Question

What is the difference between percent by mass and percent by volume?

Short answer

The difference between percent by mass and percent by volume lies in the method of measurement. Percent by mass is calculated using mass values (usually in grams) and represents the concentration of a solute in a solution or mixture in relation to the total mass. The formula is: \[\text{% by mass} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\] Meanwhile, percent by volume is calculated using volume values (usually in milliliters or liters) and represents the concentration of a solute in a solution or mixture in relation to the total volume. The formula is: \[\text{% by volume} = \frac{\text{volume of solute}}{\text{total volume of solution}} \times 100\] Percent by mass is more common for solid mixtures or solutions, while percent by volume is more often used for liquid mixtures or solutions.

Step-by-step solution

Introduction to Percentages

Percentages are used to express a part of a whole in relation to the total amount. In the context of mass and volume, percentages can be used to describe the composition of solutions, mixtures, or compounds.

Percent by Mass

Percent by mass (also known as mass percentage, weight percent, or percent weight) is the concentration of a solute in a solution or mixture, expressed in relation to the total mass of the solution or mixture. To calculate the percent by mass, you divide the mass of the solute by the total mass of the solution or mixture and multiply the result by 100. The formula for calculating percent by mass is: \[\text{% by mass} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\]

Example of Percent by Mass

For example, let's consider a solution consisting of 10 grams of sugar dissolved in 90 grams of water. The total mass of the solution is 100 grams (10 grams + 90 grams). To calculate the percent by mass of sugar in the solution, we would use the following formula: \[\text{% by mass} = \frac{10\ \text{g}}{100\ \text{g}} \times 100 = 10\%\] Thus, the sugar represents 10% of the total mass of the solution.

Percent by Volume

Percent by volume (also known as volume percentage or percent volume) is the concentration of a solute in a solution or mixture, expressed in relation to the total volume of the solution or mixture. To calculate the percent by volume, you divide the volume of the solute by the total volume of the solution or mixture and multiply the result by 100. The formula for calculating percent by volume is: \[\text{% by volume} = \frac{\text{volume of solute}}{\text{total volume of solution}} \times 100\]

Example of Percent by Volume

For example, let's consider a solution consisting of 50 milliliters of alcohol mixed with 450 milliliters of water. The total volume of the solution is 500 milliliters (50 mL + 450 mL). To calculate the percent by volume of alcohol in the solution, we would use the following formula: \[\text{% by volume} = \frac{50\ \text{mL}}{500\ \text{mL}} \times 100 = 10\%\] Thus, the alcohol represents 10% of the total volume of the solution.

Key Differences

The main difference between percent by mass and percent by volume lies in the method of measurement: percent by mass is calculated using mass values (usually in grams), while percent by volume is calculated using volume values (usually in milliliters or liters). Additionally, percent by mass is more common when dealing with solid mixtures or solutions, while percent by volume is more often used for liquid mixtures or solutions.

Key concepts

Concentration in Solutions

Concentration in solutions refers to the amount of solute present in a given quantity of solvent or solution. It shows how much of a solute is mixed with a solvent, giving us a clearer idea of how strong or weak the solution is. Understanding concentration is crucial in fields like chemistry, because it helps determine the effect and behavior of a solution in reaction.
When we talk about concentration, we often use terms like "percent by mass" and "percent by volume". These indicate the proportion of solute in the total solution, but they measure it using different metrics:

• Percent by Mass: This metric uses weight to measure concentration. It's commonly used when the solute and solution are in solid or semi-solid form.
• Percent by Volume: This calculation uses the volume of the substances involved. It's mainly used for solutions where both the solute and solvent are liquid.

The way we express concentration helps guide processes, ensuring that the right amount of ingredient is used for the desired reaction or result.

Percentage Calculation

Percentage calculation is a straightforward mathematical method of determining how a part of something relates to the whole. It involves dividing the part by the whole and then multiplying by 100 to get the percentage value.
When calculating percent by mass or volume:

• Identify the solute and its weight (for mass) or its volume (for volume)
• Determine the total mass or volume of the entire solution
• Apply the formula:
  For mass: \ \ \[\text{% by mass} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\]
  For volume: \ \ \[\text{% by volume} = \frac{\text{volume of solute}}{\text{total volume of solution}} \times 100\]

The primary purpose of these calculations is to standardize how we express concentration, making it easier to compare different solutions, and to influence outcomes in industrial, laboratory, or any experimental setting.

Chemistry Basics

The basics of chemistry involve understanding substances and how they interact. Chemistry is the science of materials, their properties, and the changes they undergo.
In the context of solutions and their percentages, key ideas include:

• Solute: The substance that is dissolved in another substance. For instance, in a sugar-water mixture, sugar is the solute.
• Solvent: The liquid in which the solute is dissolved. With sugar-water, water is the solvent.
• Solution: A homogeneous mixture composed of two or more substances. A sugar-water mix is a solution.

These concepts are fundamental to grasping how solutions form, behave, and react in various situations. By appreciating these basics, students can better understand procedures and outcomes in chemical processes.