Problem 114 - Introductory Chemistry Atoms First

Question

A solution of ethanol is prepared by combining \(22.5 \mathrm{~g}\) of ethanol with \(49.6 \mathrm{~g}\) of water. What is the percent composition by mass of alcohol in this solution?

Step-by-Step Solution

Answer

The percent composition by mass of alcohol in this solution is \(31.2\%\).

Step 1: Identify the given values

We are given the mass of ethanol (\(m_{ethanol}\)) and the mass of water (\(m_{water}\)), which are: - \(m_{ethanol} = 22.5~g\) - \(m_{water} = 49.6~g\) We will use these values to find the mass percentage of ethanol in the solution.

Step 2: Calculate the total mass of the solution

We need to find the total mass of the solution, which can be found by adding the masses of ethanol and water: Total Mass = \(m_{ethanol} + m_{water}\) Total Mass = \(22.5~g + 49.6~g = 72.1~g\)

Step 3: Calculate the mass percentage of ethanol

Now, we will apply the formula for mass percentage to find the mass percentage of ethanol: Mass Percentage = \((m_{ethanol} / Total Mass) × 100\) Mass Percentage = \((22.5~g / 72.1~g) × 100\) Mass Percentage = \((0.312~g) × 100\) Mass Percentage = \(31.2\%\) Hence, the percent composition by mass of alcohol in this solution is \(31.2\%\).

Key Concepts

Understanding Mass Percentage

The mass percentage, also known as mass percent, is a simple way of representing the concentration of a component in a mixture. It is calculated by dividing the mass of the component by the total mass of the solution, then multiplying by 100 to convert it to a percentage.

The formula can be expressed as follows:

• Mass Percentage = \((\text{mass of component} / \text{total mass}) \times 100\)

This concept is widely used in chemistry to quantify the concentration of a solute in a solution. In our example, we're finding the mass percentage of ethanol in an ethanol-water mixture. Calculating the mass percentage is beneficial because it helps understand the proportion of each component in the solution.

Ethanol Solution Basics

An ethanol solution is a liquid containing ethanol as the primary solute dissolved in a solvent, which is usually water. Ethanol, commonly known as alcohol, is a colorless, volatile substance used in beverages, sanitizers, fuels, and many chemical processes.

When ethanol is mixed with water, a homogeneous mixture or solution is formed. It is important to know that the properties of the solution, such as boiling and freezing points, will differ from those of pure substances. This is due to the interactions between ethanol and water molecules.

In chemistry, understanding the composition of these solutions in terms of mass percentage allows for precise control over the concentration of ethanol, which is crucial for various applications, whether in laboratory settings or industrial processes.

Fundamentals of Chemical Calculation

Chemical calculations involve fundamental quantitative relationships between constituents in a chemical reaction or a solution. They are used to determine concentrations, like the mass percentage of a constituent in a solution.

Let's break down the steps used in the calculation:

• First, determine the mass of each component, as given in the problem.
• Next, find the total mass of all components in the solution by simply adding up individual masses.
• Then, apply the mass percentage formula using the mass of the component of interest and the total mass.

For accuracy, ensure all measurements are in the same units and that calculations are performed with precision. Understanding these steps helps in successfully carrying out chemical calculations, which are a cornerstone of chemical problem-solving in academic and real-world scenarios.