Question

In the reaction: \[ N_2 (g) + 3H_2 (g) \rightarrow 2NH_3 (g) \] The rate of disappearance of H\(_2\) is 0.02 M/s. The rate of appearance of NH\(_3\) is:

• A. 0.0133 M/s
• B. 0.023 M/s
• C. 0.004 M/s
• D. 0.032 M/s

Hint:

The rate of appearance of products in a reaction can be determined using stoichiometric coefficients from the balanced equation.

Answer 1

The Correct Option is A

Step 1: Use Stoichiometry.
From the balanced equation, we see that 3 moles of H\(_2\) produce 2 moles of NH\(_3\). Therefore, the rate of appearance of NH\(_3\) is related to the rate of disappearance of H\(_2\) by the following stoichiometric relationship: \[ \text{Rate of appearance of NH}_3 = \frac{2}{3} \times \text{Rate of disappearance of H}_2 \] Substituting the given rate of disappearance of H\(_2\) (0.02 M/s): \[ \text{Rate of appearance of NH}_3 = \frac{2}{3} \times 0.02 \, \text{M/s} = 0.0133 \, \text{M/s} \]
Step 2: Analyzing the options.
(A) 0.0133 M/s: Correct. This is the correct rate of appearance of NH\(_3\) based on the stoichiometry of the reaction.
(B) 0.023 M/s: Incorrect. This rate is too high based on the stoichiometric relationship.
(C) 0.004 M/s: Incorrect. This rate is too low compared to the expected value.
(D) 0.032 M/s: Incorrect. This rate is also too high compared to the expected value.

Step 3: Conclusion.
The correct rate of appearance of NH\(_3\) is 0.0133 M/s, which corresponds to option (A).