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Questions and Answers
At 23C, the data for sucrose disappearance was measured in 0.5M ______.
HCl
The equation used for first order reactions is ln[A] = -kt + ln[A]______.
0
In the Arrhenius equation, the activation energy Ea is calculated using the rate coefficients at different ______.
temperatures
The rate coefficient for the decomposition of penicillin at 37°C is ______ hr−1.
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To determine the rate constant k, the concentration of the drug must be ______ at the time of analysis.
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The Arrhenius equation is represented as k = A e^(-Ea/RT), where k is the rate coefficient and Ea is the activation ______.
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A graph of lnk versus 1/T will have a slope equal to -Ea/______.
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The frequency factor, A, is related to the frequency of ______ and the probability that they are favorably oriented.
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The ______ of molecules possessing activation energy is an important factor in determining reaction rates.
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In multi-step processes, each step has a corresponding activation energy and rate ______.
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If the rate of formation of B from A is much slower than the conversion of B to C, then B does not build ______.
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The activation energy can be evaluated if you know the rate coefficient at two different ______.
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In pharmacology, evaluating activation energy is important for assessing pharmaceutical ______.
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A plot of ln[A] vs.t should give a straight line plot if ______ order kinetics (slope = −k)
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In a two-step process, k1 is the rate coefficient for conversion of A to B, while k2 is for conversion of B to ______.
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The half-life of a reaction, t½, is the time required for the concentration of a reactant to drop to ______ of its initial value.
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The smaller the rate ______, the slower the process step.
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A plot of 1/[A] vs.t should give a straight line plot if ______ order kinetics (slope = k)
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The rate of most processes increases as the ______ increases.
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In order to react, colliding molecules must have energy equal to or greater than the ______ Energy (Ea).
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The ______ factor is crucial because molecules must be oriented in a certain way for collisions to lead to a reaction.
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The increase in the rate coefficient (k) with increasing temperature affects the reaction ______.
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For zero order kinetics, the integrated form is given by the equation [A] = −kt + ______0.
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The relationship for first order kinetics is given by ln [A] = −kt + ln ______0.
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In multi-step processes, the step with the largest Ea is known as the ______ determining step.
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The rate law for the reaction A + B → C is Rate = k[A]2, which indicates that the reaction is second order with respect to [A] and ______ with respect to [B].
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When doubling the concentration of [A], the reaction rate is observed to ______.
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In zero order kinetics, the reaction rate is ______ of the concentrations of reactants.
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The general formula for zero order kinetics can be represented as [A] - [A]o = −kt, where ______ represents the initial concentration of A.
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For the reaction A + B → C, the initial rate was consistent at 4.0 x 10-5 when [A] was 0.100 and [B] was ______.
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In the table, when [A] was changed from 0.100 to 0.200 while [B] remained 0.100, the initial rate increased to ______.
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The concentration of reactant in a zero order reaction falls at a constant rate until all reactant is ______.
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In the graph plotting [A] vs. time for zero order kinetics, the relationship can be represented in the form of y = ______ + c.
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The conversion of A to B is the rate determining step for the overall process, where k1 is much less than k2: k1 ≪ k2. The rate of reaction is given by: 𝑅 = −𝑑𝐴/𝑑𝑡 = k1[A], hence k1 is the ______.
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When k1 is much greater than k2 (k1 ˃˃ k2), A is rapidly converted to B, while B is consumed in the slow ______ step.
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The conversion of B to C dominates the ______ of the process.
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Under certain circumstances, the concentration of B is assumed to be low and relatively constant, leading to the application of the ______ approximation.
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The steady state approximation leads to the equation: 𝑘1[A] = 𝑘2______, allowing us to express ______ in terms of observable parameter [A].
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In reaction kinetics, the differential form for zero order is given by: [A] = −𝑘t + ______.
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The integrated form for first order kinetics can be expressed as ln[A] = −𝑘t + ln______.
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The half-life formula for first order kinetics is defined as t1/2 = ln 2/______.
