How to Find Concentration from Solubility?

Solubility provides the maximum concentration of a solute that can dissolve in a solvent at a specific temperature. To find the concentration from solubility, you need to understand the units of solubility and convert them to a desired concentration unit, most commonly molarity.

Here's a step-by-step guide:

1. Understand Solubility Units:

• Solubility is often expressed in grams of solute per 100 mL of solvent (g/100 mL), grams per liter (g/L), or as a molar solubility (moles per liter or M).
• Make sure you know the temperature at which the solubility is measured, as solubility changes with temperature.

2. Convert Solubility to Molarity (M):

Molarity (M) is defined as moles of solute per liter of solution. If your solubility is not already in molarity, you'll need to convert it.

• If solubility is in g/100 mL:

  • Convert grams to moles using the solute's molar mass (g/mol). Moles = grams / molar mass
  • Convert 100 mL to liters: 100 mL = 0.1 L
  • Calculate molarity: Molarity (M) = Moles / Liters = (grams/molar mass) / 0.1 L

• If solubility is in g/L:

  • Convert grams to moles using the solute's molar mass (g/mol). Moles = grams / molar mass
  • Calculate molarity: Molarity (M) = Moles / Liters = (grams/molar mass) / 1 L which simplifies to Molarity (M) = grams / molar mass

3. Example:

Let's say the solubility of NaCl (sodium chloride) in water is 36 g/100 mL at 25°C. What is the molarity of a saturated NaCl solution at this temperature?

• Step 1: Find the molar mass of NaCl. Na = 22.99 g/mol, Cl = 35.45 g/mol. Molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol.

• Step 2: Convert grams to moles. Moles of NaCl = 36 g / 58.44 g/mol = 0.616 mol

• Step 3: Convert mL to L. 100 mL = 0.1 L

• Step 4: Calculate molarity. Molarity = 0.616 mol / 0.1 L = 6.16 M

Therefore, the molarity of a saturated NaCl solution at 25°C is approximately 6.16 M. This means that a liter of saturated NaCl solution contains approximately 6.16 moles of NaCl.

4. Important Considerations:

• Saturated Solution: Solubility represents the maximum concentration achievable, forming a saturated solution.
• Temperature: Solubility is temperature-dependent. Always note the temperature associated with the solubility value.
• Solvent: The solubility is specific to the solvent used.
• Units: Ensure consistent units throughout the calculation.
• Complex Ions: Some substances form complex ions in solution, which can affect the actual concentration of the metal ion.

In summary, finding the concentration from solubility involves understanding the units of solubility, converting to moles per liter (molarity) using the solute's molar mass, and noting the temperature at which the solubility was measured.