A 0.944 M solution of glucose, C₆H₁₂O₆, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (a) Mole fraction

검증된 단계별 안내

Step 1: The mole fraction is defined as the ratio of the number of moles of a component to the total number of moles of all components in the solution. To find the mole fraction of glucose, we first need to find the number of moles of glucose and the number of moles of water in the solution.

Step 2: We know the molarity of the glucose solution, which is defined as the number of moles of solute (glucose) per liter of solution. So, we can find the number of moles of glucose in 1 liter of solution by multiplying the molarity by the volume of the solution in liters.

Step 3: To find the number of moles of water, we first need to find the mass of water in the solution. We know the density of the solution and the volume of the solution, so we can find the mass of the solution by multiplying the density by the volume. Then, we subtract the mass of glucose from the total mass of the solution to get the mass of water.

Step 4: We can then convert the mass of water to moles by using the molar mass of water, which is approximately 18.015 g/mol.

Step 5: Finally, we can find the mole fraction of glucose by dividing the number of moles of glucose by the total number of moles (moles of glucose + 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 mixture. For a solution, it can be calculated using the formula: mole fraction of solute = moles of solute / (moles of solute + moles of solvent).

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this case, the glucose solution has a molarity of 0.944 M, indicating that there are 0.944 moles of glucose in every liter of solution. Understanding molarity is essential for converting to other concentration units, such as mole fraction.

Density and Volume Relationship

Density is defined as mass per unit volume and is crucial for converting between mass and volume in solutions. The density of the glucose solution is given as 1.0624 g/mL, which allows us to calculate the mass of the solution. This information is necessary to determine the total number of moles of solvent (water) in the solution, which is required for calculating the mole fraction.

A 0.944 M solution of glucose, C6H12O6, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (a) Mole fraction