Calculating the Concentration of a Saturated Solution of Sodium Chloride in Water

In this article, we focus on the calculation of the concentration of a saturated solution of sodium chloride (NaCl) in water at a specific temperature. Sodium chloride, also commonly known as table salt, is used extensively in chemical processes and household applications. Understanding its concentration in a solution is crucial for various industries. This guide will walk you through the steps to calculate the concentration of a saturated NaCl solution in water at 293 K.

Understanding the Basics

Before diving into the calculations, let's briefly review some important concepts:

Saturated Solution: A solution is considered saturated when the maximum amount of solute has been dissolved in the solvent at a given temperature. Beyond this point, no more solute can be dissolved. Molality: A measure of concentration that represents the amount of solute (moles of solute per kilogram of solvent). Molarity: A measure of concentration that represents the amount of solute (moles of solute per liter of solution). Concentration: The measure of the amount of solute in a given amount of solvent or solution.

Given Data

Given the mass of sodium chloride (NaCl) and the mass of water, we can calculate the concentration of the solution. Here are the details:

Mass of NaCl: 36 g Mass of Water: 100 g (assuming the density of water is 1 g/mL)

Steps to Calculate Concentration

Let's go through the steps to calculate the concentration of the saturated NaCl solution in water:

1. Convert the Mass of Water to Volume

When 100 g of water is assumed, this is equivalent to 100 mL, or 0.1 L, since the density of water is approximately 1 g/mL. This step is important because the volume of the solution is needed in the concentration formula.

2. Calculate the Concentration

We use the formula for concentration in terms of mass of solute and volume of solution:

Concentration C frac{mass of solute (g)}{volume of solution (L)}

C frac{36 g}{0.1 L} 360 g/L

3. Alternative Calculations

Let's explore additional methods to calculate the concentration of the NaCl solution:

Molality Calculation: Calculate the molar mass of NaCl: 36.45 g/mol 35.45 g/mol 58.4 g/mol Calculate the moles of NaCl: (frac{36 text{ g}}{58.4 text{ g/mol}} 0.615 text{ mol}) Convert the mass of water to kilograms: 100 g 0.1 kg Calculate the molality: (frac{0.615 text{ mol}}{0.1 text{ kg}} 6.15 text{ mol/kg}) Mass Percent Calculation: Total mass of the solution: 100 g 36 g 136 g Concentration (mass percent): (frac{36 text{ g}}{136 text{ g}} times 100 26.47% text{ (m/m)}

Conclusion

Therefore, the concentration of the saturated solution of sodium chloride at 293 K is 360 g/L, 6.15 mol/kg, or 26.47% (m/m).

Understanding the concentration of a saturated solution of NaCl is crucial in various applications, including pharmaceuticals, food industry, and chemical processes. By mastering these calculations, you can effectively interpret reactions and conditions in various settings.