A solution is prepared by dissolving 20.2 mL of methanol (CH₃OH) in 100.0 mL of water at 25 °C. The final volume of the solution is 118 mL. The densities of methanol and water at this temperature are 0.782 g/mL and 1.00 g/mL, respectively. For this solution, calculate the concentration in each unit. d. mole fraction

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Calculate the mass of methanol using its volume and density: \( \text{mass of methanol} = \text{volume} \times \text{density} = 20.2 \text{ mL} \times 0.782 \text{ g/mL} \).

Calculate the moles of methanol using its molar mass (32.04 g/mol): \( \text{moles of methanol} = \frac{\text{mass of methanol}}{32.04 \text{ g/mol}} \).

Calculate the mass of water using its volume and density: \( \text{mass of water} = \text{volume} \times \text{density} = 100.0 \text{ mL} \times 1.00 \text{ g/mL} \).

Calculate the moles of water using its molar mass (18.02 g/mol): \( \text{moles of water} = \frac{\text{mass of water}}{18.02 \text{ g/mol}} \).

Calculate the mole fraction of methanol: \( \text{mole fraction of methanol} = \frac{\text{moles of methanol}}{\text{moles of methanol} + \text{moles of water}} \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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. For a solution containing methanol and water, the mole fraction of methanol can be calculated by dividing the moles of methanol by the sum of the moles of methanol and water.

Density and Volume Relationships

Density is defined as mass per unit volume and is crucial for converting between mass and volume when calculating concentrations. In this problem, the densities of methanol and water allow us to determine their masses from their respective volumes. Understanding how to manipulate these relationships is essential for calculating the total moles of each component in the solution.

Concentration Units

Concentration can be expressed in various units, including molarity, mass percent, and mole fraction. Each unit provides different insights into the composition of a solution. In this case, calculating the mole fraction requires knowing the moles of each component, which can be derived from their masses and molar masses, emphasizing the importance of unit conversions in solution chemistry.