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Chapter 7: Problem 49

Assume that two different reactions are taking place at the same temperature. In reaction A, two different spherical molecules collide to yield a product. In reaction \(\mathrm{B}\), the shape of the colliding molecules is rodlike. Each reaction has the same number of collisions per second and the same activation energy. Which reaction goes faster?

Short Answer

Expert verified
Reaction A (spherical molecules) goes faster due to easier molecular orientation.

Step by step solution

01

Understand the Reaction Types

Reaction A involves two different spherical molecules colliding, while Reaction B involves rodlike molecules colliding. These different molecular shapes affect how the molecules interact during collisions.
02

Consider the Molecular Orientation

Molecular orientation plays a significant role in reaction rates. Spherical molecules have a uniform surface, making them more likely to align correctly for a reaction during a collision. Rodlike molecules, on the other hand, require specific orientations to react that are harder to achieve randomly.
03

Evaluate Impact of Shape on Reaction Rate

The shape of the molecules affects how frequently they react upon collision. Spherical molecules in Reaction A, with their uniform surface, tend to react more readily upon collision than rodlike molecules in Reaction B.
04

Analyze Activation Energy and Collision Frequency

Both reactions have the same activation energy and the same number of collisions per second, meaning these factors do not differentiate the speed of the reactions. The difference is solely due to molecular shape and orientation effects.
05

Conclusion: Determine the Faster Reaction

Given that spherical molecules react more readily upon collision due to their shape, Reaction A will proceed faster than Reaction B, despite having the same activation energy and collision frequency.

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Key Concepts

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

Molecular Orientation
In chemical reactions, the orientation of molecules during a collision is crucial for determining whether a reaction will occur. Imagine molecules as pieces of a puzzle; if they don't align properly, they won't fit together to create the desired product.
  • Spherical molecules: Thanks to their symmetrical shape, they can align more easily in multiple orientations for successful reactions. This increases the likelihood of a reaction when colliding.
  • Rodlike molecules: These require very specific alignment to react effectively. Think of them as matchsticks; only if aligned in a very particular way will they ignite.
This concept plays a critical role in reaction rates, with spherical molecules generally having a favorable orientation upon collision, thereby increasing reaction speed.
Activation Energy
Activation energy is the energy barrier that must be overcome for a reaction to proceed. It is like a hill that reactants must climb before they can transform into products.
  • Even if two reactions have identical activation energies, other factors, like molecular orientation, can affect the overall reaction rate.
  • It is specifically noted that, although both reactions A and B have the same activation energy, it is the ease of orientation for the spherical molecules that distinguishes their speed.
Thus, while activation energy is a critical threshold needed for a reaction, how molecules are configured during a collision is also important in determining how fast the reaction occurs.
Collision Theory
Collision theory explains how chemical reactions occur and why certain reactions occur faster than others. According to this theory, particles must collide with sufficient energy and in the proper orientation for a reaction to take place.
  • The rate of reaction is proportional to the number of effective collisions per second.
  • Sufficient energy: Reactants must collide with an energy equal to or greater than the activation energy.
  • Proper orientation: Particles must align in a way that allows the formation of new bonds.
In our exercise, even though the number of collisions and the activation energy are constant for both reactions, the orientation of colliding particles is the key factor. Spherical molecules have more effective collisions than the rodlike ones, making Reaction A faster.

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Most popular questions from this chapter

Consider the reaction shown below at room temperature $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{S}(g)$$ The equilibrium constant, \(\mathrm{K},\) is equal to \(1.1 \times 10^{7} . \mathrm{A}\) mixture of reactants and products at room temperature contains \(0.25 M \mathrm{H}_{2}, 0.15 \mathrm{MS}_{2},\) and \(0.50 \mathrm{M} \mathrm{H}_{2} \mathrm{S}\) (a) Is this reaction at equilibrium? (b) In which direction does the reaction proceed to reach equilibrium? (c) Assuming the reactants remain at the same equilibrium concentrations, what would the concentration of the product have to be in order to establish equilibrium?

Consider the equilibrium of phosphorus pentachloride, \(\mathrm{PCl}_{5},\) with its decomposition products, where \(K=6.3 \times 10^{-4}\) at a certain temperature. $$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$At equilibrium, it is found that the concentration of \(\mathrm{PCl}_{5}\) is three times the concentration of \(\mathrm{PCl}_{3}\). Determine the concentration of \(\mathrm{Cl}_{2}\) under these conditions.

A quart of milk quickly spoils if left at room temperature but keeps for several days in a refrigerator. Explain.

How could you increase the rate of a gaseous reaction without adding more reactants or a catalyst and without changing the temperature?

The reaction of carbon disulfide with chlorine is as follows: $$\mathrm{CS}_{2}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{CCl}_{4}(g)+\mathrm{S}_{2} \mathrm{Cl}_{2}(g)+238 \mathrm{kJ}$$ Predict the effect of the following changes to the system on the direction of equilibrium. (a) The pressure on the system is doubled. (b) \(\mathrm{CCl}_{4}\) is removed as it is generated. (c) Heat is added to the system. (d) A catalyst is added to speed up the reaction.
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