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For zero order kinetics, the half-life is calculated as t1/2 = ______0/2k.
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In the reaction of sucrose (C12H22O11) forming glucose and fructose, the balanced chemical equation is C12H22O11 + H2O → 2C______H12O6.
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Kinetics deals with the rates of ______.
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The rate of a process increases as the ______ is increased.
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Pharmacokinetics investigates the kinetics of absorption, distribution, ______, and excretion of drugs.
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Higher ______ results in faster reaction rates.
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Kinetics is key in determining how long it will take for a system to reach ______.
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Thermodynamics determines the position of ______ for a process.
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The key parameters in kinetics are variations in the concentration of ______.
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The rate of key pharmaceutical processes includes the dissolution of drug ______ and products.
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The reaction rate is the 'speed' of a ______.
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The rate of a reaction is directly proportional to the concentrations of the ______.
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In the equation Rate = k[A]x[B]y, k represents the rate ______.
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For a reaction of order zero, the rate of reaction is ______ of the concentrations of the reactants.
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The overall reaction order is represented as x + y, where x and y are called reaction ______.
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Generally, the rate of disappearance of the ______ is the same as the rate of appearance of the product.
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In the reaction 2HI(g) → H2(g) + I2(g), the rate is given by 1/2 d______/dt = d[H2]/dt = d[I2]/dt, indicating a first order with respect to ______.
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The activation ______ is the minimum energy required to initiate a reaction.
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A graph of ln[A] versus t will provide a straight line for ______ order kinetics.
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The steady state approximation leads to the equation: k1[A] = k2______, allowing us to express B in terms of observable parameter [A].
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The rate coefficient k in the Arrhenius equation is equal to A e^(-Ea/RT), where A is the ______ factor.
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In multi-step processes, each step has a corresponding activation energy and rate ______.
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If the rate of formation of B from A is much slower than the conversion of B to C, then there is no build-up of ______.
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To determine the activation energy Ea, you can compare the rate coefficients k1 and k2 at two different ______.
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A graph of ln k versus 1/T will have a slope equal to -Ea/______.
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The reaction A + B → C has a rate law of Rate = k[A]2[B]0, indicating it is ______ order with respect to [A].
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When the concentration of B was doubled, there was ______ effect on the rate of the reaction.
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In the integrated equation for zero order kinetics, the concentration of A is represented as [A] = −kt + [A]______.
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The initial rate of reaction in experiment 1 was measured at 4.0 x 10-5 when the concentrations of [A] and [B] were both ______.
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For zero order kinetics, the concentration of reactant decreases at a ______ rate until all reactant is consumed.
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In the rate law Rate = k[A]2[B]0, the term [B]0 indicates that the reaction is ______ order with respect to [B].
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Doubling the concentration of A results in the rate of the reaction being ______.
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The relationship for zero order kinetics can be expressed as [A] - [A]o = −kt, where [A]o is the ______ concentration of A.
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In the context of zero order kinetics, the rate is independent of the concentrations of ______.
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The integrated form for first order kinetics can be expressed as ln[A] = −kt + ln______.
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A plot of ln[A] vs. t should give a straight line plot if ______ order kinetics (slope = −k).
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The half-life of a reaction, t½, is the time required for the concentration of a reactant to drop to ______ of its initial value.
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The equation used for zero order kinetics is [A] = −kt + ______0.
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The rate of most processes increases as the ______ increases.
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In order to react, colliding molecules must have energy equal to or greater than the ______ Energy (Ea).
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According to the Arrhenius equation, the rate coefficient increases with increasing ______.
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For a second order reaction, the integrated rate law can be expressed as 1/[A] = kt + ______.
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The minimum energy required to initiate a process is called the ______ Energy (Ea).
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The orientation factor is crucial because molecules must be oriented in a certain way for ______ to lead to a reaction.
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The relationship for first order kinetics is given by ln [A] = −kt + ln ______0.
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Study Notes
Rate Laws
- The rate of a reaction is the speed at which reactants are converted into products.
