State what happens to the concentration of the indicated substance when each of the following equilibrium systems is compressed. (a) \(\mathrm{NO}_{2}\) (g) in \(2 \mathrm{~Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{~s})=\) \(2 \mathrm{PbO}(\mathrm{s})+4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) (b) \(\mathrm{NO}(\mathrm{g})\) in \(3 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I})=\) \(2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\) (c) \(\mathrm{HI}(\mathrm{g})\) in \(2 \mathrm{HCl}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{~s})=2 \mathrm{Hl}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (d) \(\mathrm{SO}_{2}\) (g) in \(2 \mathrm{SO}_{2}\) (g) \(+\mathrm{O}_{2}\) (g) \(\rightleftharpoons 2 \mathrm{SO}_{3}\) (g) (c) \(\mathrm{NO}_{2}(\mathrm{~g})\) in \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{NO}_{2}(\mathrm{~g})\)

Step by step solution

01

Identify the Change in Condition - Compression

Compression of an equilibrium system decreases its volume, causing an increase in pressure. According to Le Chatelier’s Principle, the system will adjust its position to counteract the change. The equilibrium will shift towards the side with fewer moles of gas to reduce the pressure.

02

Analyze Reaction (a)

The balanced chemical equation for reaction (a) is: \[2 \mathrm{Pb(NO_3)_2(s)} = 2 \mathrm{PbO(s)} + 4 \mathrm{NO_2(g)} + \mathrm{O_2(g)}\]This reaction has 5 moles of gaseous products and no gaseous reactants. When compressed, the system will react to reduce the pressure by shifting the equilibrium to the left. However, because there are no gaseous reactants, compression will not affect the position of the equilibrium for this reaction.

03

Analyze Reaction (b)

The balanced chemical equation for reaction (b) is: \[3 \mathrm{NO_2(g)} + \mathrm{H_2O(l)} = 2 \mathrm{HNO_3(aq)} + \mathrm{NO(g)}\]This reaction has 4 moles of gaseous reactants and 1 mole of gaseous product. When compressed, the equilibrium will shift towards the right to reduce the pressure, increasing the concentration of NO.

04

Analyze Reaction (c)

The balanced chemical equation for reaction (c) is: \[2 \mathrm{HCl(g)} + \mathrm{I_2(s)} = 2 \mathrm{HI(g)} + \mathrm{Cl_2(g)}\]This reaction has 2 moles of gaseous reactants and 3 moles of gaseous products. When compressed, the equilibrium will shift towards the left to reduce the pressure, decreasing the concentration of HI.

05

Analyze Reaction (d)

The balanced chemical equation for reaction (d) is: \[2 \mathrm{SO_2(g)} + \mathrm{O_2(g)} \rightleftharpoons 2 \mathrm{SO_3(g)}\]All reactants and products in this reaction are gases, with 3 moles of gaseous reactants and 2 moles of gaseous products. When compressed, the equilibrium will shift towards the right to reduce the pressure, increasing the concentration of SO3 and decreasing the concentration of SO2.

06

Analyze Reaction (e)

The balanced chemical equation for reaction (e) is: \[2 \mathrm{NO(g)} + \mathrm{O_2(g)} = 2 \mathrm{NO_2(g)}\]This reaction has 3 moles of gaseous reactants and 2 moles of gaseous products. When compressed, the equilibrium will shift towards the right to reduce the pressure, increasing the concentration of NO2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equilibrium Systems

An equilibrium system in chemistry refers to a state in which both reactants and products are present in concentrations which have no further tendency to change with time. This happens when the rate at which the reactants are transformed into products is equal to the rate at which products revert back to reactants.

Imagine a crowded room where people are constantly moving from one side to the other. Eventually, there will be a steady flow of individuals where, despite the movement, the number of people on either side remains constant. Similarly, in a chemical system at equilibrium, the number of moles of reactants converting to products is balanced by the number of moles of products converting back to reactants.

• What makes such a system dynamic is the fact that the forward and reverse reactions do not stop; they are continuously occurring.
• The concept of equilibrium applies not only to chemical reactions but also to physical processes, such as the dissolution of salts or the evaporation of water.
• Le Chatelier’s Principle is invaluable for predicting how an equilibrium system will react to various changes, like pressure or concentration changes.

Chemical Equilibrium

Chemical equilibrium represents a balance in a reversible chemical reaction wherein no net change in the amount of reactants and products occurs. It can be described quantitatively by the equilibrium constant, denoted as K, which is a ratio of the concentrations of the products over the reactants, each raised to the power of their coefficients from the balanced chemical equation.

At a given temperature, this constant value reflects the extent to which a reaction proceeds before reaching equilibrium:

• If K is a large number, the reaction strongly favors the formation of products at equilibrium.
• If K is small, reactants are favored in the equilibrium state.
• If K is close to 1, neither reactants nor products are favored, and significant amounts of both will be present at equilibrium.

It's essential to understand that K is constant only if the temperature stays constant. Changes in temperature can alter the value of K, hence shifting the chemical equilibrium.

Changes in Concentration

When the concentration of a reactant or product in an equilibrium system is altered, Le Chatelier’s Principle helps us predict the direction in which the equilibrium will shift. Increasing the concentration of a reactant typically leads the system to produce more products, in an attempt to restore equilibrium. Conversely, increasing the concentration of a product will result in the formation of more reactants.

For instance, if you add more of a reactant to a system:

• The reaction will 'use up' some of this extra reactant to produce additional products.
• This process continues until the new equilibrium concentrations are achieved that conform to the equilibrium constant for the reaction.

On the other hand, if a product is removed from the system, for example by taking gas out of a reaction vessel, the reaction will proceed in the forward direction to try and replace it, again until equilibrium is reestablished.

Gas Volume and Pressure

For reactions involving gases, changes in volume and pressure can affect the equilibrium position significantly. The connection between volume and pressure in gases is described by Boyle's Law, which states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional. This means that when you decrease the volume of a gas, the pressure increases, and vice versa.

In terms of Le Chatelier’s Principle, an increase in pressure, which can be achieved by compressing a gas (decreasing its volume), will cause the equilibrium to shift in the direction that will decrease pressure. This is usually the side with fewer moles of gas. Here are the key takeaways:

• Increasing pressure (by decreasing volume) favors the direction with fewer moles of gas.
• Decreasing pressure (by increasing volume) favors the direction with more moles of gas.
• If the number of moles of gas is equal on both sides, changes in pressure and volume don't affect the position of the equilibrium much.