Problem 154 - Chemistry

Question

Calculate the concentrations of all the species in a \(0.100 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) solution.

Step-by-Step Solution

Answer

\([\text{Na}^+] = 0.200 \, \text{M}, [\text{CO}_3^{2-}] = 0.100 \, \text{M}\).

Step 1: Identify the Initial Concentration

Start by identifying the initial concentration of sodium carbonate, \( \text{Na}_2\text{CO}_3 \). We are given that the concentration is \(0.100 \, \text{M} \).

Step 2: Dissolution into Ions

When sodium carbonate dissolves in water, it dissociates into its ions:\[ \text{Na}_2\text{CO}_3 \rightarrow 2\text{Na}^+ + \text{CO}_3^{2-} \]Hence, for every mole of sodium carbonate that dissolves, it produces 2 moles of \(\text{Na}^+\) ions and 1 mole of \(\text{CO}_3^{2-}\).

Step 3: Determine Sodium Ion Concentration

Based on the dissociation, the concentration of sodium ions \( (\text{Na}^+) \) will be twice that of sodium carbonate, because there are 2 sodium ions for each sodium carbonate:\[ [\text{Na}^+] = 2 \times 0.100 \, \text{M} = 0.200 \, \text{M} \]

Step 4: Determine Carbonate Ion Concentration

The concentration of carbonate ions \( (\text{CO}_3^{2-}) \) is the same as that of the original sodium carbonate solution, as each formula unit produces one carbonate ion:\[ [\text{CO}_3^{2-}] = 0.100 \, \text{M} \]

Step 5: Determine Hydrogen Carbonate Ion Equilibrium

In aqueous solution, \( \text{CO}_3^{2-} \) can react with water producing \( \text{HCO}_3^- \):\[ \text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftarrows \text{HCO}_3^- + \text{OH}^- \]However, given the nature of carbonate as a weak base, the concentration of \( \text{HCO}_3^- \) will be very small and we assume it does not affect the initial concentrations drastically without additional equilibria calculations.

Key Concepts

Sodium carbonate

Sodium carbonate, often known as soda ash or washing soda, is an important chemical compound. In chemistry, its formula is written as \( \text{Na}_2\text{CO}_3 \). This compound is an example of a salt made of sodium and carbonate ions. It's widely used in various industries, including glass manufacturing and detergents.

In an aqueous solution, sodium carbonate provides carbonate ions \( (\text{CO}_3^{2-}) \) and sodium ions \((\text{Na}^+)\). Because of its structure, sodium carbonate readily dissolves in water, making it a versatile choice for many chemical reactions. It's important to understand how such dissolutions impact concentrations in solution, as this plays a crucial role in reactions involving sodium carbonate.

Ion dissociation

Ion dissociation is a fundamental chemical process, especially when dealing with ionic compounds like sodium carbonate. When sodium carbonate is introduced into water, it separates into its constituent ions. This is known as dissociation.

The dissociation reaction for sodium carbonate in water can be written as:

• \( \text{Na}_2\text{CO}_3 \rightarrow 2\text{Na}^+ + \text{CO}_3^{2-} \)

This equation shows that a single formula unit of sodium carbonate results in two sodium ions and one carbonate ion. This is crucial for calculating the resulting ion concentrations. For instance, if the initial concentration of sodium carbonate is 0.100 M, following dissociation, the concentration of sodium ions will be 0.200 M because each unit releases two sodium ions.

By understanding dissociation, students can appreciate how ionic compounds behave in aqueous solutions and predict concentrations of involved species accurately.

Equilibrium in solutions

Equilibrium in solutions involves a steady state where concentrations of reactants and products remain constant. This is especially relevant for reactions in solution that do not proceed to completion.

In the case of sodium carbonate, though it dissociates into sodium and carbonate ions, an equilibrium situation can also be formed with the carbonate ion. The carbonate ions can interact with water in a reversible manner:

• \( \text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^- \)

Though this equilibrium exists, the extent of reaction in water is determined by the weak base nature of carbonate ions. This means the shift towards products \( \text{HCO}_3^- \) and hydroxide ions \( \text{OH}^- \) is minimal. As such, for practical purposes without additional calculations, the initial concentration changes are assumed to be insignificant.

Understanding this concept helps recognize that while ionic solutions may reach an equilibrium, the immediate result of dissociation heavily influences concentrations present in the solution.

Weak base reaction

Weak base reactions are critical to understanding aqueous chemistry. A weak base is a substance that does not completely ionize in solution. Carbonate ions \((\text{CO}_3^{2-})\) derived from sodium carbonate act as a weak base.

A typical weak base reaction involves the weak base—to which carbonate ions belong—reacting with water to form bicarbonate \((\text{HCO}_3^-)\) and hydroxide \((\text{OH}^-)\) ions:

• \( \text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^- \)

Due to their weak nature, only a small portion of carbonate ions undergo this reaction, which means they have a limited effect on the overall concentrations at equilibrium.

Recognizing the behavior of weak bases in solution is vital for predicting the pH and the behavior of the solution. For example, because the degree of reaction is minor, we can assume that the increase in \( \text{OH}^- \) is minimal, reflecting the weak base nature of carbonate ions in sodium carbonate solutions.