Calculate the % v/v of a glycerol-water mixture prepared by adding 100 g of glycerol (specific gravity 1.263) to 1 liter of water. (ONE DECIMAL PLACE)
The correct answer and explanation is:
To calculate the % v/v (volume/volume percent) of a glycerol-water mixture, we need to find the volume of glycerol and the total volume of the solution, then use the formula: Percent v/v=(Volume of solute (glycerol)Total volume of solution)×100\text{Percent v/v} = \left(\frac{\text{Volume of solute (glycerol)}}{\text{Total volume of solution}}\right) \times 100
Step 1: Calculate the volume of glycerol
The specific gravity of glycerol is 1.263, which means that 1 mL of glycerol weighs 1.263 grams. Therefore, we can calculate the volume of glycerol using the formula: Volume of glycerol (mL)=Mass of glycerol (g)Specific gravity of glycerol\text{Volume of glycerol (mL)} = \frac{\text{Mass of glycerol (g)}}{\text{Specific gravity of glycerol}}
Substitute the values: Volume of glycerol=100 g1.263 g/mL≈79.2 mL\text{Volume of glycerol} = \frac{100 \text{ g}}{1.263 \text{ g/mL}} \approx 79.2 \text{ mL}
Step 2: Calculate the total volume of the solution
Since we are adding glycerol to 1 liter (1000 mL) of water, we can assume that the total volume is approximately the sum of the volume of water and the volume of glycerol. In reality, there might be slight volume contraction or expansion when mixing, but for simplicity, we’ll ignore that.
So, the total volume of the solution is: Total volume=1000 mL+79.2 mL=1079.2 mL\text{Total volume} = 1000 \text{ mL} + 79.2 \text{ mL} = 1079.2 \text{ mL}
Step 3: Calculate the % v/v of glycerol
Now, we can calculate the % v/v using the formula: Percent v/v=(79.2 mL1079.2 mL)×100≈7.3%\text{Percent v/v} = \left(\frac{79.2 \text{ mL}}{1079.2 \text{ mL}}\right) \times 100 \approx 7.3\%
Final Answer:
The % v/v of the glycerol-water mixture is 7.3%.