- Rate laws express the relationship between the rate of reaction and the concentration of reactants
- The order of a reaction with respect to a particular reactant is the exponent to which the concentration of that reactant is raised in the rate law.
- Zero order: Rate of reaction is independent of the concentration of reactants.
- First Order: Rate of reaction is directly proportional to the concentration of the reactant
- Second Order: Rate of reaction is proportional to the square of the concentration of the reactant
Half-Life
- Half-life is the time it takes for the concentration of a reactant to decrease to half its initial value.
- Half-life (t½) for a zero order reaction is dependent on initial concentration.
- Half-life (t½) for a first order reaction is independent of initial concentration.
- There are different mathematical formulas for calculating the half-life for different orders of reactions
### Temperature and Rate
- Rate of reaction increases with increasing temperature.
- The rate coefficient (k) increases as temperature increases.
Collision Model
- The collision model explains the effect of temperature on reaction rate.
- Molecules must collide in order to react.
- Not all collisions lead to reaction, only collisions with correct orientation and sufficient energy will react.
- The activation energy (Ea) is the minimum energy that reacting molecules must possess in order to react.
Arrhenius Equation
- The Arrhenius equation relates the rate coefficient (k), activation energy (Ea), and temperature (T).
- The Arrhenius equation can be used to determine the activation energy for a reaction.
- Activation energy is important to evaluate pharmaceutical stability.
Multi-step processes
- Many chemical reactions occur in multiple steps.
- Each step has its own activation energy and rate coefficient.
- The slowest step in a multi-step process is the rate-determining step.
Steady State Approximation
- The steady state approximation is a method for simplifying the rate law for a multi-step process.
- The steady state approximation assumes that the concentration of an intermediate is constant over time.
- This approximation is used to derive the rate law for a complex reaction by using a single step.
Kinetics
- Kinetics studies the speed and duration of processes.
- It analyzes how quickly a process reaches equilibrium and how long it takes.
- This information is relevant for drug product shelf-life and drug absorption, distribution, and excretion.
Kinetics vs. Thermodynamics
- Thermodynamics predicts the equilibrium state of a process.
- Kinetics determines the time needed to reach that equilibrium.
- Thermodynamics clarifies the relative energies of initial and final states.
- Kinetics focuses on the energy of the process pathway, reflecting the rate.
Kinetics in a Pharmaceutical Context
- It examines the stability of drug substances (Active Pharmaceutical Ingredients) and drug products (formulations) over time.
- It analyzes the rate of manufacturing processes for both drug substances and products.
- It explores the dissolution of drug substances and products.
- It investigates the pharmacological and biochemical processes related to drugs.
Pharmacokinetics
- It investigates the kinetics of drug absorption, distribution, metabolism, and excretion.
- Also known as pharmacokinetics & drug metabolism.
- A complex specialized field.
- Requires understanding the fundamentals of kinetics.
Concentrations of Components
- Key parameters in kinetics include variations in component concentrations.
- Increasing the concentration of one or more components accelerates the process.
- Higher concentration translates to a faster reaction rate.
Temperature
- Temperature significantly impacts kinetics.
- Increasing temperature accelerates the process.
- Molecules must collide for a reaction to occur.
- Higher temperatures increase the collision frequency, leading to a faster reaction rate.
Consumption and Production During a Process
- The rate of a process can be measured by monitoring the change in concentration of components over time.
- Instantaneous rate at a specific time can be determined.
The Reaction Rate
- The reaction rate is the speed of a process.
- Rate = change in concentration of reactants or products with respect to time.
- Rate = d(products)/dt = -d(reactants)/dt.
Kinetics: Example
- Example reaction: C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
- Reaction rates usually decrease over time as reactants are consumed.
Showing the Data Graphically
- Instantaneous rate can be determined from the slope of a tangent to the concentration-time curve.
- The initial rate can be estimated by rapid monitoring.
Reaction Rates and Stoichiometry
- Example 1: C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
- Rate of reactant disappearance is equal to the rate of product appearance.
