Pure ethonal has a density of 0.709 g/mL. What volume of pure ethonal should be mixed with water in order to make 375mL of a 0.400 M solution?
The correct answer and explanation is:
Let’s analyze the problem step by step.
Given data:
- Density of pure ethanol = 0.709 g/mL
- Desired final volume of solution = 375 mL
- Desired molarity (M) of ethanol solution = 0.400 M
Goal: Find the volume of pure ethanol needed to prepare 375 mL of 0.400 M ethanol solution.
Step 1: Understand the molarity definition
Molarity (M) is defined as moles of solute per liter of solution: M=moles of solutevolume of solution in litersM = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
For 0.400 M ethanol in 375 mL: moles of ethanol=M×V=0.400 mol/L×0.375 L=0.150 mol\text{moles of ethanol} = M \times V = 0.400 \, \text{mol/L} \times 0.375 \, \text{L} = 0.150 \, \text{mol}
Step 2: Calculate the mass of ethanol needed
The molar mass of ethanol (C₂H₅OH) is approximately 46.07 g/mol. mass of ethanol=moles×molar mass=0.150 mol×46.07 gmol=6.91 g\text{mass of ethanol} = \text{moles} \times \text{molar mass} = 0.150 \, \text{mol} \times 46.07 \, \frac{g}{mol} = 6.91 \, g
Step 3: Calculate the volume of pure ethanol corresponding to this mass
Use the density to find volume: density=massvolume ⟹ volume=massdensity\text{density} = \frac{\text{mass}}{\text{volume}} \implies \text{volume} = \frac{\text{mass}}{\text{density}} volume of ethanol=6.91 g0.709 g/mL=9.74 mL\text{volume of ethanol} = \frac{6.91 \, g}{0.709 \, g/mL} = 9.74 \, mL
Answer:
To prepare 375 mL of a 0.400 M ethanol solution, 9.74 mL of pure ethanol should be mixed with enough water to reach the total volume of 375 mL.
Explanation:
Molarity is a measure of concentration defined by the number of moles of solute dissolved per liter of total solution. Here, the solute is ethanol, and the solvent is water. To get the desired molarity of 0.400 M in a total solution volume of 375 mL, the number of moles of ethanol must be calculated first using molarity times volume in liters. After finding moles, the mass of ethanol required is determined using the molar mass of ethanol.
Because ethanol’s density is given, converting the mass of ethanol to volume is straightforward. Using the mass divided by density yields the volume of pure ethanol to use. The remainder of the solution volume is filled with water. This ensures the final volume is correct and the ethanol concentration matches the target molarity.
By following these steps, the problem is solved by combining concepts of molarity, molar mass, density, and volume relationships in solution preparation.