Chemical Kinetics: Integrated Rate Laws
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Questions and Answers

What is the formula for the integrated rate law of a first-order reaction?

  • [A]t = -kt + [A]0
  • K[A]1 = ln[A]t - ln[A]0
  • ln[A]t = -kt + ln[A]0 (correct)
  • 1/[A]t = kt + 1/[A]0

Which reaction order would yield a plot of [A] against time that is a straight line?

  • Exponential Order
  • Second Order
  • Zero Order (correct)
  • First Order

Which equation corresponds to the integrated rate law for a second-order reaction?

  • 1/[A]t = kt + 1/[A]0 (correct)
  • K[A]2 = [A]t / time
  • [A]t = -kt + [A]0
  • ln[A]t = -kt + ln[A]0

How can one determine the order of a reaction?

<p>By plotting data according to different integrated rate laws (D)</p> Signup and view all the answers

What does the variable 't' represent in the integrated rate laws?

<p>Time elapsed in the reaction (D)</p> Signup and view all the answers

What is the relationship between the initial concentration and shelf life in a zero order reaction?

<p>Shelf life increases as initial concentration increases. (C)</p> Signup and view all the answers

What is the formula for half-life in a zero order reaction?

<p>t½ = 0.5 [A]0 / k (A)</p> Signup and view all the answers

If the zero order rate constant (k) is 2.88 x 10^-3 mg mL^-1 hour^-1 and the initial concentration [A]0 is 25 mg/mL, what is the time for 90% of the shelf life (t90)?

<p>434 hours (C)</p> Signup and view all the answers

What effect does a decrease in solubility have on the shelf life of a zero order reaction?

<p>Decreases the shelf life (D)</p> Signup and view all the answers

For a zero order reaction, what is the equation for the integrated rate law?

<p>[A]t = [A]0 – kt (B)</p> Signup and view all the answers

What is the definition of a pseudo first order reaction?

<p>A reaction that behaves as first order when one reactant concentration remains constant. (D)</p> Signup and view all the answers

Which expression represents the integrated rate law for a first order reaction?

<p>$ ext{ln}[A]t = -kt + ext{ln}[A]0$ (B)</p> Signup and view all the answers

What is the time required for the concentration of a reactant to fall to 50% of its initial value in a first order reaction?

<p>$t_{1/2} = rac{0.693}{k}$ (A)</p> Signup and view all the answers

In the hydrolysis of ampicillin, what factor determines the reaction's pseudo first order behavior?

<p>Concentration of ampicillin being significantly higher than water. (A)</p> Signup and view all the answers

What is the formula to calculate the time taken to reach 90% reduction of a first order reaction?

<p>$t_{90} = rac{0.105}{k}$ (B)</p> Signup and view all the answers

What does the equation for the zero order integrated rate law indicate about the rate of a reaction?

<p>It is constant regardless of reactant concentration. (D)</p> Signup and view all the answers

How is the half-life for a zero order reaction determined?

<p>It is constant and independent of initial concentration. (C)</p> Signup and view all the answers

Given the relationship Kt = [A]0 - [A]t, what can be concluded about the reactant concentration over time?

<p>It decreases linearly with time. (A)</p> Signup and view all the answers

What does the term 't50' represent in the context of zero order reactions?

<p>The time taken for the concentration to decrease from 100% to 50%. (C)</p> Signup and view all the answers

Which of the following correctly describes the graphical representation of zero order kinetics?

<p>The plot of [A] versus time gives a straight line. (D)</p> Signup and view all the answers

What is the rate equation for a second order reaction where A reacts with itself?

<p>Rate = k[A]^2 (C)</p> Signup and view all the answers

Which of the following describes the relationship for the integrated rate law of a second order reaction?

<p>1/[A]t = kt + 1/[A]0 (A), 1/[A]t = 1/[A]0 + kt (C)</p> Signup and view all the answers

What does the term 'half-life' refer to in the context of second order reactions?

