Problem 42 - Chemistry and Chemical Reactivity

Question

What is the mass of solute, in grams, in \(125 \mathrm{mL}\) of a \(1.023 \times 10^{-3} \mathrm{M}\) solution of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) ? What is the molar concentration of the \(\mathrm{Na}^{+}\) and \(\mathrm{PO}_{4}^{3-}\) ion?

Step-by-Step Solution

Answer

The mass of solute is 0.02094 g. The \( \text{Na}^+ \) concentration is \( 3.069 \times 10^{-3} \text{ M} \) and the \( \text{PO}_4^{3-} \) concentration is \( 1.023 \times 10^{-3} \text{ M} \).

Step 1: Calculate Moles of Solute

The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. To find the moles of solute, use the formula: \( \text{Moles of solute} = \text{Molarity} \times \text{Volume in liters} \). Given, \( \text{Molarity} = 1.023 \times 10^{-3} \text{ M} \) and \( \text{Volume} = 125 \text{ mL} = 0.125 \text{ L} \), we have:\[ \text{Moles of Na}_3\text{PO}_4 = (1.023 \times 10^{-3} \text{ M}) \times 0.125 \text{ L} = 1.27875 \times 10^{-4} \text{ moles} \]

Step 2: Calculate Mass of Solute

The mass of solute can be calculated by multiplying the moles by the molar mass. The molar mass of \( \text{Na}_3\text{PO}_4 \) is \( 3(22.99) + 30.97 + 4(16.00) = 163.94 \text{ g/mol} \). Thus, the mass of the solute is: \[ \text{Mass} = 1.27875 \times 10^{-4} \text{ moles} \times 163.94 \text{ g/mol} = 0.02094 \text{ g} \]

Step 3: Determine Ion Concentrations

One mole of \( \text{Na}_3\text{PO}_4 \) dissociates into three \( \text{Na}^+ \) ions and one \( \text{PO}_4^{3-} \) ion. Therefore, the concentration of \( \text{Na}^+ \) ions is three times the concentration of \( \text{Na}_3\text{PO}_4 \), and the \( \text{PO}_4^{3-} \) ions concentration is the same as \( \text{Na}_3\text{PO}_4 \) concentration. Thus,\[ [\text{Na}^+] = 3 \times 1.023 \times 10^{-3} \text{ M} = 3.069 \times 10^{-3} \text{ M} \] \[ [\text{PO}_4^{3-}] = 1.023 \times 10^{-3} \text{ M} \]

Key Concepts

Moles of Solute

Understanding the concept of moles of solute is crucial in chemistry, especially when working with solutions. A mole is a standard unit in chemistry that represents a specific number of molecules or atoms, comparable to a dozen representing twelve items.
When dealing with solutions, we often express concentration in terms of molarity, which is the number of moles of solute per liter of solution.

• To find the moles of solute, use the formula: \( \text{Moles of solute} = \text{Molarity} \times \text{Volume in liters} \).
• In the given problem, the molarity of the solution is \(1.023 \times 10^{-3} \text{ M} \), and the volume is \(125 \text{ mL} \), which converts to \(0.125 \text{ L} \).
• Hence, we calculate: \( \text{Moles of Na}_3\text{PO}_4 = (1.023 \times 10^{-3} \text{ M}) \times 0.125 \text{ L} = 1.27875 \times 10^{-4} \text{ moles} \).

This calculation shows us how many moles of solute are present in the solution. Knowing this is the first step towards determining the mass of solute and the concentration of ions dissolved in the solution.

Ion Concentration

The concept of ion concentration becomes essential when a compound dissociates in a solution to form its constituent ions. Knowing the concentration of each ion allows us to predict how these ions will interact with other substances in a solution.
When a solute like \( \text{Na}_3\text{PO}_4 \) dissolves in water, it dissociates into sodium ions (\( \text{Na}^+ \)) and phosphate ions (\( \text{PO}_4^{3-} \)).

• A single molecule of \( \text{Na}_3\text{PO}_4 \) breaks down into three \( \text{Na}^+ \) ions and one \( \text{PO}_4^{3-} \) ion in the solution.
• The concentration of \( \text{Na}^+ \) ions is thus three times the molarity of the original \( \text{Na}_3\text{PO}_4 \) solution.
• Practically, this translates to: \([\text{Na}^+] = 3 \times 1.023 \times 10^{-3} \text{ M} = 3.069 \times 10^{-3} \text{ M}\).
• The \( \text{PO}_4^{3-} \) ion concentrations are equal to the initial molarity: \([\text{PO}_4^{3-}] = 1.023 \times 10^{-3} \text{ M}\).

Comprehending ion concentration helps in predicting the chemical behavior of a solution, such as its reactivity or its use in various applications like titration.

Molar Mass

Molar mass is a critical concept in chemistry that allows us to convert between the mass of a substance and the number of moles. It's defined as the mass of one mole of a given substance, expressed in grams per mole (g/mol).
Calculating the molar mass involves summing the atomic masses of all the atoms in the molecular formula.

• For \( \text{Na}_3\text{PO}_4 \), you sum the atomic masses: \(3(22.99 \text{ g/mol for Na}) + 30.97 \text{ g/mol for P} + 4(16.00 \text{ g/mol for O}) = 163.94 \text{ g/mol}\).
• Once the molar mass is known, you can calculate the mass of a solute in a solution by multiplying the number of moles by the molar mass.\( \text{Mass} = 1.27875 \times 10^{-4} \text{ moles} \times 163.94 \text{ g/mol} = 0.02094 \text{ g}\).

Understanding molar mass is vital for not only calculating solute masses but also for comprehending stoichiometry in chemical reactions, which is key in many areas of chemistry.