Question

If a solution contains $255\mathrm{mL}$ of ethanol and $375\mathrm{mL}$ of water, what is the percent of ethanol in the solution?

Short answer

The percent of ethanol in the solution is approximately 40.48%.

Step-by-step solution

Calculate Total Volume

First, we need to find the total volume of the solution by adding the volume of ethanol to the volume of water. The total volume is:$$255\text{ mL (ethanol)}+375\text{ mL (water)}=630\text{ mL (total solution)}$$

Calculate the Percent of Ethanol

To find the percent of ethanol in the solution, divide the volume of ethanol by the total volume of the solution, and then multiply by 100 to convert it to a percentage. The formula is:$$\text{Percent of Ethanol}=\left(\frac{255\text{ mL}}{630\text{ mL}}\right)\times 100$$

Compute the Value

Calculate the numerical value for the percentage:$$\text{Percent of Ethanol}=\left(\frac{255}{630}\right)\times 100\approx 40.48\mathrm{\%}$$

Key concepts

Understanding Ethanol Solution

An ethanol solution is a mixture consisting of ethanol and another substance, often water. This blend is common in both commercial and laboratory settings. In this context, we have an ethanol and water solution. Ethanol solutions are widely used due to their antiseptic properties and ability to dissolve substances that water alone might not. For example, ethanol is often found in hand sanitizers and household cleaning products.

• Ethanol is a type of alcohol, scientifically known as ethyl alcohol, and is commonly used in beverages, fuels, and as a solvent.
• Solutions are formed when a solute (like ethanol) is dissolved in a solvent (like water).
• Concentration refers to the amount of solute per unit volume of solution, which in our case, is expressed as a percentage.

Understanding ethanol solutions help in grasping how we calculate concentrations and make them suitable for various applications.

Performing Volume Calculation

Volume calculation is crucial when dealing with solutions, as it determines the proportions of substances involved. Here, the total volume of the solution is calculated by adding the individual volumes of ethanol and water together. This gives us valuable information about the entire mixture. To find the total volume of the solution:

• Add the volume of ethanol: 255 mL
• Add the volume of water: 375 mL
• The total volume = 255 mL + 375 mL = 630 mL

This total volume (630 mL) becomes the denominator in our percentage concentration formula. Knowing how to calculate volumes ensures accurate concentration determinations and proper mixing of solutions, essential in scientific experiments and industrial applications.

Applying the Percentage Formula

The percentage formula is used to find out what portion one part of the whole represents when expressed as a percentage. To do this, divide the part by the whole and multiply the result by 100.In the given exercise:

• The part is the volume of ethanol, 255 mL.
• The whole is the total solution volume, 630 mL.

The formula looks like this:$$\text{Percent of Ethanol}=\left(\frac{255\text{ mL}}{630\text{ mL}}\right)\times 100$$Once computed, this equals approximately 40.48%, meaning about 40.48% of the solution's total volume consists of ethanol. Applying the percentage formula is a fundamental skill across various disciplines, especially chemistry and biology, where understanding solution compositions is key.