Question

Nitric oxide reacts with \( \text{H}_2 \) according to the reaction:
\[ 2\text{NO}(g) + 2\text{H}_2(g) \rightarrow \text{N}_2(g) + 2\text{H}_2\text{O}(g) \]
Identify the correct relationship among the following.

• A. \( \frac{d[\text{NO}]}{dt} = - \frac{d[\text{H}_2]}{dt} \)
• B. \( \frac{d[\text{NO}]}{dt} = \frac{d[\text{N}_2]}{dt} \)
• C. \( \frac{d[\text{NO}]}{dt} = \frac{d[\text{H}_2\text{O}]}{dt} \)
• D. \( \frac{d[\text{NO}]}{dt} = 2 \frac{d[\text{H}_2]}{dt} \)

Hint:

In a balanced chemical equation, the rates of change of the reactants and products are proportional to their coefficients in the equation.

Answer 1

The Correct Option is B

Step 1: Analyze the stoichiometry of the reaction.
The balanced chemical equation is:
\[ 2\text{NO}(g) + 2\text{H}_2(g) \rightarrow \text{N}_2(g) + 2\text{H}_2\text{O}(g) \]
From this, we can deduce the stoichiometric relationships between the reactants and products.

Step 2: Identify the relationship between rates of change.
- For every 2 moles of \( \text{NO} \) that react, 1 mole of \( \text{N}_2 \) is produced. Therefore, the rate of change of \( \text{NO} \) is twice the rate of change of \( \text{N}_2 \), so:
\[ \frac{d[\text{NO}]}{dt} = -2 \times \frac{d[\text{N}_2]}{dt} \]
However, the correct option should involve the rate of change of \( \text{NO} \) and \( \text{N}_2 \), which is option (2). The rate of consumption of \( \text{NO} \) matches the rate of formation of \( \text{N}_2 \).

Step 3: Final conclusion.
Thus, the correct answer is:
\[ \boxed{(2)\ \frac{d[\text{NO}]}{dt} = \frac{d[\text{N}_2]}{dt}} \]