Problem 127 - Introductory Chemistry Atoms First

Question

Would you expect a reaction in which all reactants are in the gas phase to go faster, slower, or remain at the same rate if the size of the container is increased while everything else is held constant? Explain.

Step-by-Step Solution

Answer

In summary, a reaction with all reactants in the gas phase will go slower if the size of the container is increased while everything else is held constant. The decrease in pressure due to increased volume leads to reduced collision frequency between reactant molecules, ultimately resulting in a slower reaction rate.

Step 1: Understand the relationship between volume and pressure

According to Boyle's law, for a given amount of gas at a constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this can be represented as: \(P_1V_1=P_2V_2\) where \(P_1\) and \(V_1\) are the initial pressure and volume, and \(P_2\) and \(V_2\) are the final pressure and volume of the system.

Step 2: Explain the impact of increasing the volume of the container

If the volume of the container is increased while everything else is held constant, the pressure of the gaseous reactants will decrease, according to Boyle's law. This is because, with more space available, the gas particles will collide less frequently with the walls of the container, resulting in a lower pressure.

Step 3: Connect the change in pressure to the reaction rate

The reaction rate is related to the concentration of the reactants present. In a gas-phase reaction, the concentration of the reactants can be related to their pressure. For a reaction where all reactants are gases, the rate of the reaction often depends on the pressure of the reactants. As pressure decreases due to the increase in container size, the collision frequency between reactant molecules will reduce, leading to a slower reaction rate.

Step 4: Conclusion

We would expect a reaction in which all reactants are in the gas phase to go slower if the size of the container is increased while everything else is held constant. This is because the pressure of the gaseous reactants will decrease with the increase in volume, leading to a reduced collision frequency and thus a slower reaction rate.

Key Concepts

Boyle's Law

Boyle's Law is a fundamental principle in physical chemistry that describes the inverse relationship between the pressure and the volume of a gas at constant temperature. Effectively, if you increase the volume of a gas, its pressure will decrease, assuming temperature remains unchanged. This relationship is crucial in understanding how changes in the condition of a sealed environment might affect gas phase reactions.

In the mathematical form, Boyle's Law is expressed as \(P_1V_1 = P_2V_2\), where \(P_1\) and \(V_1\) represent the initial pressure and volume, and \(P_2\) and \(V_2\) signify the final pressure and volume after the change. For example, when you inflate a balloon, the pressure of the gas inside increases as the volume decreases when you let go of the balloon's opening. Conversely, if you were to place a gas in a larger container without adding more of the gas, the pressure would decrease as the molecules have more space to move about without colliding as often with the container's walls.

Gas Phase Reactions

Gas phase reactions involve reactants that are all in the gaseous state. In these reactions, molecules move freely and randomly at high speeds, and reactions occur when they collide with sufficient energy and correct orientation. The rate of these reactions can be directly affected by changes in conditions such as pressure and temperature.

Given that gases are compressible, changing the volume of the container holding the gas can lead to a change in pressure, which consequently affects reaction rates. If the pressure is high, molecules are more closely packed, and thus collisions between reactant molecules are more frequent, which often increases the rate at which they react. This dynamic of gases is critical to industrial processes, such as synthesizing ammonia in the Haber process, where gases are reacted under high pressures to increase yields.

Collision Frequency

Collision frequency is a term used to describe how often molecules in a gas collide with each other. It is a key factor in the kinetics of gas phase reactions because only through collisions can molecules react together. Factors that increase the chance of collisions usually raise the rate of a reaction and vice versa.

When the volume of a gas container is increased and the gas expands, the molecules become more spread out. This reduced density leads to a decrease in collision frequency, as there are fewer molecules per unit volume to collide with one another. Consequently, this influences reaction rates because a reaction cannot occur if reactant molecules do not collide. Therefore, in the context of the original exercise, increasing the container size while maintaining everything else constant would decrease the reaction rate due to a decrease in collision frequency.