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Ch.13 - Chemical KineticsWorksheetSee all chapters

# Integrated Rate Law

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Sections
Intro to Chemical Kinetics
Energy Diagrams
Catalyst
Factors Influencing Rates
Average Rate of Reaction
Stoichiometric Rate Calculations
Instantaneous Rate
Collision Theory
Arrhenius Equation
Rate Law
Reaction Mechanism
Integrated Rate Law
Half-Life

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

###### Understanding the Integrated Rate Laws

Concept #1: Zero-Order Integrated Rate Law

Example #1: A plot of [NO3] vs time with a slope of 0.260 gives a straight line. What was the initial concentration of NO3 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 is known to be zero order in A with 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 × 103 sec where [A]0 was 0.750 M at 25°C; assume [C]0 = 0 M.

Practice: For the decomposition of urea, NH2CONH2 (aq) + H+(aq) + 2 H2O (l) → 2 NH4+ (aq) + HCO3 (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.