Problem 15 - Chemistry Matter and Change

Question

If 18 mL of methanol is used to make an aqueous solution that is 15% methanol by volume, how many milliliters of solution is produced?

Step-by-Step Solution

Answer

The total volume of the solution produced is 120 mL.

Step 1: 1. Define the variables and set up the equation

Let x be the total volume of the solution. Since the solution is 15% methanol by volume, it also means that the volume of methanol (18 mL) represents 15% of the total volume (x) of the solution. So, we can write the equation as: \(0.15x = 18\)

Step 2: 2. Solve for x

To solve for x, simply divide both sides of the equation by 0.15: \(x = \frac{18}{0.15}\)

Step 3: 3. Calculate the volume of the solution

Perform the division to find the volume of the solution: \(x = \frac{18}{0.15} = 120\) So, the total volume of the solution produced is 120 mL.

Key Concepts

Volume Percent

Volume percent is a way to express the concentration of a particular solute in a solution. It is widely used for "aqueous solutions" where liquids are mixed. Volume percent (\(\% \, \text{v/v} \)) refers to the ratio of the volume of the solute to the total volume of the solution, multiplied by 100. Here is how you can calculate it:

• Divide the volume of the solute by the total volume of the solution.
• Multiply the result by 100 to get a percentage.

For example, if 18 mL of methanol is mixed in a solution and represents 15% of the total volume, it means the methanol takes up 15% of the entire mixture's volume. Understanding volume percent is crucial in fields like chemistry where precise concentrations are key to reactions.

Aqueous Solution

An "aqueous solution" is when a substance, known as the solute, is dissolved in water. Water is considered an ideal solvent because it can dissolve many different substances. Aqueous solutions are essential in many chemical processes. Some characteristics of aqueous solutions include:

• Water as the solvent.
• Potential for conducting electricity if ions are present.
• It can be crucial for reactions where substances need to be mixed uniformly.

In our example, the methanol is dissolved in water to make an aqueous solution. The term is significant because the solution's properties can vastly differ from its components when isolated.

Methanol Volume

The methanol volume is an important part of calculating the solution's composition. Methanol is often used in labs due to its simplicity and volatility. When preparing solutions, knowing the exact volume of methanol is key to achieving the desired concentration. In this problem:

• The methanol volume is given as 18 mL.
• This represents the solute in the aqueous solution.

By knowing the volume of methanol, you can calculate other properties of the solution, such as its total volume when the desired concentration is given. Methanol's properties and volume can affect how the solution behaves, especially in chemical reactions.

Equation Solving

Equation solving allows us to find unknown quantities in chemistry problems. With the provided information, correctly setting up and solving equations is vital.Here's how to solve the equation in the given exercise:

• Identify variables and their relationships based on percentages.
• Write the equation representing the situation, for example, 0.15x = 18.
• Solve for the unknown variable, in this case, x, by isolating it on one side of the equation.
• Perform the arithmetic operation, dividing both sides by 0.15 to find x.

The solution for the equation \( x = \frac{18}{0.15} \) lands at 120 mL, indicating the total volume of the solution. This method is straightforward, allowing even complex mixture problems to be broken down into manageable calculations.