- Example 2: 2HI(g) → H2(g) + I2(g)
- Rate = -1/2 * d(HI)/dt = d(H2)/dt = d(I2)/dt
- General equation: 2A + 3B → 2C + 4D
- Rate = -1/2 * d(A)/dt = -1/3 * d(B)/dt = 1/2 * d(C)/dt = 1/4 * d(D)/dt
- The choice of component for rate measurement depends on experimental monitoring capabilities.
The Rate Law
- The rate of a reaction is proportional to the concentration of reactants.
- General equation: aA + bB → cC + dD
- Rate Law: Rate = k[A]x[B]y
- k is the rate coefficient (constant at a given temperature).
- x and y are the orders of reaction with respect to A and B.
Reaction Order
- The overall reaction order is x + y.
- Zero order: x + y = 0.
- First order: x + y = 1.
- Second order: x + y = 2.
- Reaction order cannot be determined from stoichiometry.
Determining Reaction Order
- Example: 3A + 2B → 2C + 3D
- If the process is second order in A (x = 2) and zero order in B (y = 0) then: Rate = k[A]2 and NOT Rate = k[A]3
Using the Initial Rates Method
- Example: A + B → C
- Change in [B] doesn't affect the rate, indicating zero order in B.
- Doubling [A] quadruples the rate, indicating second order in A.
- Rate Law: Rate = k[A]2[B]0 = k[A]2
Zero Order Kinetics
- Rate is independent of reactant concentration.
- Concentration falls linearly until all reactants are consumed, after which the rate drops to zero.
- Plot of [A] vs. t is linear, with the negative slope representing -k.
First Order Kinetics
- Rate is directly proportional to reactant concentration.
- Doubling [A] doubles the rate, and quartering [A] quarters the rate.
- ln[A] = -kt + ln[A]0, plot of ln[A] vs. t is linear, with the negative slope representing -k.
Second Order Kinetics
- Rate is proportional to the square of reactant concentration.
- Plot of 1/[A] vs. t is linear, with the slope representing k.
Half-life
- The half-life (t1/2) for a reaction is the time it takes for the reactant concentration to decrease to half its initial value.
- [A]t1/2 = 1/2 [A]0.
Half-life Formulas
- Zero order: t1/2 = [A]0 / 2k.
- First order: t1/2 = ln 2 / k.
- Second order: t1/2 = 1 / k[A]0.
Temperature and Rate
- Rates of most processes increase as temperature increases.
- Increased rate occurs due to a higher rate coefficient (k) with increasing temperature.
The Collision Model
- Increased temperature makes molecules move faster, leading to more collisions, thus increasing rate.
- Only a tiny fraction of collisions lead to reaction, influenced by the orientation factor and activation energy (Ea).
The Orientation Factor
- Molecules must be correctly aligned for collisions to result in reactions.
Activation Energy
- Molecules must possess sufficient energy (Ea) to react upon collision.
- This minimum energy requirement is called activation energy.
- Reactions have different Ea values.
- Multi-step processes have multiple Ea values, with the largest Ea defining the rate-determining step.
Arrhenius Equation
- k = Ae-Ea/RT
- k is the rate coefficient.
- Ea is the activation energy.
- R is the gas constant.
- T is the temperature.
- A is the frequency factor, relating to collision frequency and orientation favorability.
Arrhenius Equation Graphically
- A plot of lnk vs 1/T is linear, with slope -Ea/R and y-intercept lnA.
Multi-step Processes
- Many pharmaceutical processes involve multiple steps.
- Each step has a corresponding activation energy and rate coefficient (k).
- Example: A → B → C, with rate coefficients k1 and k2 for each step. The slower step has a smaller rate coefficient.
Rate Determining Steps
- The slowest step dictates the overall reaction kinetics.
- If the conversion from A to B is much slower than B to C, no build-up of intermediate B occurs.
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Description
This quiz covers the essential concepts of rate laws and half-life in chemical reactions. It includes definitions, order of reactions, and the implications of half-life on different reaction orders. Test your understanding of these fundamental topics in physical chemistry.
