Problem 35 - Chemistry: Atoms First

Question

If 4.12 L of a 0.850 \(M-\mathrm{H}_{3} \mathrm{PO}_{4}\) solution is be diluted to a volume of 10.00 \(\mathrm{L},\) what is the concentration of the resulting solution?

Step-by-Step Solution

Answer

The concentration of the resulting solution is 0.3472 M.

Step 1: Understand Dilution Concept

Dilution is the process of reducing the concentration of a solution by adding more solvent. The number of moles of solute before dilution and after dilution remains the same.

Step 2: Calculate Moles of Solute Before Dilution

Using the initial concentration and volume of the solution, calculate the number of moles of the solute before dilution using the formula: moles of solute = molarity (M) * volume (L).

Step 3: Calculate the Final Concentration

After dilution, the total volume of the solution increases, but the number of moles of solute remains the same. To find the new concentration, use the formula: final molarity (M2) = moles of solute / final volume (L2).

Key Concepts

Molarity

Molarity, often denoted as 'M', is a measure of the concentration of a solution. It indicates how many moles of a solute are present in one liter of solution. The formula to calculate molarity is \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). Molarity is a central concept in chemistry as it allows scientists and students to easily communicate and reproduce the concentration of solutions.

When diluting a solution, understanding molarity becomes essential. As more solvent is added, the volume of the solution increases, but the molarity decreases since the amount of solute remains unchanged. A high molarity means a more concentrated solution, whereas a low molarity indicates a more diluted solution. For students tackling dilution problems, it's crucial to grasp that regardless of the changes in volume, the total moles of solute do not change.

Moles of Solute

The mole is a fundamental unit in chemistry that quantifies the amount of substance. One mole is defined as exactly 6.022 x 10^23 particles, which could be atoms, molecules, ions, or electrons. When it comes to solutions, the term 'moles of solute' refers to the amount of substance dissolved in a solvent to form the solution.

Calculating the moles of solute is critical for solution preparation and dilution problems. Before dilution, the moles of solute is determined by multiplying the molarity of the solution by its volume in liters using the formula: \( \text{moles of solute} = M \times V \). This quantity will remain constant throughout the dilution process, providing the link between the initial and final concentration of the solution. Comprehending this relationship is vital in ensuring the accuracy of dilution and concentration calculations.

Solution Volume

In the context of solutions, 'solution volume' is the total amount of space that the solution occupies. It's typically measured in liters (L) or milliliters (mL). This volume comprises both the solute (the substance dissolved) and the solvent (the substance that dissolves the solute).

During the process of dilution, the solution volume plays a crucial role. As more solvent is added to the original solution, the total volume increases which in turn lowers the concentration of the solute, given the number of moles of solute stays constant. Understanding how to manipulate the solution volume is useful for achieving desired concentrations in lab settings. In many chemical procedures, adjusting the molarity of a solution by changing the volume is a common practice. It's a fundamental skill for students to learn how to accurately measure and calculate solution volumes to solve concentration problems.