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.

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.

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 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.