Problem 73 - Chemistry

Question

For the following reactions, predict whether the mole fraction of the reactants or products increases or remains the same when the volume of the reaction vessel is increased. a. \(\operatorname{Br}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{HBr}(g)\) b. \(2 \mathrm{CH}_{4}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)\) c. \(2 \mathrm{HI}(g) \leftrightharpoons \mathrm{I}_{2}(s)+\mathrm{H}_{2}(g)\)

Step-by-Step Solution

Answer

For each reaction: a. The mole fraction of reactants and products remains the same. b. The mole fraction of reactants decreases, while the mole fraction of products increases. c. The mole fraction of reactants increases, while the mole fraction of products decreases.

Step 1: (Balancing the equation)

First, we need to make sure the given equation is balanced: \[ \mathrm{Br}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{HBr}(g) \] Here, the reaction is already balanced.

Step 2: (Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (1 mole of Br2 and 1 mole of H2). On the product side, there are 2 moles of gas molecules (2 moles of HBr).

Step 3: (Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, both sides have the same number of gas moles, so the reaction will be unaffected, and the mole fraction of the reactants and products will remain the same. #b. Reaction 2:

Step 4: (Balancing the equation)

First, we need to make sure the given equation is balanced: \[ 2 \mathrm{CH}_{4}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g) \] Here, the reaction is already balanced.

Step 5: (Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (2 moles of CH4). On the product side, there are 4 moles of gas molecules (1 mole of C2H2 and 3 moles of H2).

Step 6: (Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, the reaction will shift to the right (toward the products). So, the mole fraction of the reactants will decrease, while the mole fraction of the products will increase. #c. Reaction 3:

Step 7: (Balancing the equation)

First, we need to make sure the given equation is balanced: \[ 2 \mathrm{HI}(g) \leftrightharpoons \mathrm{I}_{2}(s)+\mathrm{H}_{2}(g) \] Here, the reaction is already balanced.

Step 8: (Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (2 moles of HI). On the product side, there is 1 mole of gas molecule (1 mole of H2; note that I2 is a solid and thus not included in gas mole counting).

Step 9: (Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, the reaction will shift to the left (toward the reactants). So, the mole fraction of the reactants will increase, while the mole fraction of the products will decrease.

Key Concepts

Equilibrium Reactions

In chemistry, equilibrium reactions occur when the rates of the forward and reverse reactions are equal, resulting in a stable balance of reactants and products. This balance is known as chemical equilibrium, and it is crucial to understand it to predict how a reaction will respond to changes in conditions such as temperature, pressure, or concentration. When a system is at equilibrium, the concentrations of reactants and products remain constant over time.

• In an equilibrium reaction, adjustments like temperature and pressure can alter the position of equilibrium without changing the equilibrium constant itself.
• Knowing the position of equilibrium helps chemists control the outcomes of reactions and make predictions about reaction behavior.

Gas Moles

The number of gas moles in a chemical reaction refers to the quantity of gaseous reactants or products involved in the reaction. Identifying the gas moles on each side of a balanced chemical equation is essential for understanding how changes in pressure and volume affect the reaction.

• When considering gas reactions, keep in mind the ideal gas law which states that pressure and volume are inversely related, assuming temperature and mole number are constant.
• Gas moles play a significant role in determining how the equilibrium will shift when alterations in pressure or volume occur, particularly when these changes are influenced by an external factor such as the expansion or compression of the reaction vessel.

Reaction Direction

Le Chatelier’s Principle provides insight into the direction in which a reaction will shift under imposed changes. When an equilibrium reaction is subjected to a change, such as a variation in pressure or volume, the system tends to counteract this change to re-establish equilibrium.

• In a situation where the volume is increased, the pressure decreases. According to Le Chatelier's Principle, the system will shift in the direction that results in an increase in pressure, generally towards the side of the reaction with more gas moles.
• By predicting the reaction direction, chemists can manipulate reaction conditions to favor the formation of desired products or reactants, optimizing industrial chemical processes.

Mole Fraction Changes

The mole fraction of a substance in a mixture is the ratio of the number of moles of that substance to the total number of moles of all substances present. This concept is crucial in understanding how volume changes affect the distribution of reactants and products in a gaseous equilibrium.

• When the volume of a reaction vessel is increased, the mole fractions of reactants and products can shift depending on the change in the number of gas moles, reflecting the system's effort to re-equilibrate.
• If the side of the reaction with more gas moles is favored, the mole fraction of that side will increase, impacting how concentrations are distributed within the system.

Understanding mole fraction changes is vital for predicting the outcomes of reactions and designing chemical processes that are efficient and yield high-quality products.