Calculate the mole fraction of each component in the following solutions: (a) \(2.5 .0 \mathrm{~g}\) of water and \(50.0 \mathrm{~g}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\); (b) \(25.0 \mathrm{~g}\) of water and \(50.0 \mathrm{~g}\) of methanol, \(\mathrm{CH}_{3} \mathrm{OH}\); (c) a glucowe solution that is \(0.10 \mathrm{~m}\) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)\).

Understanding the concept of molar mass is vital for a range of chemistry calculations, including the determination of mole fractions. Molar mass is defined as the mass (in grams) of one mole of any substance. A mole is a unit of measurement used in chemistry to express amounts of a chemical substance, represented by Avogadro's number, which is approximately 6.022 x 10²³ particles (atoms, molecules, ions or electrons).

To calculate molar mass, we sum the atomic masses of all the atoms in a molecule. These atomic masses are found on the periodic table, usually beneath the symbol for each element, and are measured in atomic mass units (u). For example, the molar mass of water (H₂O) is obtained by adding the atomic masses of two hydrogen atoms (1.008 g/mol each) and one oxygen atom (16.00 g/mol), giving us 18.02 g/mol.

Example:

In the case of ethanol (C₂H₅OH), we calculate molar mass by adding the molar masses of two carbon atoms, six hydrogen atoms, and one oxygen atom. This addition gives us the molar mass of ethanol as 46.07 g/mol.

Conversion of mass to moles is a fundamental step in chemical calculations and is used to compare quantities of different substances on a common scale. To convert mass to moles, we simply divide the mass of the substance by its molar mass.

The formula for this conversion is:
\[\begin{equation} \text{Number of moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}} \end{equation}\]
Looking at our earlier example, if we have 50.0 g of ethanol, to find the number of moles we divide by its molar mass, yielding:\[\begin{equation} \text{Number of moles ethanol} = \frac{50.0 \text{ g}}{46.07 \text{ g/mol}} \end{equation}\]
Carrying out this calculation allows us to express the mass of ethanol as a quantity of moles, which can then be used to find the mole fraction in a mixture.

Solution concentration often refers to the amount of substance dissolved in a certain volume of solvent. There are different ways to express this concentration, and they are crucial for accurately describing the composition of a solution. The most common units of solution concentration are molarity (M), molality (m), and mole fraction.

Molarity is defined as the number of moles of solute per liter of solution. Molality, on the other hand, is moles of solute per kilogram of solvent. Unlike molarity, molality is unaffected by changes in temperature and pressure because it's based on the mass of the solvent rather than its volume.

Mole fraction is another way to express concentration, particularly useful in calculations involving partial pressures or colligative properties. The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components of the solution.

Molality is an important concentration unit used in chemistry for various calculations, particularly when dealing with temperature or pressure variations. It is defined as the number of moles of solute divided by the kilograms of solvent in the solution.

The formula for calculating molality (m) is given by:\[\begin{equation} \text{Molality} = \frac{\text{Moles of solute}}{\text{Kilograms of solvent}} \end{equation}\]
For instance, if a question states that a glucose solution has a molality of 0.10 m, this means that in every kilogram of water, there are 0.10 moles of glucose dissolved. This unit of measurement is especially useful because it does not change with temperature, making it ideal for studies involving temperature-dependent phenomena such as boiling point elevation or freezing point depression.

Pro tip:

When dealing with molality, always ensure to convert the mass of the solvent to kilograms and use the correct molar mass for the solute for an accurate calculation.