Question

Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Short answer

(a) False - Reactions with higher activation energies have fewer molecules with enough energy to overcome the activation energy barrier, resulting in slower reaction rates. (b) False - A small rate constant does not necessarily imply a small frequency factor, as the value of the rate constant is also influenced by the activation energy and the temperature. (c) True - Increasing the reaction temperature increases the kinetic energy of the molecules, causing them to move faster, leading to an increased number of successful collisions and a faster reaction rate.

Step-by-step solution

(Statement a: Comparing reactions with similar collision factors and activation energies)

For two reactions with similar collision factors, we have to determine if the one with a larger activation energy will be faster. Activation energy is the minimum amount of energy required for a reaction to occur. Reactions with higher activation energies have fewer molecules with enough energy to overcome the activation energy barrier. As a result, these reactions have a lower probability of successful collisions and slower reaction rates. Therefore, this statement is false.

(Statement b: Small rate constant and small frequency factor)

A reaction that has a small rate constant is said to have a small frequency factor. The rate constant is governed by the Arrhenius equation, which states that \(k = Ae^{-E_a/RT}\), where 'k' is the rate constant, 'A' is the frequency factor (pre-exponential factor), 'Ea' is the activation energy, 'R' is the gas constant, and 'T' is the temperature. A small rate constant does not necessarily imply a small frequency factor, as the value of the rate constant is also influenced by the activation energy and the temperature. Therefore, this statement is false.

(Statement c: Increasing reaction temperature and successful collisions)

Increasing the reaction temperature increases the fraction of successful collisions between reactants. According to the collision theory, the rate of a reaction is proportional to the number of successful collisions between reactant molecules. When the temperature increases, the kinetic energy of the molecules increases, causing them to move faster. This increased speed leads to an increased number of collisions between reactant molecules and a higher probability of successful collisions, resulting in a faster reaction rate. Therefore, this statement is true.

Key concepts

Activation Energy

Activation energy is a vital concept in understanding why certain chemical reactions occur at different rates. Imagine activation energy as a barrier that reactant molecules must overcome to transform into products. When we think about activation energy, it's helpful to visualize a hill. Reactant molecules are on one side, and the products are on the other. The top of the hill represents the activation energy barrier. Molecules must possess enough energy to reach the top and tumble down the other side, forming products.

However, not all molecules have the same amount of energy. At any given moment, only a fraction of them have sufficient energy to climb the 'energy hill.' This scenario explains why raising the temperature usually increases reaction rates: it's like giving the molecules a 'push,' increasing their chances of overcoming the barrier. With a larger activation energy, fewer molecules can make it over the hill, which leads to a slower reaction rate. So, while high activation energy implies a more stable system, it also means a less reactive one.

Arrhenius Equation

We delve into the mathematical realm to describe reaction rates with the Arrhenius equation. This crucial equation links the rate of a chemical reaction with temperature and activation energy, providing essential insight into the kinetic nature of reactions. Pioneered by Svante Arrhenius, the equation is depicted as \( k = Ae^{-\frac{E_a}{RT}} \), where:\
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• \( k \) is the rate constant reflecting the reaction speed.
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• \( A \) is the frequency factor indicating the number of times reactants collide with proper orientation.
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• \( E_a \) is the activation energy needed to initiate the reaction.
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• \( R \) is the universal gas constant, connecting energy with temperature and amount of substance.
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• \( T \) is the absolute temperature, measured in Kelvins, influencing the kinetic energy of molecules.
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The equation showcases how a higher temperature (\( T \)) or lower activation energy (\( E_a \)) increases the rate constant (\( k \)), hence speeding up the reaction. Understanding this equation empowers us to predict how a change in conditions affects reaction rates, which is invaluable in industries that rely on precise chemical reactions.

Collision Theory

Collision theory provides a microscopic view of how chemical reactions proceed. According to this theory, for a reaction to happen, reactants must collide with the correct orientation and sufficient energy to overcome the activation energy. It's similar to scoring a goal in soccer; the ball (reactants) must be kicked (collide) with enough force (energy) and the correct angle (orientation) to find the net (form products).

Thus, when we increase the temperature, we're essentially 'training' our soccer players to be faster and stronger, which relates directly to the number of goals they'll score, i.e., the rate of reaction. More energetic collisions lead to a higher probability that those collisions will surpass the activation energy threshold, resulting in a faster reaction rate. This underpins why certain reactions only occur at high temperatures or why refrigeration can preserve food—cooler temperatures result in fewer 'goals' or reaction events.