Question

For the reaction: 2SO₂ + O₂ → 2SO₃,
the rate of disappearance of O₂ is \( 2 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \).
What is the rate of appearance of SO₃?

• A. \( 2 \times 10^{-4} \) mol L$^{-1}$ s$^{-1}$
• B. \( 4 \times 10^{-4} \) mol L$^{-1}$ s$^{-1}$
• C. \( 1 \times 10^{-1} \) mol L$^{-1}$ s$^{-1}$
• D. \( 6 \times 10^{-4} \) mol L$^{-1}$ s$^{-1}$

Hint:

In rate calculations, use the balanced chemical equation to determine the relationship between reactant disappearance and product formation.

Answer 1

The Correct Option is B

To solve the problem, we need to determine the rate of appearance of SO₃ based on the given rate of disappearance of O₂ for the reaction:
2SO₂ + O₂ ⇌ 2SO₃.

The stoichiometry of the reaction provides the key relationships between the rates:
1 mol of O₂ produces 2 mol of SO₃.

Let:

• Rate of disappearance of O₂ = \(2 \times 10^{-4}\) mol L^-1 s^-1
• The rate of appearance of SO₃ is equal to twice the rate of disappearance of O₂ based on stoichiometry (1:2 ratio for O₂:SO₃)

Thus, the rate of appearance of SO₃ = 2 × Rate of disappearance of O₂ = 2 × \(2 \times 10^{-4}\) = \(4 \times 10^{-4}\) mol L^-1 s^-1.

The correct answer is:
\(4 \times 10^{-4}\) mol L^-1 s^-1.

Answer 2

Step 1: Understanding the Reaction Stoichiometry
The given reaction is: \[ 2SO_2 + O_2 \rightleftharpoons 2SO_3 \] Step 2: Relating the Rate of Disappearance and Appearance
The rate of disappearance of O$_2$ is related to the rate of appearance of SO$_3$ using stoichiometry: \[ \frac{-d[O_2]}{dt} = \frac{1}{2} \frac{d[SO_3]}{dt} \] Step 3: Substituting Values and Solving
Given: \[ \frac{-d[O_2]}{dt} = 2 \times 10^{-4} { mol L}^{-1} { s}^{-1} \] Solving for \( \frac{d[SO_3]}{dt} \): \[ \frac{d[SO_3]}{dt} = 2 \times (2 \times 10^{-4}) \] \[ = 4 \times 10^{-4} { mol L}^{-1} { s}^{-1} \] Thus, the correct answer is (B).