Question

Nitric oxide reacts with \(\mathrm{H}_2\) according to reaction, \(2 \mathrm{NO}_{(\mathrm{g})}+2 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{N}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{g})}\), identify the correct relationship among the following.

• A. \(-\frac{1}{2}\frac{\text{ }\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{H}_{2}\mathrm{O}]}{\mathrm{dt}}\)
• B. \(-\frac{\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{H}_{2}\mathrm{O}]}{\mathrm{dt}}\)
• C. \(-\frac{3}{2}\frac{\text{ }\mathrm{d}[\mathrm{NO}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{H}_{2}\mathrm{O}]}{\mathrm{dt}}\)
• D. \(2\frac{\text{ }\mathrm{d}[\mathrm{H}_{2}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{N}_{2}]}{\mathrm{dt}}\)

Hint:

Divide the rate of change of each species by its stoichiometric coefficient to write the rate of reaction.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For \(a\text{A}+b\text{B}\rightarrow c\text{C}+d\text{D}\), the rate is \(-\dfrac{1}{a}\dfrac{d[A]}{dt}=-\dfrac{1}{b}\dfrac{d[B]}{dt}=\dfrac{1}{c}\dfrac{d[C]}{dt}=\dfrac{1}{d}\dfrac{d[D]}{dt}\).

Step 2: Apply to the Reaction
\(2\text{NO}+2\text{H}_2\rightarrow \text{N}_2+2\text{H}_2\text{O}\)
Rate \(=-\dfrac{1}{2}\dfrac{d[\text{NO}]}{dt}=-\dfrac{1}{2}\dfrac{d[\text{H}_2]}{dt}=\dfrac{d[\text{N}_2]}{dt}=\dfrac{1}{2}\dfrac{d[\text{H}_2\text{O}]}{dt}\)

Step 3: Simplify
Multiplying the equality of NO and water by 2 gives \(-\dfrac{d[\text{NO}]}{dt}=\dfrac{d[\text{H}_2\text{O}]}{dt}\).

Step 4: Compare the options
The second relation is correct. The other options use wrong coefficients or a wrong sign.

Final Answer:
NO disappears at the same rate at which water forms. \[ \boxed{\text{(B) }-\dfrac{d[\text{NO}]}{dt}=\dfrac{d[\text{H}_2\text{O}]}{dt}} \]