What is the mass/vol % ethanol in an ethanol-water solution with density of 0.875 g/ml and containing 65.0% ethanol by volume? The density of pure ethanol is 0.789 g/ml.
To find the mass/volume percentage (mass/vol %) of ethanol in the solution, we need to understand the relationship between volume percentage, density, and mass/volume percentage.
First, let's understand what the given information tells us:
1. The density of the solution is 0.875 g/ml.
2. The solution contains 65.0% ethanol by volume.
3. The density of pure ethanol is 0.789 g/ml.
To solve this problem, we'll follow these steps:
Step 1: Calculate the volume of the solution.
Given that the density of the solution is 0.875 g/ml, we can assume that the solution has a volume of 1 ml. Therefore, the volume of the solution is 1 ml.
Step 2: Calculate the mass of the solution.
Using the equation: mass = density x volume, we can calculate the mass of the solution.
mass of the solution = 0.875 g/ml x 1 ml = 0.875 g
Step 3: Calculate the volume of ethanol in the solution.
The solution contains 65.0% ethanol by volume, so the volume of ethanol can be calculated as:
volume of ethanol = 65.0% of 1 ml = 0.65 ml
Step 4: Calculate the mass of ethanol in the solution.
To calculate the mass of ethanol, we'll use the density of pure ethanol, which is 0.789 g/ml.
mass of ethanol = density x volume = 0.789 g/ml x 0.65 ml = 0.51185 g
Step 5: Calculate the mass/vol % of ethanol in the solution.
mass/vol % = (mass of ethanol / mass of solution) x 100
mass/vol % = (0.51185 g / 0.875 g) x 100 ≈ 58.53%
Therefore, the mass/volume percentage of ethanol in this solution is approximately 58.53%.