Calculating the Mass of NaOH in an Aqueous Solution: A Practical Example

In this article, we will walk through a step-by-step example of how to calculate the mass of NaOH in an aqueous solution given its molality and the mass of the solvent. We'll break down the process and provide the necessary calculations in detail. This guide will help you develop a thorough understanding of the concepts and enable you to solve similar problems efficiently.

Introduction to Molality

Molality, denoted by m, is a measure of concentration that describes the number of moles of solute per kilogram of solvent. It is an important parameter in chemistry, particularly for colligative properties. In our example, we'll use molality to determine the mass of sodium hydroxide (NaOH) in a given aqueous solution.

Problem Statement

We are given an aqueous solution of NaOH with a molality of 2.5 m. The solution contains 0.5 kg of water. Our goal is to calculate the mass of NaOH in the solution. This problem requires an understanding of the relationship between molality, the number of moles of solute, and the molar mass of the solute.

Step-by-Step Solution

The first step is to understand the formula for molality:

m moles of solute / mass of solvent (kg)

Given that the molality of the solution is 2.5 m and the mass of the solvent water is 0.5 kg, we can rearrange the formula to find the number of moles of NaOH:

moles of NaOH m × mass of solvent (kg)

Plugging in the values:

moles of NaOH 2.5 mol/kg × 0.5 kg 1.25 mol

Next, we need to calculate the mass of NaOH using its molar mass. The molar mass of NaOH is calculated as follows:

Molar mass of Na (sodium) 22.99 g/mol Molar mass of O (oxygen) 16.00 g/mol Molar mass of H (hydrogen) 1.01 g/mol

Therefore, the molar mass of NaOH is:

Molar mass of NaOH 22.99 16.00 1.01 40.00 g/mol

Now we can calculate the mass of NaOH:

mass of NaOH moles of NaOH × molar mass of NaOH

Substituting the values:

mass of NaOH 1.25 mol × 40.00 g/mol 50.00 g

Therefore, the mass of NaOH in the solution is 50.00 grams.

Practical Application and Tips

Understanding this process is crucial for solving similar problems related to molality and molar mass. Here are a few tips:

Make sure to accurately identify the solute and solvent in a given solution. Recall that molality is independent of temperature and concentration. Always double-check your calculations, especially when dealing with unit conversions.

By applying these concepts, you can solve complex problems related to solutions and colligative properties on your own. This problem serves as a practical example to reinforce your understanding of these fundamental principles.