disappearance of reactant B under the same conditions.

Step 2: Key Formula or Approach:
For a generalized chemical reaction, the unique rate of reaction is calculated by dividing the rate of change of concentration of any participant by its stoichiometric coefficient.
For the reaction $2\text{A} + \text{B} \rightarrow 3\text{C}$, the mathematical relationship between the rates is:
$$\text{Rate} = -\frac{1}{2}\frac{d[\text{A}]}{dt} = -\frac{d[\text{B}]}{dt} = +\frac{1}{3}\frac{d[\text{C}]}{dt}$$
Therefore, the rate of disappearance of B is directly related to the rate of appearance of C by:
$$-\frac{d[\text{B}]}{dt} = \frac{1}{3}\frac{d[\text{C}]}{dt}$$

Step 3: Detailed Explanation:
We are given that the rate of appearance of C is:
$$\frac{d[\text{C}]}{dt} = 1.3 \times 10^{-4}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$$
Substitute this value into our rate relationship formula to compute the rate of disappearance of B:
$$-\frac{d[\text{B}]}{dt} = \frac{1}{3} \times \left(1.3 \times 10^{-4}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}\right)$$
$$-\frac{d[\text{B}]}{dt} = 0.4333 \times 10^{-4}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$$
Shifting the decimal point to convert into standard scientific notation yields:
$$-\frac{d[\text{B}]}{dt} = 4.33 \times 10^{-5}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$$

Step 4: Final Answer:
The rate of disappearance of B is $4.33 \times 10^{-5}\ \text{mol}\ \text{L}^{-1}\ \text{s}^{-1}$, which corresponds to option (A).