<p>The time required for half the reactant to be converted into products. (A)</p> Signup and view all the answers

What is the formula for calculating the time required to fall to 90% of the initial concentration for a second order reaction?

<p>t90 = 1/9[A]0 k (B)</p> Signup and view all the answers

In a second order reaction A + A → Products, what is the significance of the natural logarithm?

<p>It is used to quantify changes over time. (B)</p> Signup and view all the answers

What role does initial concentration [A]0 play in second order reactions?

<p>It influences the half-life of the reaction. (B)</p> Signup and view all the answers

For a reaction A + B → C + D, what happens if [A]0 ≠ [B]0?

<p>The formulation of the integrated rate law changes. (D)</p> Signup and view all the answers

What indicates that a reaction follows second order kinetics when analyzing concentration over time?

<p>A linear relationship between 1/[A] and time. (D)</p> Signup and view all the answers

What does an increase in the concentration of dissolved drug influence regarding shelf life?

<p>Shelf life increases as concentration increases. (C)</p> Signup and view all the answers

How is the activation energy (Ea) derived from the Arrhenius Equation?

<p>By taking the negative of the slope and dividing it by R. (A)</p> Signup and view all the answers

Which temperature shows the highest rate constant (k) for Bupivacaine hydrolysis?

<p>50 °C (C)</p> Signup and view all the answers

What is the significance of plotting ln(k) against 1/T in chemical kinetics?

<p>It provides a way to calculate activation energy. (D)</p> Signup and view all the answers

Which of the following statements is true about zero order kinetics?

<p>Only the dissolved drug in solution degrades appreciably. (B)</p> Signup and view all the answers

What does the intercept in the Arrhenius Equation represent?

<p>The natural logarithm of the rate constant A. (D)</p> Signup and view all the answers

How can the rate constant (k) at 15 °C be predicted based on the provided data?

<p>It requires plotting ln(k) against 1/T and applying linear regression. (A)</p> Signup and view all the answers

What is the activation energy (Ea) calculated from the given data?

<p>51.7 kJ mol-1 (A)</p> Signup and view all the answers

What is indicated by a drug's degradation over time when assessed as a percentage of its initial value?

<p>The drug's shelf life decreases. (D)</p> Signup and view all the answers

Which parameter in the Arrhenius Equation relates to temperature?

<p>Gas constant (R) (C)</p> Signup and view all the answers

Flashcards

Reaction Order

Represents the relationship between the change in the concentration of a reactant and time. It describes how fast a reaction proceeds. It doesn't dictate the mechanism of the reaction.

Integrated Rate Law

A mathematical expression that relates the concentration of a reactant to reaction time. It allows us to predict the concentration of a reactant at any given time.

Zero Order

The concentration of a reactant remains constant regardless of the time passed. The rate of the reaction is independent of reactant concentration.

First Order

The rate of the reaction is directly proportional to the concentration of the reactant. The reaction slows down as time passes.

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Second Order

The rate of the reaction is proportional to the square of the concentration of the reactant. The reaction slows down very quickly.

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Pseudo first order reaction

A reaction that appears to be first order, but actually has a higher order, because the concentration of one reactant is kept constant.

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Half-life (t1/2)

This is the time it takes for the concentration of a reactant to decrease to half of its initial concentration. It's used to describe the rate of a chemical reaction.

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Half-life equation for first order reactions

For a first order reaction, the time it takes for the concentration of a reactant to fall to 50% of its initial value can be calculated using this formula: t1/2 = 0.693/k. The half-life is independent of the initial concentration.

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Time to reach 90% initial concentration (t90)

The time required for a reactant to reach 90% of its initial concentration is calculated using the formula t90 = ln 100/90 /k.

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First order reaction

A reaction that occurs in only one step. The rate of the reaction depends on the concentration of just one reactant.

