Practice: For the reaction A → B, the rate constant is 0.0837 M^{–1}•sec^{–1}. How long would it take for [A] to decrease by 85%?

When we include the variable of time to our Rate Law then we obtain the Integrated Rate Laws.

Concept #1: Zero-Order Integrated Rate Law

Example #1: A plot of [NO_{3}] vs time with a slope of 0.260 gives a straight line. What was the initial concentration of NO_{3} if after 35 seconds its concentration dropped to 2.75 x 10^{-2 }M?

Concept #2: First-Order Integrated Rate Law

Example #2: A certain reaction has a rate constant of 0.289 s^{-1}. How long (seconds) would it take for the concentration of reactant A to decrease from 1.43 M to 0.850 M?

Concept #3: Second-Order Integrated Rate Law

Example #3: The reactant concentration for a second-order reaction was 0.670 M after 300 s and 7.3 x 10^{-2} M after 750 s. What is the rate constant k for this reaction?

Practice: For the reaction A → B, the rate constant is 0.0837 M^{–1}•sec^{–1}. How long would it take for [A] to decrease by 85%?

Practice: The following reaction has a rate constant of 3.7 × 10^{–3} M•s^{–1} at 25°C:

A → B + C

Calculate the concentration of C after 2.7 × 10^{–}^{3} sec where [A]_{0} was 0.750 M at 25°C; assume [C]_{0} = 0 M.

Practice: For the decomposition of urea, NH_{2}CONH_{2} (aq) + H^{+}(aq) + 2 H_{2}O (l) → 2 NH_{4}^{+} (aq) + HCO_{3}^{–} (aq), the rate constant is 3.24 × 10^{–4} s^{–1} at 35°C. The initial concentration of urea is 2.89 mol/L. What fraction of urea has decomposed after 3.5 minutes?

Practice: Iodine-123 is used to study thyroid gland function. As this radioactive isotope breaks down, after 5.7 hrs the concentration of iodine-123 is 56.3% complete. Find the rate constant of this reaction.