Question

At \(444^{\circ} \mathrm{C}, \mathrm{HI}\) is \(30 \%\) dissociated. If initially 3 moles of HI are taken, the number of moles of \(\mathrm{HI}\) at equilibrium is (a) \(0.9\) (b) \(2.1\) (c) \(0.45\) (d) \(1.8\)

Short answer

At equilibrium, the number of moles of HI is 2.1.

Step-by-step solution

Establish the Chemical Equilibrium Expression

Since hydrogen iodide (HI) is dissociating, the chemical equation can be expressed as: HI(g) ⇌ H2(g) + I2(g). At equilibrium, some HI will have dissociated into H2 and I2.

Calculate the Initial and Equilibrium Concentrations

Initially there are 3 moles of HI, with no H2 or I2 present. Since 30% of HI dissociates, 0.3 * 3 moles = 0.9 moles of HI will dissociate.

Calculate the Number of Moles of HI at Equilibrium

At equilibrium, the number of moles of HI remaining is the initial moles minus the moles that dissociated: 3 moles - 0.9 moles = 2.1 moles.

Key concepts

Understanding Chemical Equilibrium

The concept of chemical equilibrium is fundamental in the field of chemistry and is vital for solving problems related to chemical reactions. At its core, chemical equilibrium refers to the state of a reaction where the rates of the forward and reverse reactions are equal, resulting in no overall change in the concentrations of the reactants and products.

A classic illustration of this concept is the dynamic equilibrium within a sealed container where a reversible reaction takes place. Even though the reactants and products are constantly converting into each other, the amount of each remains constant over time. When dealing with problems involving chemical equilibrium, it's important to understand Le Chatelier's principle, which states that a system at equilibrium will adjust to counter any changes imposed on it, such as changes in concentration, temperature, or pressure.

Utilizing these concepts allows us to predict the behavior of a system when subjected to different conditions and to calculate the equilibrium concentrations or pressures of the involved species.

Dissociation of Gases

The dissociation of gases is another key concept in the study of chemical reactions. When a gaseous compound such as hydrogen iodide (HI) breaks down into its constituent elements, like hydrogen (H2) and iodine (I2), this process is known as dissociation. This can be represented by a chemical equation showing the reaction in both the forward (breaking down) and reverse (re-forming) directions, symbolized by a double arrow (⇌).

For example, at elevated temperatures, HI gas dissociates into hydrogen and iodine gas. To solve problems related to the dissociation of gases, we look at the equilibrium constant (Kc or Kp), which depends on the concentrations or partial pressures of the gases at equilibrium. In the case of partial pressures, the equilibrium constant is represented as Kp and can be used to find the degree of dissociation, thus helping to determine the pressures or moles of each gas at equilibrium. Awareness of conditions like temperature and pressure that can shift the equilibrium position is essential for correctly interpreting and manipulating the dissociation of gases.

Moles Calculation in Chemical Reactions

The concept of moles calculation is a fundamental skill in chemistry that involves determining the number of moles of reactants or products in a chemical reaction. A mole is a unit of measurement that represents a very large number of particles, typically used to express the amount of substance. One mole corresponds to Avogadro's number (\( 6.022 × 10^{23} \) particles).

To find the number of moles of a substance, we often use the molar mass of the substance and the mass given in the problem. For reactions at equilibrium, particularly with gases, it's crucial to understand how the changes in the system affect the amount in moles of the reactants and products. As demonstrated in our exercise, using the initial number of moles and the percentage dissociation, we can calculate the remaining amount of an undissociated substance at equilibrium.

Keeping in mind the stoichiometry of the reaction, which dictates the proportions in which substances react, is vital when calculating moles during chemical reactions. For example, in the dissociation of HI, knowing that one mole of HI will produce one mole of H2 and one mole of I2 can assist in determining the mole equilibrium for each gas.