Question

An aqueous solution with density \(0.988 \mathrm{g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\) is prepared by dissolving \(12.8 \mathrm{mL} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) \((d=0.803 \mathrm{g} / \mathrm{mL})\) in enough water to produce \(75.0 \mathrm{mL}\) of solution. What is the percent \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) expressed as (a) percent by volume; (b) percent by mass; (c) percent (mass/volume)?

Short answer

The percentage of \(CH_{3}CH_{2}CH_{2}OH\) expressed as percent by volume, percent by mass and percent mass/volume can be calculated using the relevant formulas. Solve the equations obtained in steps 1, 2, and 3 to get the respective percentages.

Step-by-step solution

Calculate the volume Percentage

To find the volume of ethanol (CH3CH2CH2OH) in the solution, we can simply divide the volume of ethanol by the total volume of the solution and multiply by 100. Mathematically, it would look like this: \[ Volume\% = \left( \frac{Volume\, of\, ethanol}{Total\, volume\, of\, solution} \right) x 100 = \left( \frac{12.8\, mL}{75.0\, mL} \right) x 100 \]

Calculate the Mass Percentage

For the mass percentage we need to find the mass of the alcohol and total mass of the solution. The mass of alcohol can be calculated by multiplying its density by volume (Mass = density x volume). Then, we find the total mass by adding the mass of alcohol and mass of water (which can be found by multiplying the volume of water (total volume - volume of alcohol) with its density). Finally, the mass percentage is calculated as follows: \[ Mass\% = \left( \frac{Mass\, of\, ethanol}{Total\, mass\, of\, solution} \right) x 100 \]

Calculate the mass/volume Percentage

For the mass/volume percentage, we divide the mass of the solute with the total volume and multiply the result by 100. \[ Mass/Volume\% = \left( \frac{Mass\, of\, ethanol}{Total\, volume\, of\, solution} \right) x 100 \] The mass of ethanol is calculated as earlier explained in step 2, while the total volume of the solution is already given.

Key concepts

Percent by Volume

Percent by volume is a simple way to express concentration in a mixture. It helps you understand how much of one substance is present per 100 parts of total solution. This concept is particularly useful when dealing with liquid solutions. To calculate it, you divide the volume of the component of interest (in this case, ethanol) by the total volume of the solution, then multiply by 100 to convert it into a percentage.

For instance, if you are given the volume of ethanol as

• 12.8 mL (component)
• and the total volume of the solution as 75.0 mL

you can find the percent by volume using the formula:
\[Volume\% = \left( \frac{12.8\, \text{mL}}{75.0\, \text{mL}} \right) \times 100 = 17.07\%\]
So, the ethanol makes up 17.07% of the total volume.

Percent by Mass

Understanding percent by mass helps to know how much of one component is mixed in terms of weight or mass in a solution. This calculation becomes vital in many chemical experiments where exact mass ratios are crucial. The calculation involves a few steps, starting with finding the mass of the solute (substance being dissolved) and the total mass of the solution.

To kick off, you need to calculate the mass of the ethanol using its density (0.803 g/mL) and given volume (12.8 mL). This involves:

• Density = Mass/Volume
• So, Mass = Density × Volume = 0.803 g/mL × 12.8 mL = 10.2784 g

Then, determine the mass of the water. Since the total volume is 75.0 mL and ethanol occupies 12.8 mL, the water volume equals 62.2 mL. The water mass becomes 62.2 mL × 0.988 g/mL = 61.4416 g.

The entire mass of the solution equals the sum of masses of ethanol and water: 10.2784 g + 61.4416 g = 71.72 g.

Finally, calculate the mass percent:\[Mass\% = \left( \frac{10.2784\, \text{g}}{71.72\, \text{g}} \right) \times 100 = 14.33\%\]Thus, ethanol constitutes 14.33% of the solution by mass.

Mass/Volume Percentage

The mass/volume percentage provides insight into how much mass of a solute is present per unit volume of solution. This format is particularly handy when preparing standardized solutions in laboratories, where precise concentrations are imperative.

To find the mass/volume percentage, the key is to take the mass of the solute, which is the mass of ethanol, and express it per the total volume of the solution. The mass has already been calculated in the earlier steps as 10.2784 g.

Given the total solution volume of 75.0 mL, the mass/volume percentage is computed as:\[Mass/Volume\% = \left( \frac{10.2784\, \text{g}}{75.0\, \text{mL}} \right) \times 100 = 13.70\%\]This means 13.70 g of ethanol is present in every 100 mL of the solution, making it easy to visualize the concentration in everyday liquid measures.