Question

For the reaction, \(\text{NO}_{2(\text{g})} + \text{CO}_{(\text{g})} \longrightarrow \text{NO}_{(\text{g})} + \text{CO}_{2(\text{g})}\), rate of formation of \(\text{NO}_{(\text{g})}\) is \(\text{Y mol dm}^{-3}\text{ s}^{-1}\). Find the rate of disappearance of \(\text{CO}_{(\text{g})}\).

• A. \(\text{Y mol dm}^{-3}\text{ s}^{-1}\)
• B. \(2\text{Y mol dm}^{-3}\text{ s}^{-1}\)
• C. \(\frac{\text{Y}}{2}\text{ mol dm}^{-3}\text{ s}^{-1}\)
• D. \(\frac{3}{2}\text{Y mol dm}^{-3}\text{ s}^{-1}\)

Hint:

Always compare stoichiometric coefficients. If all are equal, rates of disappearance and formation are equal in magnitude.

Answer 1

The Correct Option is A

Concept:
For a general reaction: \[ aA + bB \rightarrow cC + dD \] Rate is defined as: \[ -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt} \] Step 1: Write the given reaction with coefficients. \[ \text{NO}_2 + \text{CO} \rightarrow \text{NO} + \text{CO}_2 \] Here, \[ a = b = c = d = 1 \]
Step 2: Write the rate expression. \[ -\frac{d[\text{NO}_2]}{dt} = -\frac{d[\text{CO}]}{dt} = \frac{d[\text{NO}]}{dt} = \frac{d[\text{CO}_2]}{dt} \]
Step 3: Use given information. Rate of formation of NO: \[ \frac{d[\text{NO}]}{dt} = Y \] Thus, \[ -\frac{d[\text{CO}]}{dt} = Y \]
Step 4: Interpret the result. Negative sign indicates disappearance, so magnitude of rate of disappearance of CO is: \[ Y \text{ mol dm}^{-3}\text{ s}^{-1} \]
Step 5: Conclusion. \[ \text{Rate of disappearance of CO} = Y \text{ mol dm}^{-3}\text{ s}^{-1} \]