Question

A solution contains \(20.5 \mathrm{~g}\) of sodium chloride dissolved in sufficient water to give a total mass of \(166.2 \mathrm{~g}\). What is the molality of this solution?

Short answer

The molality of the solution is \(2.41 \, m\).

Step-by-step solution

Determine the molar mass of sodium chloride

The first step in calculating the molality of a solution is to determine the molar mass of the solute. The molar mass of sodium chloride (NaCl) can be calculated by adding the atomic masses of sodium (Na) and chlorine (Cl). Sodium has an atomic mass of 22.99 g/mol and chlorine has an atomic mass of 35.45 g/mol. The sum of the two is \(22.99 \mathrm{g/mol} + 35.45 \mathrm{g/mol} = 58.44 \mathrm{g/mol}\).

Calculate the number of moles of sodium chloride

The number of moles of sodium chloride can be calculated by dividing the mass of the sodium chloride by its molar mass. This gives \(20.5 \mathrm{g} / 58.44 \mathrm{g/mol} = 0.351 \mathrm{mol}\).

Calculate the mass of the water

The mass of the water (solvent) can be obtained by subtracting the mass of sodium chloride (solute) from the total mass of solution: \(166.2 \mathrm{g} - 20.5 \mathrm{g} = 145.7 \mathrm{g}\). This mass needs to be converted to kilograms because molality is given in mol/kg. Which gives \(145.7 \mathrm{g} * 1 \mathrm{kg/1000g} = 0.1457 \mathrm{kg}\).

Calculate molality of the solution

Molality is defined as the number of moles of solute per kilogram of solvent. Therefore, divide the number of moles of sodium chloride by the kilograms of water to get the molality: \(0.351 \mathrm{mol} / 0.1457 \mathrm{kg} = 2.41\mathrm{m}\). 'm' stands for molality.

Key concepts

Sodium Chloride Solubility

Understanding the solubility of sodium chloride (NaCl), commonly known as table salt, is pivotal in many chemical processes and applications, such as in cooking and preservation. Solubility is a measure of how much a particular solute, in this case sodium chloride, can dissolve in a given solvent at a specific temperature until reaching saturation. Water is an excellent solvent for sodium chloride and many salts in general because of its polar nature, which allows it to surround and separate ionic compounds into their respective ions.

When discussing the solubility of sodium chloride, it's important to note that it has a relatively high solubility in water. At room temperature, approximately 360 grams of NaCl can dissolve in a liter of water. This property is critical when calculating the concentration of solutions, such as molality, since it ensures that a given amount of NaCl can indeed be dissolved in the amount of water used in various practical applications.

Molar Mass Determination

The concept of molar mass is a fundamental aspect of chemistry that allows scientists and students to understand the mass of a given substance in relation to the amount of substance (moles). Determining the molar mass of a compound involves calculating the sum of the atomic masses of all the atoms present in a molecule of that compound. In our exercise, the molar mass of sodium chloride is determined by adding the atomic masses of sodium and chlorine.

To perform this calculation, one must consult a periodic table to obtain the standard atomic weights of these elements. It is necessary to be precise with the values and units during this process since the molar mass is critical in converting between grams and moles, leading to accurate concentration calculations such as molality.

Moles of Solute

The calculation of moles of solute is a vital step in various chemical calculations, especially when working with concentration measurements. A mole is a unit that measures the amount of substance and, in practice, enables us to count particles such as atoms, ions, or molecules by weighing. The number of moles in a given mass of a substance can be determined using the formula:

moles of solute = mass of solute (g) / molar mass of solute (g/mol).

Knowing the moles of solute, like sodium chloride in our example, helps to determine the concentration of the solution, allowing us to assess how much of the compound is present in a specific amount of solvent. This measurement is crucial for both theoretical and practical applications, such as chemical reactions and creating solutions of a desired concentration for experimental procedures.

Concentration of Solutions

Concentration is a measure of how much solute is contained in a given amount of solvent or solution. It can be expressed in various ways, including molarity (moles per liter), molality (moles per kilogram of solvent), and percent composition by mass or volume, among others. In this context, the focus is on molality, which is used when the temperature of the solution is likely to change, as it does not depend on volume, which can vary with temperature.

Molality is defined as the moles of solute divided by the kilograms of solvent and is represented by the symbol 'm'. It is particularly useful in the study of colligative properties which are properties of solutions that depend on the concentration of the solute particles, such as boiling point elevation and freezing point depression. For instance, calculating the molality of a sodium chloride solution is essential for predicting how it will affect the freezing point of water, which is a factor in applications such as road deicing.