Question

For \(2N_2O_5 \rightarrow 4NO_2 + O_2\), if rate is \(1.02 \times 10^{-4}\) and \(k = 3.4 \times 10^{-5}\,s^{-1}\), find the concentration of \(N_2O_5\).

• A. \(1.0\,\text{mol/L}\)
• B. \(2.0\,\text{mol/L}\)
• C. \(3.0\,\text{mol/L}\)
• D. \(4.0\,\text{mol/L}\)

Hint:

In first–order reactions, concentration can be directly found using \(Rate = k[\text{Reactant}]\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Given the rate of a reaction and the rate constant, we need to determine the molar concentration of the reactant.
Step 2: Key Formula or Approach:
The units of the rate constant (\(s^{-1}\)) indicate that this is a first-order reaction. The rate law is:
\[ \text{Rate} = k[N_2O_5] \]
Step 3: Detailed Explanation:
Substitute the given values into the rate equation:
\[ 1.02 \times 10^{-4} = (3.4 \times 10^{-5}) \times [N_2O_5] \]
Isolate the concentration term:
\[ [N_2O_5] = \frac{1.02 \times 10^{-4}}{3.4 \times 10^{-5}} \]
Convert the exponents to be the same to simplify division:
\[ [N_2O_5] = \frac{10.2 \times 10^{-5}}{3.4 \times 10^{-5}} \]
\[ [N_2O_5] = \frac{10.2}{3.4} = 3.0\,\text{mol/L} \]
Step 4: Final Answer:
The concentration of \(N_2O_5\) is \(3.0\,\text{mol/L}\).