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Chapter 9: Problem 95

How many milliliters of a \(12 \%\) (v/v) propyl alcohol solution would you need to obtain \(4.5 \mathrm{~mL}\) of propyl alcohol? (9.4)

Short Answer

Expert verified
37.5 mL

Step by step solution

01

- Understand the Problem

We need to determine how many milliliters of a 12% (v/v) propyl alcohol solution are required to obtain 4.5 mL of pure propyl alcohol. The percentage (v/v) indicates the volume of solute (propyl alcohol) per 100 mL of solution.
02

- Set Up the Equation

Let鈥檚 denote the volume of the 12% propyl alcohol solution needed as \(V_{solution}\). The relationship between the volume of the solution and the volume of propyl alcohol can be expressed as \(\frac{12}{100} \times V_{solution} = 4.5 \).
03

- Solve for the Solution Volume

Rearrange the equation to solve for \(V_{solution}\): \[ V_{solution} = \frac{4.5 \text{ mL}}{0.12} \]
04

- Calculate the Solution Volume

Calculate \( V_{solution} \): \[ V_{solution} = \frac{4.5}{0.12} = 37.5 \text{ mL} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

volume/volume percentage
To solve problems involving solution concentrations, it's critical to understand the concept of volume/volume percentage, often abbreviated as (v/v). This notation refers to the volume of a solute (in our case, propyl alcohol) compared to the total volume of the solution. Calculated as \(\frac{\text{volume of solute}}{\text{volume of solution}} \times 100\), it tells us how much of the solution is made up of the solute. For example, a 12% (v/v) propyl alcohol solution means there are 12 mL of propyl alcohol in every 100 mL of the total solution.
propyl alcohol solution
A propyl alcohol solution is a mixture where propyl alcohol acts as the solute. This solution can have various concentrations, often expressed as a percentage (v/v). Propyl alcohol is used in many sectors, including pharmaceuticals and manufacturing. In this problem, we are dealing with a 12% v/v solution. That means for every 100 mL of solution, 12 mL is pure propyl alcohol. By understanding this ratio, we can calculate how much propyl alcohol we have or need in a given volume of solution.
solute and solvent relationship
In any solution, the solute is the substance dissolved, and the solvent is the substance that dissolves the solute. For our 12% (v/v) propyl alcohol solution, propyl alcohol is the solute while water (or another solvent) forms the remainder of the solution. To determine how much of the solution we need to get a specific amount of solute, we use the given percentage. For example, to get 4.5 mL of propyl alcohol from a 12% solution, we set up the relationship: \(\frac{12\text{ mL}}{100\text{ mL}} \). Then we solve for the total volume needed to match the desired amount of solute.
problem-solving steps
Solving this type of concentration problem requires a clear approach. Follow these steps:
  • Understand the Problem: Know what the question is asking. Here, you need to find out how much solution is needed to get 4.5 mL of propyl alcohol.
  • Set Up the Equation: Use the concentration percentage to create an equation. For a 12% solution, use \( \frac{12}{100} \) in your calculations.
  • Solve for the Required Volume: Rearrange the equation to solve for the unknown variable, usually the volume of the solution needed. For example, \( V_{solution} = \frac{4.5 \text{mL}}{0.12} \).
  • Calculate: Use arithmetic to find the volume. Here, \( \frac{4.5}{0.12} \) gives us 37.5 mL.
By following these systematic steps, you can tackle similar problems more easily.

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