Question

In the reaction $2SO_2 + O_2 \rightarrow 2SO_3$, the rate of appearance of $SO_3$ is $4 \times 10^{-4}\text{M s}^{-1}$. The rate of disappearance of $O_2$ is

• A. $1.0 \times 10^{-4}\ \text{M s}^{-1}$
• B. $2.0 \times 10^{-4}\ \text{M s}^{-1}$
• C. $6.0 \times 10^{-4}\ \text{M s}^{-1}$
• D. $4.0 \times 10^{-4}\ \text{M s}^{-1}$

Hint:

Always use stoichiometric coefficients while relating rates of appearance and disappearance.

Answer 1

The Correct Option is B

Step 1: Write the rate relation using stoichiometry.
For the reaction \[ 2SO_2 + O_2 \rightarrow 2SO_3 \] the rate relation is:
\[ \text{Rate} = \frac{1}{2}\frac{d[SO_3]}{dt} = \frac{d[O_2]}{dt} \]
Step 2: Substitute the given value.
Rate of appearance of $SO_3 = 4 \times 10^{-4}\ \text{M s}^{-1}$
\[ \text{Rate} = \frac{1}{2} \times 4 \times 10^{-4} \]
Step 3: Calculate the rate of disappearance of $O_2$.
\[ \text{Rate} = 2.0 \times 10^{-4}\ \text{M s}^{-1} \]
Step 4: Conclusion.
The rate of disappearance of oxygen is $2.0 \times 10^{-4}\ \text{M s}^{-1}$.