Question

A crystal of dinitrogen tetroxide (melting point, \(\left.-9.3^{\circ} \mathrm{C} ; \text { boiling point, } 21.3^{\circ} \mathrm{C}\right)\) is added to an equilibrium mixture of dintrogen tetroxide and nitrogen dioxide that is at \(20.0^{\circ} \mathrm{C} .\) Will the pressure of nitrogen dioxide increase, decrease, or remain the same? Explain.

Short answer

According to the predications made based on Le Chatelier's Principle, the pressure of the nitrogen dioxide (\(NO_2\)) will increase.

Step-by-step solution

Understand Le Chatelier's Principle

According to Le Chatelier's principle, an equilibrium system will react to minimise any changes imposed upon it. When a system in equilibrium is disturbed, it will shift the equilibrium to oppose the change. In this case, we need to figure out whether adding the solid \(N_2O_4\) will disturb the equilibrium and, if so, how will the system counteract that disturbance.

Consider the Temperature

The solid \(N_2O_4\) will start to melt at temperatures above \(-9.3^{\circ}C\) and will completely convert to gas at temperatures above its boiling point (\(21.3^{\circ}C\)). In this case, we are at \(20.0^{\circ}C\), which is above the melting point but below the boiling point. Therefore, the added solid \(N_2O_4\) will turn into a liquid and will eventually vaporise and establish a new equilibrium with the \(NO_2\) gas.

Predict the Change in Pressure

When the \(N_2O_4\) is added and eventually vaporises, it will decompose as per the reaction \(N_2O_4(s) \leftrightarrow 2NO_2(g)\). This will increase the amount of \(NO_2\) gas in the system, which in turn increases its partial pressure. Thus, the system at the new equilibrium will have a higher partial pressure of \(NO_2\) as it shifts to counter the addition of more \(N_2O_4\) in accordance with Le Chatelier's Principle.

Key concepts

Chemical Equilibrium

The concept of chemical equilibrium is central to understanding how reactions occur in closed systems. When a chemical reaction reaches a state of balance, in which the forward and reverse reaction rates are equal, we say the reaction is at equilibrium. At this point, the concentrations of reactants and products become constant. It's important to note that this doesn't mean the reactants and products are in equal concentrations, but rather that their rates of formation are stable.

Le Chatelier's Principle is a vital tool for predicting the behavior of a system in equilibrium when it is subjected to changes. If you disturb the equilibrium by altering concentration, temperature, or pressure, the system will adjust itself to counteract the effect of the disturbance and re-establish equilibrium. Understanding this principle allows us to predict whether nitrogen dioxide pressure will increase or decrease when a crystal of dinitrogen tetroxide is added to an equilibrium mixture at a specific temperature.

Phase Change

A phase change is a physical process where a substance transitions from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. Each substance has specific temperatures at which these changes occur, known as the melting and boiling points. For dinitrogen tetroxide, the melting point is -9.3°C and the boiling point is 21.3°C. These thresholds are crucial in determining the behavior of the substance under various temperature conditions.

When we introduce a solid into an environment where the temperature is between its melting and boiling points, we can expect it to undergo a phase change from solid to liquid and eventually to gas. In the case of our equilibrium mixture at 20.0°C, the dinitrogen tetroxide solid will melt, and then the liquid will begin to vaporize into the gas phase, eventually affecting the equilibrium and the partial pressure of nitrogen dioxide in the system.

Partial Pressure

Partial pressure is a term used to describe the pressure that a specific gas in a mixture of gases would exert if it alone occupied the entire volume of the mixture at the same temperature. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture, as stated by Dalton's Law of Partial Pressures.

When the exercise mentions that a crystal of dinitrogen tetroxide is added to an equilibrium mixture at a certain temperature, what we're examining is how this addition affects the partial pressure of nitrogen dioxide. As more dinitrogen tetroxide becomes gas and decomposes into nitrogen dioxide, the partial pressure of nitrogen dioxide in the mixture will increase due to the rise in the number of nitrogen dioxide molecules in the system. This form of analysis is used to predict changes in the system based on Le Chatelier's Principle and provides insights into how equilibrium reactions respond to changes in the amount of substances involved.