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Raoult's Law is a principle used to predict the vapor pressure of a solution. It states that the partial vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. The formula is given by: \( P_{\text{solution}} = X_{\text{solvent}} \times P_{\text{pure solvent}} \) where:

• \(P_{\text{solution}}\) = vapor pressure of the solution
• \(X_{\text{solvent}}\) = mole fraction of the solvent
• \(P_{\text{pure solvent}}\) = vapor pressure of the pure solvent

In our exercise, the pure solvent is water, and its vapor pressure at 25°C is 3.2 kPa. By calculating the mole fraction of water in the solution and applying Raoult's Law, we determine the vapor pressure of the final solution. This method is especially useful because it connects directly to the concept of how different components in a mixture affect each other.

The mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a particular component to the total number of moles in the solution. Mathematically, it can be written as: \( X_{\text{A}} = \frac{n_{\text{A}}}{n_{\text{total}}} \) where:

• \(X_{\text{A}}\) = mole fraction of component A
• \(n_{\text{A}}\) = number of moles of component A
• \(n_{\text{total}}\) = total number of moles in the mixture

For our solution, we calculated the moles of the solute \( \text{MgCl}_2 \) and the solvent water. The mole fraction of water ( the solvent ) is given by: \( X_{\text{H}_2\text{O}} = \frac{n_{\text{H}_2\text{O}}}{n_{\text{H}_2\text{O}} + n_{\text{MgCl}_2}} = \frac{29.97}{31.966} \text{ mol} \roughly 0.937 \) By knowing the mole fraction, we help to quantify how much of the solution consists of the solvent, which is critical for determining properties like vapor pressure.

Molar mass, also known as molecular weight, is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. It's usually expressed in units of grams per mole (g/mol). To calculate the molar mass of a compound, you add up the atomic masses of each element in its chemical formula. For example, the molar mass of magnesium chloride, \(\text{MgCl}_2\), is determined by:

• Atomic mass of Mg = 24.305 g/mol
• Atomic mass of Cl = 35.453 g/mol

Since \(\text{MgCl}_2\) contains one magnesium atom and two chlorine atoms, its molar mass is: \( \text{24.305 g/mol} + 2\times \text{35.453 g/mol} = 95.211 \text{ g/mol} \) This calculation aids us in converting between mass and moles, which is essential for further calculations, such as determining mole fractions and using Raoult's Law.