Question

When the volume of a vessel containing a gaseous equilibrium system is decreased, the \(\quad\) of the gaseous substances present is initially increased.

Short answer

When the volume of a vessel containing a gaseous equilibrium system is decreased, the parameter of the gaseous substances that initially increases is the pressure. This increase in pressure occurs due to the compression of the gas into a smaller space, as explained by Boyle's law (\(P_1V_1 = P_2V_2\)). The system responds to this disturbance according to Le Chatelier's principle, shifting the equilibrium to minimize the pressure change.

Step-by-step solution

Understand the initial condition

We have a gaseous equilibrium system inside a vessel. It is important to recognize that the system is initially at equilibrium, which means the rate of the forward reaction is equal to the rate of the reverse reaction, and the concentration of gaseous substances remains constant.

The effect of decreasing volume on gas pressure

When the volume of the container is decreased, the gaseous substances are compressed into a smaller space. According to Boyle's law (provided the temperature remains constant), the pressure of the gas increases as the volume decreases. Mathematically, this can be represented as: \(P_1V_1 = P_2V_2\) Where \(P_1\) is the initial pressure, \(V_1\) is the initial volume, \(P_2\) is the final pressure, and \(V_2\) is the final volume.

The effect of increased pressure on equilibrium

When the pressure of the gaseous substances is increased, this disturbance affects the equilibrium of the system. According to Le Chatelier's principle, the system will react in a way to minimize the effect of the disturbance and restore the equilibrium. In this case, the equilibrium will shift in the direction that produces fewer moles of gas, effectively reducing the pressure. Note that this step is relevant only if the equilibrium involves reactions with different numbers of moles of gas on either side of the reaction. If the number of moles is the same, the increase in pressure will have no effect on the equilibrium position.

Determine the parameter that initially increases

From Step 2, we find that when the volume is decreased, the pressure of the gaseous substances is initially increased. Hence, the parameter of the gaseous substances that initially increases upon decreasing the volume of the vessel is the pressure.

Key concepts

Le Chatelier's Principle

Understanding Le Chatelier's principle is fundamental to predicting how a chemical system at equilibrium reacts to changes in conditions. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change.

Take the gaseous equilibrium system in our exercise for example. When you decrease the volume of the vessel, you are upsetting the equilibrium by increasing the pressure of the gas inside. According to Le Chatelier's principle, the system will adjust to minimize this increase in pressure. It achieves this by shifting the equilibrium toward the side of the reaction with fewer moles of gas, thus reducing the total gas volume and, consequently, the pressure. This behavior is crucial for chemists who want to manipulate the yield of reactions in industrial processes.

Boyle's Law

Boyle's law is an essential part of understanding gas behaviors. It describes the inverse relationship between the volume and pressure of a gas at constant temperature; as one increases, the other decreases. This law can be expressed mathematically as:
\(P_1V_1 = P_2V_2\)
where \(P_1\) and \(V_1\) represent the initial pressure and volume, and \(P_2\) and \(V_2\) represent the final pressure and volume, respectively. In the context of our exercise, when the volume of the gaseous system is decreased, Boyle's law helps us understand that the pressure must increase if the temperature remains unchanged. This concept is pivotal when working with gases in closed systems, such as syringes or pistons.

Chemical Equilibrium

Chemical equilibrium is a state where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentration of reactants and products. However, it's important to note that reaching equilibrium doesn't mean the reactants and products are equal in concentration, but that their ratios remain stable over time.

At equilibrium, any change induced to a system—whether it's pressure, temperature, or concentration—will cause the equilibrium to shift in a direction that opposes the change, an application of Le Chatelier's principle. This balance is delicate and can be exploited for various purposes, including industrial synthesis and controlling reaction yields.

Gas Pressure

Gas pressure is the force that a gas exerts on the walls of its container, and it is a critical variable in the behavior of gases. It's caused by gas molecules colliding with the container walls. A crucial thing to remember is that when the volume of a container is reduced, the gas molecules have less space to move in, which leads to more frequent collisions and, as a result, increased pressure.

This concept is directly observed in the exercise problem, where decreasing the volume of the container leads to an increase in the pressure of the gaseous equilibrium system. Understanding how pressure works is vital for studying gaseous behavior in both natural phenomena and in engineered systems like engines and HVAC units.