In a laboratory exercise, a student mixes \(2.5 .0 \mathrm{~g}\) of cthanol, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\), with \(150 \mathrm{~g}\) of water. (a) What is the mole fraction of ethanol in the solution? (b) What is the molality of cthanol in the solution?

Understanding the mole fraction of a component within a solution is essential for many chemical calculations. The mole fraction, denoted as 'X', represents the proportion of a constituent to the total number of moles in the mixture. To calculate it, you simply divide the moles of the component by the total moles in the solution.

For instance, in our given exercise, the mole fraction of ethanol in the solution can be calculated by taking the number of moles of ethanol and dividing it by the sum of moles of ethanol and water combined. The formula is as follows:
\[\begin{equation}X_{\text{ethanol}} = \frac{n_{\text{ethanol}}}{n_{\text{ethanol}} + n_{\text{water}}}\end{equation}\]
Calculating the mole fraction is a straightforward process, however, ensuring accuracy in the number of moles for each component is crucial. Properly balancing the chemical equation, if applicable, is also an important preliminary step.

Molality, often represented by the symbol 'b', is a measure of the concentration of a solution that refers to the moles of solute per kilogram of solvent. Unlike molarity, molality is not affected by temperature changes because it's based on mass rather than volume. To calculate molality, we use the equation:
\[\begin{equation}b = \frac{n_{\text{solute}}}{m_{\text{solvent}}}\end{equation}\]
where 'n' is the moles of the solute, and 'm' is the mass of the solvent in kilograms. In the laboratory exercise, the mass of ethanol is first converted to moles, and then divided by the mass of water used as the solvent, with careful conversion to kilograms. By doing this, we can find the molality of ethanol in the solution. This step is crucial for many applications such as boiling point elevation and freezing point depression where solution concentration plays a significant role.

Molar mass, the mass of one mole of a substance, is expressed in grams per mole (g/mol). It is a fundamental concept for converting between mass and moles of a substance. Each element's molar mass can be found on the periodic table, and the molar mass of a compound is the sum of the molar masses of its constituent atoms.

In this exercise, the molar mass of ethanol, C2H5OH, is calculated by summing the molar masses of two carbon atoms, six hydrogen atoms, and one oxygen atom. The accurate determination of molar mass is critical for subsequent calculations, such as mole fraction and molality. Understanding how to calculate molar mass allows students to transition smoothly from the mass of a substance to moles, a fundamental skill in chemistry.

Solution concentration is a measure of the amount of solute in a given amount of solution or solvent and is key in controlling the properties of a solution. There are several ways to express concentration, including molarity, molality, normality, and mole fraction. Each term provides valuable information depending on the nature of the problem being solved.

Molarity is moles of solute per liter of solution, while molality is moles of solute per kilogram of solvent, as explained earlier. Normality refers to equivalents of a solute per liter of solution and is often used in acid-base chemistry. Mole fraction is the ratio of the number of moles of a component to the total number of moles in the mixture. Understanding these different concepts is essential for correctly interpreting reaction conditions, predicting the outcomes of reactions, and in various industrial applications where precise concentrations are necessary.