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Zero Order Reaction

The rate of a reaction is constant regardless of the concentration of the reactant. This means the reaction proceeds at the same speed no matter how much of the starting material is present.

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Zero Order Integrated Rate Law

A mathematical equation that describes the relationship between the concentration of a reactant and time for a zero-order reaction.

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Zero Order Half-Life

The time it takes for the concentration of a reactant to decrease by half in a zero-order reaction.

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Rate Constant (k) in Zero Order Reactions

The rate constant of a reaction is independent of the concentration of the reactant. It simply represents the rate at which the reaction occurs.

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Concentration vs. Time Graph for Zero Order Reactions

The concentration of the reactant decreases linearly with time. This means the concentration decreases at a constant rate.

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Zero-order 90% shelf life

The time it takes for 90% of the initial concentration of a reactant to be consumed in a zero-order reaction. It is significantly larger than the half-life, meaning the reaction proceeds slowly once the concentration drops.

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Integrated rate law for zero-order reaction

The integrated rate law for a zero-order reaction describes the relationship between the concentration of the reactant at any time (t) and the initial concentration ([A]0). It shows a linear decrease in concentration over time.

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Zero-order shelf life

The time it takes for the concentration of a reactant to fall to a specific value (e.g., 5% of the initial concentration) in a zero-order reaction. It is directly proportional to the initial concentration and inversely proportional to the rate constant.

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Zero-order rate constant (k)

The rate constant for a zero-order reaction is the rate of the reaction, independent of the concentration of the reactant. It is expressed in units of concentration per unit time.

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Second Order Reaction (i)

A type of reaction where the rate is directly proportional to the square of the concentration of a single reactant. The rate constant, 'k', is a proportionality constant that describes the rate of reaction at a given temperature.

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Half-life (t1/2) for Second Order Reaction (i)

The time taken for the concentration of a reactant to decrease to half its initial value. In a second order reaction (i), it depends on the initial concentration of the reactant.

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Shelf Life (t90) for Second Order Reaction (i)

The time taken for the concentration of a reactant to decrease to 10% of its initial value. In a second order reaction (i), it depends on the initial concentration of the reactant and the rate constant.

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Second Order Reaction (ii)

A type of reaction where the rate is dependent on the concentrations of two different reactants. The rate constant, 'k', is a proportionality constant that describes the rate of reaction at a given temperature.

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Integrated Rate Law for Second Order Reaction (ii)

The integrated rate law for a second-order reaction (ii) with non-equal initial concentrations of the reactants. It relates the concentrations of the reactants at time 't' to the initial concentrations and the rate constant.

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No Simple Equation for t1/2 for Second Order Reaction (ii)

In a second-order reaction (ii), the half-life is not a constant value and depends on the initial concentrations of both reactants. This makes it more complex to calculate.

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Rate Constant (k)

The constant of proportionality that relates the rate of a reaction to the concentrations of the reactants raised to their respective reaction orders. A higher value indicates a faster reaction.

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Arrhenius Equation

A mathematical equation used to describe the relationship between the rate constant of a reaction and its activation energy and temperature.

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Activation Energy (Ea)

The energy difference between reactants and the transition state of a reaction.

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Arrhenius Constant (A)

The rate constant of a reaction at an infinitely high temperature.

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Arrhenius Plot

The graph obtained by plotting ln(k) against 1/T, which is used to determine the activation energy of a reaction.

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Zero-Order Kinetics (Suspensions)

A first-order reaction in which the rate of degradation depends only on the concentration of the dissolved drug.

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First-Order Kinetics

A chemical reaction where the rate of the reaction is directly proportional to the concentration of the reactant.

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Shelf Life

A measure of how long it takes for a substance to degrade to a certain extent under specific conditions.

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Hydrolysis

The process of breaking down a molecule by the addition of water.

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Bupivacaine

A drug that is used to numb a certain area of the body, often for a short duration.

