A solution is made containing 14.6 g of CH3OH in 184 g of H2O. Calculate (a) the mole fraction of CH3OH.

Verified step by step guidance

Step 1: Calculate the number of moles of CH3OH. Use the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). The molar mass of CH3OH (methanol) is approximately 32.04 g/mol.

Step 2: Calculate the number of moles of H2O. Use the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). The molar mass of H2O (water) is approximately 18.02 g/mol.

Step 3: Determine the total number of moles in the solution by adding the moles of CH3OH and the moles of H2O.

Step 4: Calculate the mole fraction of CH3OH using the formula: \( \text{mole fraction of CH3OH} = \frac{\text{moles of CH3OH}}{\text{total moles in solution}} \).

Step 5: Express the mole fraction as a dimensionless number, ensuring it is less than 1, as it represents a part of the whole.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the mass of a substance to the number of particles it contains. One mole of any substance contains Avogadro's number (approximately 6.022 x 10^23) of molecules or atoms. This concept is essential for converting grams of a substance to moles, which is necessary for calculating mole fractions.

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 mixture. The mole fraction is a dimensionless quantity and is useful for understanding the composition of solutions and gases.

Solution Composition

The composition of a solution refers to the relative amounts of solute and solvent present. In this case, CH3OH (methanol) is the solute, and H2O (water) is the solvent. Understanding the mass of each component is crucial for calculating the mole fraction, as it requires determining the number of moles of both the solute and solvent.

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