Problem 64 - Chemistry The Molecular Science

Question

Predict what effect each would have on this equilibrium: $$ \mathrm{PbCl}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq}) $$ (a) Addition of lead(II) nitrate solution (b) Addition of silver nitrate solution (c) Addition of \(\mathrm{NaCl}\) solution

Step-by-Step Solution

Answer

(a) Shift left, (b) Shift right, (c) Shift left.

Step 1: Identify the Reaction

The given reaction is the dissolution of lead(II) chloride in water, forming lead ions \( \mathrm{Pb}^{2+} \) and chloride ions \( \mathrm{Cl}^{-} \): \[ \mathrm{PbCl}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq}) \] Here, the equilibrium is between a solid and its dissolved ions.

Step 2: Effect of Lead(II) Nitrate Solution

Adding lead(II) nitrate increases the concentration of \( \mathrm{Pb}^{2+} \) ions in the solution. According to Le Chatelier's principle, the equilibrium will shift to the left to decrease the concentration of \( \mathrm{Pb}^{2+} \) by forming more solid \( \mathrm{PbCl}_{2} \).

Step 3: Effect of Silver Nitrate Solution

Silver nitrate reacts with chloride ions to form solid silver chloride \( \mathrm{AgCl} \), effectively removing \( \mathrm{Cl}^{-} \) ions from the solution. This causes the equilibrium to shift to the right to produce more \( \mathrm{Cl}^{-} \) ions by dissolving more \( \mathrm{PbCl}_{2} \).

Step 4: Effect of NaCl Solution

Adding \( \mathrm{NaCl} \) increases the concentration of \( \mathrm{Cl}^{-} \) ions in the solution. According to Le Chatelier's principle, the equilibrium will shift to the left to reduce the \( \mathrm{Cl}^{-} \) concentration by forming more solid \( \mathrm{PbCl}_{2} \).

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction. This means that the concentrations of the reactants and products remain constant over time. Chemical equilibrium does not mean that the concentrations are equal, but rather that their ratios remain constant. It's an essential concept in chemistry because it describes how reactions can reach a state of balance.

• When a system is disturbed by changing conditions, it responds in a way that counteracts the change and restores equilibrium.
• This dynamic process of balance means that reactants and products are continuously interconverted, but their overall concentrations do not change.

Understanding chemical equilibrium involves appreciating that reactions are happening in both directions at the same time. Even when it looks like nothing is happening, molecules continue to react in both directions at equal rates. Le Chatelier's Principle is a key part of predicting how changes in conditions will affect this balance.

Solubility Equilibrium

Solubility equilibrium specifically refers to the state of balance in a saturated solution where the rate of dissolution of a solute is equal to its rate of precipitation. This is often represented in chemical equations that show a solid substance in equilibrium with its ions in solution, such as \\[ \mathrm{PbCl}_{2}(\ ext{s}) ightleftharpoons \mathrm{Pb}^{2+}(\ ext{aq})+ 2 \mathrm{Cl}^{-}(\ ext{aq}) \]
This type of equilibrium helps us understand how much of a solute can be dissolved in a solvent before the solution becomes saturated.

• In this state, if additional solute or any of the ions are added to the solution, it can cause the equilibrium to shift to either produce more of the solid or dissolve more of it.
• For example, introducing more \( \mathrm{Pb}^{2+} \) ions shifts the equilibrium towards forming more solid \( \mathrm{PbCl}_{2} \).

In solubility equilibria, factors like the common ion effect come into play, where introducing more of one ion in solution leads to a decrease in solubility of the solute.

Effect of Concentration on Equilibrium

The effect of concentration changes on a system in equilibrium is best understood through Le Chatelier's Principle. This principle states when a system at equilibrium experiences a concentration change, the equilibrium will adjust to counterbalance that change.
For example:

• Adding a solute that increases the concentration of one of the ions at equilibrium will cause the system to shift in the direction that reduces that ion's concentration.
• This can involve shifting towards the formation of more precipitate or, in other cases, producing more dissolved ions.

In practice, if lead(II) nitrate is added to a system equilibrated with \( \mathrm{PbCl}_{2} \), the increased \( \mathrm{Pb}^{2+} \) shifts equilibrium left, forming more solid to reduce ion concentration. Conversely, removing ions, such as with silver nitrate, causes more ions to dissolve to regain balance. Similarly, adding \( \mathrm{NaCl} \) contributes more \( \mathrm{Cl}^{-} \) and shifts the equilibrium left, promoting precipitate formation to compensate.