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Chemical Kinetics

The study of chemical reactions and their rates of reaction.

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Study Notes

Chemical Kinetics: Application

  • Chemical kinetics studies reaction rates
  • Integrated rate laws describe reactant concentration changes over time

Integrated Rate Laws

  • Integrated rate laws allow predicting reactant concentration at any time
  • They also help calculate how long it takes for a reaction to reach a certain concentration
  • Reaction order 0,1 & 2 have unique integrated rate laws
  • Zero order: [A]t = -kt + [A]0
  • First order: ln[A]t = -kt + ln[A]0
  • Second order: 1/[A]t = kt + 1/[A]0

Reaction Order

  • Reaction order can be determined by plotting reaction data (concentration vs. time)
  • The graph revealing a straight line indicates the reaction order.
  • A zero order reaction graph shows a straight line when concentration is plotted against time
  • A first order reaction plot shows a straight line when the natural logarithm of concentration is plotted against time.
  • A second order reaction graph shows a straight line when the reciprocal of concentration is plotted against time
  • Data plots help determine reaction order

Pseudo First Order Reactions

  • In certain reactions, one reactant's concentration is significantly higher than another
  • This makes the reaction appear first order
  • Example: Hydrolysis of benzocaine – Rate=k[benzocaine][OH-]
  • [OH-] remains constant, making the reaction appear first order

First Order Reactions (ii)

  • This focuses on hydrolysis of ampicillin
  • Ampicillin hydrolysis follows pseudo first order in excess water

Zero Order Integrated Rate Law

  • A → Product is a basic zero order reaction
  • Rate = k [A]0
  • The rate of this type of reaction does not depend on the concentration of the reactant.
  • rate = k (where k is the rate constant)
  • [A]t = −kt + [A]0
  • The integrated rate law resembles y = mx + b

Zero Order Half Life

  • Fractional loss depends on [A]0 (initial concentration)
  • Half-life is when [A]t = [A]0 / 2. Calculating this time is key to understanding the zero order reaction.
  • t50 =[A]o/2k

Zero Order Shelf Life

  • Shelf life is determined by time taken for concentration (x of A) to reduce to a predetermined level
  • t= [(1−x)A0] / k, where x represents the fractional loss

Zero Order Shelf Life Example

  • Ampicillin suspension hydrolysis is example demonstrating zero order reactions
  • Shelf life depends on initial concentration and rate constant

Using the Arrhenius Equation

  • The Arrhenius equation describes the relationship between reaction rate constant (k), temperature (T) and activation energy (Ea).
  • ln k = ln A − Ea/RT
  • Plotting ln k against 1/T gives a straight line.
  • Slope=-Ea/R
  • Intercept = ln A

Hydrolysis of Bupivacaine

  • Data presented as percentage of the initial value
  • Data points recorded at different temperatures
  • Demonstrates how temperature affects degradation of bupivacaine

First Order Plots

  • Plots that graphically display first order reactions in various systems
  • These graphs illustrate the decay patterns of reactants and how it changes with time.
  • Graphs reveal the relationship between the natural logarithm of the concentration and time

Arrhenius Plot

  • Arrhenius plots reveal the temperature dependence of chemical reactions
  • Graphical representation helps visualize the relation between rate constant and reciprocal of temperature in various reaction systems

Arrhenius Calculations

  • Calculations to determine the rate constant (k) of hydrolysis reactions at different temperatures
  • Arrhenius equation provides the framework for these calculations.

Prediction of Degradation

  • Calculations to determine the half-life (t50), and shelf-life (t90) for a reaction at a specific temperature
  • Based on the rate constant and predetermined level of loss

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Related Documents

PHA 111 Chemical Kinetics PDF

Description

Explore the principles of chemical kinetics and the application of integrated rate laws in predicting reactant concentrations over time. This quiz will test your understanding of reaction orders and how to determine them using graphical data analysis.

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