Problem 57 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

(a) False: Reactions with larger activation energy generally take longer to occur, making them slower, not faster. (b) False: Having a small rate constant does not necessarily mean having a small frequency factor. (c) True: Higher temperatures result in higher kinetic energy, boosting the probability of successful collisions between molecules and increasing the overall reaction rate.

Step 1: Statement (a) Analysis

To determine whether the statement is true or false, we need to understand the relationship between activation energy and the rate of a reaction. Activation energy is the minimum energy required for a chemical reaction to take place. Reactions with lower activation energy generally proceed faster, whereas reactions with higher activation energy proceed slower. Now, let's examine the statement.

Step 2: Statement (a) Solution

The statement says, "If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster." This statement is \(\textbf{false}\) since reactions with larger activation energy generally take longer to occur, making them slower, not faster.

Step 3: Statement (b) Analysis

We need to understand the role of the rate constant (k) and the frequency factor (A) in a reaction's rate. The rate constant is a proportionality constant that relates the rate of a reaction to the concentration of the reactants, while the frequency factor is a measure of the number of collisions between molecules per unit time. The Arrhenius equation relates the rate constant, activation energy, and temperature, as follows: \(k = Ae^{\frac{-E_a}{RT}}\) In the equation, k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Let's analyze the statement.

Step 4: Statement (b) Solution

The statement says, "A reaction that has a small rate constant must have a small frequency factor." According to the Arrhenius equation, a small rate constant (k) could result from either a small frequency factor (A), high activation energy (Ea), or low temperature (T). Therefore, the statement is \(\textbf{false}\) because having a small rate constant does not necessarily mean having a small frequency factor.

Step 5: Statement (c) Analysis

Let's analyze the relationship between reaction temperature and the fraction of successful collisions between reactants. The number of successful collisions depends on the kinetic energy of the molecules. As the temperature increases, the molecules have more kinetic energy, which in turn leads to an increased likelihood of successful collisions. Let's examine the statement.

Step 6: Statement (c) Solution

The statement says, "Increasing the reaction temperature increases the fraction of successful collisions between reactants." This statement is \(\textbf{true}\) as higher temperatures result in higher kinetic energy, boosting the probability of successful collisions between molecules and increasing the overall reaction rate.