water (150 mL) having a density of 1 g/cm
. (a) Determine the volume percent of methanol (b) Determine the mass percent of water.m
is mixed with water (150 mL) having a density of 1 g/cm
. (a) Determine the volume percent of methanol (b) Determine the mass percent of water.
The Correct Answer and Explanation is:
a) The volume percent of methanol is 14.29%.
(b) The mass percent of water is 88.34%.
Explanation
This problem requires the calculation of solution concentration in two different ways: volume percent and mass percent. These are common methods for expressing the amount of a solute (methanol) dissolved in a solvent (water).
Part (a): Volume Percent of Methanol
The volume percent of a component in a mixture is the volume of that component divided by the total volume of the solution, multiplied by 100 to express it as a percentage. The formula is:
Volume % = (Volume of Component / Total Volume of Solution) × 100%
First, we must determine the total volume of the solution. Assuming the volumes are additive upon mixing, we sum the volumes of the individual components:
Total Volume = Volume of Methanol + Volume of Water
Total Volume = 25 mL + 150 mL = 175 mL
Next, we use this total volume to find the volume percent of methanol:
Volume % Methanol = (25 mL / 175 mL) × 100% = 14.29%
Part (b): Mass Percent of Water
The mass percent of a component is its mass divided by the total mass of the solution, multiplied by 100. The formula is:
Mass % = (Mass of Component / Total Mass of Solution) × 100%
The problem provides volumes and densities, so we must first calculate the mass of each component using the relationship: Mass = Density × Volume. Note that 1 cm³ is equivalent to 1 mL, allowing for direct calculation.
Mass of Methanol = 0.792 g/cm³ × 25 mL = 19.8 g
Mass of Water = 1 g/cm³ × 150 mL = 150 g
Now, we calculate the total mass of the solution by summing the individual masses:
Total Mass = Mass of Methanol + Mass of Water
Total Mass = 19.8 g + 150 g = 169.8 g
Finally, we apply the mass percent formula for water:
Mass % Water = (150 g / 169.8 g) × 100% = 88.34%
This demonstrates how the same solution has different concentration values depending on whether it is expressed by volume or by mass, due to the different densities of the components.
