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Chapter 6: Problem 47

Indicate which factors affect the rate of a reaction. a. \(\Delta{G}^\circ\) b. \(\Delta{H}^\circ\) c. \(E_a\) d. temperature e. concentration f. \(K_{eq}\) g. \(k\) h. catalysts i. \(\Delta{S}^\circ\)

Short Answer

Expert verified
Factors affecting reaction rate: \(E_a\), temperature, concentration, \(k\), catalysts.

Step by step solution

01

Identifying Reaction Parameters

First, let's identify what each given symbol represents: \(\Delta{G}^\circ\) is the standard Gibbs free energy change, \(\Delta{H}^\circ\) is the standard enthalpy change, \(E_a\) is the activation energy, temperature is a measure of the kinetic energy, concentration refers to the amount of reactant present, \(K_{eq}\) is the equilibrium constant, \(k\) is the rate constant, catalysts are substances that increase the rate of reaction without being consumed, and \(\Delta{S}^\circ\) is the standard entropy change.
02

Understanding Factors Influencing Reaction Rate

The rate of a reaction is primarily influenced by factors that affect how quickly reactants can transform into products. This includes activation energy \(E_a\), temperature, concentration of reactants, the rate constant \(k\), and the presence of catalysts, which lower the activation energy.
03

Analyzing Each Factor

- \(\Delta{G}^\circ\), \(\Delta{H}^\circ\), and \(\Delta{S}^\circ\) describe thermodynamic properties but don't directly affect reaction rates unless through \(E_a\).- \(E_a\) directly affects how quickly reactants overcome the energy barrier.- Temperature increases kinetic energy, often increasing reaction rate.- Higher concentration generally increases reaction rate due to more frequent collisions.- \(K_{eq}\) is related to equilibrium position, not reaction rate.- \(k\) directly determines the reaction speed and is influenced by temperature.- Catalysts lower \(E_a\), thus increasing the reaction rate.
04

Identifying Relevant Factors

Upon reviewing each factor: \(E_a\), temperature, concentration, \(k\), and catalysts directly affect the reaction rate. The remaining thermodynamic parameters like \(\Delta{G}^\circ\), \(\Delta{H}^\circ\), \(\Delta{S}^\circ\), and \(K_{eq}\) do not directly influence the rate under standard conditions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Activation Energy
Activation energy, denoted by \(E_a\), is a crucial factor that affects the rate of a chemical reaction. It is the minimum energy that reactant molecules must possess to successfully collide and transform into products. Think of \(E_a\) as an energy barrier that needs to be overcome for the reaction to occur.Several important points about activation energy:
  • Higher \(E_a\) means a slower reaction rate. Reactants need more energy to reach the required energy barrier.
  • Lower \(E_a\) leads to a faster reaction, as it's easier for reactants to transform into products.
  • Changes in temperature or the use of a catalyst can alter the \(E_a\) of a reaction.
Mobilizing enough energy to surpass the activation energy is vital, which is why we sometimes have to heat or provide other forms of energy to initiate certain reactions. Understanding \(E_a\) helps in predicting how a reaction will proceed and how to manipulate conditions to achieve desired reaction speeds.
Temperature Effects
Temperature significantly impacts the rate of a chemical reaction. Simply put, as temperature increases, the kinetic energy of the molecules also rises. More energetic molecules are more likely to have successful collisions:Key facts about temperature effects:
  • An increase in temperature generally increases the reaction rate by allowing more molecules to surpass the activation energy barrier.
  • This is often quantified by the Arrhenius Equation: \( k = A \exp\left(\frac{-E_a}{RT}\right) \) where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.
  • A 10掳C rise can often double the reaction rate, a rule of thumb known as the **van 't Hoff rule**.
Knowing how temperature affects reactions helps in controlling industrial processes and predicting reaction behaviors under different environmental conditions.
Catalysts
Catalysts play a fundamental role in speeding up chemical reactions without undergoing permanent chemical changes themselves. They operate by lowering the activation energy \(E_a\), making it easier for reactant molecules to transition to the product side:Important aspects of catalysts:
  • Catalysts provide an alternative pathway with a lower \(E_a\). Thus, even at lower temperatures, reactions can proceed faster.
  • They don't alter the equilibrium position; instead, they help the system reach equilibrium more quickly.
  • Enzymes are natural catalysts that play essential roles in biological processes by significantly enhancing reaction rates.
Understanding catalysts allows chemists to design better processes for everything from industrial synthesis to pharmaceutical production, ensuring reactions are both efficient and timely. Catalysts help in reducing energy requirements and costs, making them valuable in many sectors.

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Most popular questions from this chapter

Explain why HC \(\equiv\) CH is more acidic than CH\(_3\)CH\(_3\), even though the C - H bond in HC \(\equiv\) CH has a higher bond dissociation energy than the C- H bond in CH\(_3\)CH\(_3\).

Draw an energy diagram for a two-step reaction, A \(\rightarrow\) B \(\rightarrow\) C, where the relative energy of these compounds is C < A < B, and the conversion of B \(\rightarrow\) C is rate-determining.

For each rate equation, what effect does the indicated concentration change have on the overall rate of the reaction? [1] rate= \(k\)[CH\(_3\)CH\(_2\)Br][\(^-\)OH] a. tripling the concentration of CH\(_3\)CH\(_2\)Br only b. tripling the concentration of \(^-\)OH only c. tripling the concentration of both CH\(_3\)CH\(_2\)Br and \(^-\)OH [2] rate = \(k\)[(CH\(_3)_3\)COH] a. doubling the concentration of (CH\(_3)_3\)COH b. increasing the concentration of (CH\(_3)_3\)COH by a factor of 10

Draw an energy diagram for the Br\(\emptyset\)nsted-Lowry acid-base reaction of CH\(_3\)CO\(_2\)2H with \(^-\)OC(CH\(_3)_3\) to form CH\(_3\)CO\({_2}^-\) and (CH\(_3)_3\)COH. Label the axes, starting materials, products, \(\Delta{H}^\circ\), and $E_a. Draw the structure of the transition state.

Without looking at a table of bond dissociation energies, determine which bond in each pair has the higher bond dissociation energy. a. H - Cl or H - Br b. CH\(_3\) - OH or CH\(_3\) - SH
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