Question

For the reaction \( 2N_2O_5 \rightarrow 4NO_2 + O_2 \), rate and rate constant are \( 1.02 \times 10^{-4} \, \text{mol} \, \text{lit}^{-1} \, \text{s}^{-1} \) and \( 3.4 \times 10^{-5} \, \text{s}^{-1} \), respectively when the concentration of \( N_2O_5 \) at that time will be:

• A. \( 1.732 \, \text{M} \)
• B. 3M
• C. \( 3.4 \times 10^{-5} \, \text{M} \)
• D. \( 1.02 \times 10^{-6} \, \text{M} \)

Hint:

In first-order reactions, the rate constant and the concentration of reactants are related by the rate law equation.

Answer 1

The Correct Option is A

Step 1: From the rate law, we can find the concentration of \( N_2O_5 \). The rate law equation is given by: \[ \text{Rate} = k [N_2O_5], \] where \( k \) is the rate constant and \( [N_2O_5] \) is the concentration.
Step 2: Substituting the values, we get the concentration to be \( 1.732 \, \text{M} \).

Final Answer: \[ \boxed{1.732 \, \text{M}} \]