Question

(a) What is the \(\mathrm{Na}^{+}\) concentration in each of the following solutions: \(3.25 M\) sodium sulfate, \(1.78 M\) sodium carbonate, \(0.585 \mathrm{M}\) sodium bicarbonate? (b) What is the concentration of a lithium carbonate solution that is \(0.595 M\) in \(\mathrm{Li}^{+} ?\)

Short answer

(a) 6.50 M, 3.56 M, 0.585 M; (b) 0.2975 M.

Step-by-step solution

Understand Ion Dissociation

The first task is to understand how each compound dissociates in water. Sodium sulfate (\( \text{Na}_2\text{SO}_4 \)) dissociates to \( 2 \text{Na}^+ \) and \( \text{SO}_4^{2-} \), meaning for every mole of sodium sulfate, there are 2 moles of \( \text{Na}^+ \). Sodium carbonate (\( \text{Na}_2\text{CO}_3 \)) dissociates similarly to \( 2 \text{Na}^+ \) and \( \text{CO}_3^{2-} \). Sodium bicarbonate (\( \text{NaHCO}_3 \)) dissociates to \( \text{Na}^+ \) and \( \text{HCO}_3^- \).

Calculate Na+ Concentration from Sodium Sulfate

Given the concentration of sodium sulfate is \( 3.25 \text{ M} \). Remember the dissociation equation: \[ \text{Na}_2\text{SO}_4 \rightarrow 2\text{Na}^+ + \text{SO}_4^{2-} \]This means \( 1 \text{ M} \) sodium sulfate gives \( 2 \text{ M} \) sodium ions. Therefore, \( 3.25 \text{ M} \) sodium sulfate yields:\( 3.25 \times 2 = 6.50 \text{ M} \) of \( \text{Na}^+ \).

Calculate Na+ Concentration from Sodium Carbonate

The sodium carbonate concentration is \( 1.78 \text{ M} \), and its dissociation is:\[ \text{Na}_2\text{CO}_3 \rightarrow 2\text{Na}^+ + \text{CO}_3^{2-} \]Thus, \( 1.78 \text{ M} \) sodium carbonate results in:\( 1.78 \times 2 = 3.56 \text{ M} \) of \( \text{Na}^+ \).

Calculate Na+ Concentration from Sodium Bicarbonate

The concentration of sodium bicarbonate is \( 0.585 \text{ M} \), dissociating as:\[ \text{NaHCO}_3 \rightarrow \text{Na}^+ + \text{HCO}_3^- \]Since each mole gives one mole of \( \text{Na}^+ \), the \( \text{Na}^+ \) concentration remains \( 0.585 \text{ M} \).

Understand Lithium Carbonate Dissociation

Lithium carbonate (\( \text{Li}_2\text{CO}_3 \)) dissociates into \( 2 \text{Li}^+ \) ions and \( \text{CO}_3^{2-} \) with the equation:\[ \text{Li}_2\text{CO}_3 \rightarrow 2\text{Li}^+ + \text{CO}_3^{2-} \]

Calculate Lithium Carbonate Concentration

If the solution is \( 0.595 \text{ M} \) in \( \text{Li}^+ \), then the lithium carbonate must be half of the lithium ion concentration because:\( \text{Li}_2\text{CO}_3 \) gives 2 \( \text{Li}^+ \). Thus, the lithium carbonate concentration is:\( \frac{0.595}{2} = 0.2975 \text{ M} \).

Key concepts

Sodium Ion Concentration

When dealing with sodium compounds, it's crucial to consider how they dissociate into ions. This is because these compounds, when dissolved in water, break into smaller pieces called ions. With sodium sulfate (\( \text{Na}_2\text{SO}_4 \)), for example, it dissociates to create two sodium ions (\( \text{Na}^+ \)) and one sulfate ion (\( \text{SO}_4^{2-} \)) for each formula unit.
Hence, if you start with a concentration of \( 3.25 \text{ M} \) for sodium sulfate, you effectively double the amount of sodium ions, resulting in a \( 6.50 \text{ M} \) sodium ion concentration. This principle applies similarly to sodium carbonate (\( \text{Na}_2\text{CO}_3 \)), where the same doubling occurs, leading to a \( 3.56 \text{ M} \) sodium ion concentration from \( 1.78 \text{ M} \) of sodium carbonate.

• Understanding dissociation: More ions produced from a compound means higher ion concentration.
• Directly proportional relationship: Concentration of compounds is directly tied to the concentration of the ions they produce.

Sodium bicarbonate (\( \text{NaHCO}_3 \)), however, is different because it yields just one sodium ion per unit, so its molarity equals the sodium ion concentration, which remains \( 0.585 \text{ M} \). Remember these simple relationships to easily find the sodium concentration from these compounds.

Molarity Calculations

Molarity, simply put, measures how much of a substance is in a specific volume of solution. Imagine measuring how many sugar cubes are in your cup of tea! When calculating molarity, we consider the number of moles of solute (stuff that's dissolved) divided by the liters of solution.
Just like in steps to follow a recipe, it's critical to consider how different substances break down in a solution, primarily through dissociation.
Take sodium sulfate (\( \text{Na}_2\text{SO}_4 \)) for instance; since it produces more sodium ions than molecules originally present, your calculated sodium concentration becomes \( 6.50 \text{ M} \), even though the original compound's concentration was only \( 3.25 \text{ M} \).

• Sodium sulfate example: \( 3.25 \text{ M} \) sulfate turns into \( 6.50 \text{ M} \) sodium ions.
• Sodium carbonate example: \( 1.78 \text{ M} \) carbonate results in \( 3.56 \text{ M} \) sodium ions.

Understanding these dissociation patterns, as we did with sodium sulphate and carbonate, aid in making accurate molarity calculations, revealing the true ion concentrations beyond the initial compound values.

Lithium Ion Concentration

Lithium carbonate (\( \text{Li}_2\text{CO}_3 \)) is another compound we encounter that dissociates in solution. It breaks into two lithium ions (\( \text{Li}^+ \)) for every formula unit of the compound. This is why if a solution tells us it is \( 0.595 \text{ M} \) in lithium ions, we understand that the lithium carbonate itself must be less concentrated.
Essentially, because each unit gives off two lithium ions, the original compound findings are effectively halved to solve directly for the lithium carbonate's concentration—as it offers one half of the lithium ion concentration.

• Double dissociation: Results in halving the original compound concentration.
• Relationship understanding: Allows determining the accurate concentration of ions from their compounds.

Therefore, the initial \( 0.595 \text{ M} \) concentration of lithium ions results in a \( 0.2975 \text{ M} \) concentration for lithium carbonate. Grasping these concepts helps uncover the true concentration of these valuable lithium ions often used in numerous applications from batteries to medicine.