The density of acetonitrile (CH₃CN) is 0.786 g/mL and the density of methanol (CH₃OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH₃OH in 98.7 mL of CH₃CN. (a) What is the mole fraction of methanol in the solution?

Verified step by step guidance

1. Calculate the mass of methanol (CH_3OH) using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).
2. Calculate the mass of acetonitrile (CH_3CN) using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).
3. Convert the mass of methanol to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
4. Convert the mass of acetonitrile to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
5. Calculate the mole fraction of methanol by dividing the moles of methanol by the total moles of both methanol and acetonitrile: \( \text{mole fraction} = \frac{\text{moles of methanol}}{\text{moles of methanol} + \text{moles of acetonitrile}} \).

Key Concepts

Mole Fraction

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 specific component to the total number of moles of all components in the solution. This concept is crucial for calculating the mole fraction of methanol in the solution, as it allows us to quantify the relative amount of methanol compared to acetonitrile.

Density and Volume Relationship

Density is defined as mass per unit volume and is a key property of substances. In this problem, the densities of acetonitrile and methanol are provided, which allows us to convert their volumes into masses. Understanding how to use density to find mass is essential for determining the number of moles of each component, which is necessary for calculating the mole fraction.

Calculating Moles from Mass

To find the number of moles of a substance, one can use the formula: moles = mass (g) / molar mass (g/mol). This concept is important in this question because, after determining the masses of methanol and acetonitrile from their respective volumes and densities, we need to convert these masses into moles to compute the mole fraction of methanol in the solution.