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?

By plotting data according to different integrated rate laws Signup and view all the answers

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

Time elapsed in the reaction Signup and view all the answers

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

Shelf life increases as initial concentration increases. Signup and view all the answers

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

t½ = 0.5 [A]0 / k 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)?

434 hours Signup and view all the answers

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

Decreases the shelf life Signup and view all the answers

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

[A]t = [A]0 – kt Signup and view all the answers

What is the definition of a pseudo first order reaction?

A reaction that behaves as first order when one reactant concentration remains constant. Signup and view all the answers

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

$ ext{ln}[A]t = -kt + ext{ln}[A]0$ 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?

$t_{1/2} = rac{0.693}{k}$ Signup and view all the answers

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

Concentration of ampicillin being significantly higher than water. Signup and view all the answers

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

$t_{90} = rac{0.105}{k}$ Signup and view all the answers

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

It is constant regardless of reactant concentration. Signup and view all the answers

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

It is constant and independent of initial concentration. Signup and view all the answers

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

It decreases linearly with time. Signup and view all the answers

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

The time taken for the concentration to decrease from 100% to 50%. Signup and view all the answers

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

The plot of [A] versus time gives a straight line. Signup and view all the answers

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

Rate = k[A]^2 Signup and view all the answers

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

1/[A]t = kt + 1/[A]0 Signup and view all the answers

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

The time required for half the reactant to be converted into products. 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?

t90 = 1/9[A]0 k Signup and view all the answers

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

It is used to quantify changes over time. Signup and view all the answers

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

It influences the half-life of the reaction. Signup and view all the answers

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

The formulation of the integrated rate law changes. Signup and view all the answers

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

A linear relationship between 1/[A] and time. Signup and view all the answers

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

Shelf life increases as concentration increases. Signup and view all the answers

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

By taking the negative of the slope and dividing it by R. Signup and view all the answers

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

50 °C Signup and view all the answers

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

It provides a way to calculate activation energy. Signup and view all the answers

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

Only the dissolved drug in solution degrades appreciably. Signup and view all the answers

What does the intercept in the Arrhenius Equation represent?

The natural logarithm of the rate constant A. Signup and view all the answers

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

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

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

51.7 kJ mol-1 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?

The drug's shelf life decreases. Signup and view all the answers

Which parameter in the Arrhenius Equation relates to temperature?

Gas constant (R) Signup and view all the answers

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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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.