Problem 208 - Introductory Chemistry Atoms First

Question

A solution is prepared by combining \(4.00 \mathrm{~mL}\) of hexane with a sufficient volume of ethanol to obtain \(250.0 \mathrm{~mL}\) of solution. What is the percent by volume concentration of hexane?

Step-by-Step Solution

Answer

The percent by volume concentration of hexane in the solution is calculated using the formula \(\%\,v/v = \dfrac{\text{Volume of solute (mL)}}{\text{Total volume of solution (mL)}} \times 100\). With the given values, initial volume of hexane \(4.00\,\text{mL}\) and total volume of the solution \(250.0\,\text{mL}\), we find that the percent by volume concentration of hexane is \(1.6\%\), meaning 1.6% of the solution's volume consists of hexane.

Step 1: Write the formula for calculating percent by volume concentration

Percentage by volume (\(\%\,v/v\)) is calculated using the formula: \[\%\,v/v = \dfrac{\text{Volume of solute (mL)}}{\text{Total volume of solution (mL)}} \times 100\] In this exercise, the solute is hexane.

Step 2: Identify the values in the problem

We are given the following values in the problem: - Initial volume of hexane (solute): \(4.00\,\text{mL}\) - Total volume of the solution: \(250.0\,\text{mL}\)

Step 3: Calculate the percent by volume concentration

Now, apply the formula in step 1 to find the percentage by volume concentration of hexane in the solution. \[ \%\,v/v = \dfrac{4.00\,\text{mL}}{250.0\,\text{mL}} \times 100\] Calculate the result: \[ \%\,v/v = (0.016) \times 100 = 1.6\%\]

Step 4: Interpret the result

The percent by volume concentration of hexane in the solution is \(1.6\%\). This means that in the final 250.0 mL solution, 1.6% of its volume consists of hexane.

Key Concepts

Solution Preparation

When preparing a solution, it's essential to understand both the solute and the solvent involved. A solute is the substance being dissolved, while the solvent does the dissolving. In this exercise, hexane acts as the solute and ethanol as the solvent. Combining these two substances creates a homogeneous mixture known as a solution.

To prepare a solution, you need precise measurements of both the solute and the total volume required. For this specific task, we have 4.00 mL of hexane mixed with enough ethanol to make the total volume 250.0 mL. There are two main steps involved in solution preparation:

• Firstly, accurately measure the volume of the solute – in this case, hexane.


• Secondly, add your solvent until the desired total solution volume is reached. This requires careful measurement with calibrated equipment, like a volumetric flask, to ensure accuracy.

Preparing your solution correctly ensures that the concentration—the amount of solute in a given volume of solvent—will be accurate, which is crucial for any further experiments or calculations.

Calculation of Concentration

To calculate the percent by volume concentration, you need to know the volume of the solute and the total volume of the solution. Concentration is a way to express how much solute is present in a solution and can be represented as a percentage, making it more intuitive to understand.

The formula for percent by volume concentration is straightforward:\[\%\,v/v = \dfrac{\text{Volume of solute (mL)}}{\text{Total volume of solution (mL)}} \times 100\]
In the given exercise, hexane is the solute with a volume of 4.00 mL, and the total solution volume is 250.0 mL. Plugging these into the formula gives:\[\%\,v/v = \dfrac{4.00\,\text{mL}}{250.0\,\text{mL}} \times 100\]
This calculation results in:\[0.016 \times 100 = 1.6\%\]
This means that 1.6% of the entire solution's volume is comprised of hexane. Such calculations are crucial in fields ranging from chemistry to pharmaceuticals, where precise concentrations can drastically affect outcomes.

Hexane and Ethanol Mixture

A mixture of hexane and ethanol is intriguing due to the contrasting properties of these two substances. Hexane is a non-polar solvent, while ethanol is polar due to its hydroxyl ( OH) group.

Despite these differences, mixing hexane with ethanol can form a solution as long as the amount of hexane is relatively small compared to ethanol. Ethanol can solubilize small amounts of non-polar solvents like hexane due to its ability to participate in both polar and non-polar interactions to some extent.

Understanding the behavior of mixtures like this is key:

• Non-polarity of hexane implies it won't dissolve in water, but it can in ethanol when mixed appropriately.


• Such mixtures are applicable in areas where solvent properties aim to combine both polar and non-polar characteristics for various chemical reactions and industrial applications.

Appreciating the interactions at play when combining hexane and ethanol can provide insights into solvent effectiveness for different solutes, thereby assisting in targeted solution creation in lab work.