Textbook Question
(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?
15. Chemical Kinetics
Integrated Rate Law
Multiple Choice
For the reaction 2N2O5(g) → 4NO2(g) + O2(g) with a rate constant k = 2.8×10⁻³ sec⁻¹, if the initial concentration of [N2O5] is 1.58 mol/L, what is the concentration of N2O5 after 300 seconds?
A
1.55 mol/L
B
0.68 mol/L
C
0.75 mol/L
D
0.27 mol/L
Verified step by step guidance1
Identify the type of reaction: The given reaction is a first-order reaction with respect to N2O5, as indicated by the rate constant k with units of sec⁻¹.
Use the first-order integrated rate equation: The formula for a first-order reaction is \( [A] = [A]_0 e^{-kt} \), where \([A]\) is the concentration at time t, \([A]_0\) is the initial concentration, k is the rate constant, and t is the time elapsed.
Substitute the known values into the equation: \([A]_0 = 1.58 \text{ mol/L}\), \(k = 2.8 \times 10^{-3} \text{ sec}^{-1}\), and \(t = 300 \text{ sec}\).
Calculate the exponent: Compute \(-kt\) which is \(-2.8 \times 10^{-3} \times 300\).
Determine the concentration \([A]\): Use the calculated exponent in the equation \([A] = 1.58 e^{-kt}\) to find the concentration of N2O5 after 300 seconds.
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