Question

A sample of a substance that has a density of 0.824 \(\mathrm{g} / \mathrm{mL}\) has a mass of 0.451 \(\mathrm{g}\) . Calculate the volume of the sample.

Short answer

The volume of the sample is approximately 0.547 mL.

Step-by-step solution

- Understand the Formula

Recall the formula for density, which is the ratio of mass to volume: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]This can be rearranged to solve for volume:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

- Identify Given Values

From the problem, the given density (\(d\)) is 0.824 \( \text{g} / \text{mL} \). The mass (\(m\)) given is 0.451 \(\text{g}\).

- Plug in the Values

Substitute the given mass and density into the volume formula:\[ \text{Volume} = \frac{0.451 \text{g}}{0.824 \text{g/mL}} \]

- Perform the Calculation

Calculate the volume by performing the division:\[ \text{Volume} = \frac{0.451}{0.824} \approx 0.547 \text{mL} \]

Key concepts

Volume Calculation

Calculating the volume of a substance is a crucial concept in many scientific fields. To calculate the volume, we need to understand the relationship between mass, volume, and density. In this exercise, we use the formula: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Given the mass and density of a substance, we rearrange the standard density formula \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] to solve for volume.

By substituting the known values from the problem (0.451 g and 0.824 g/mL), we perform a simple division to find the volume. This step-by-step method is useful in ensuring accuracy and understanding the process. The final calculation: \[ \text{Volume} = \frac{0.451 \text{g}}{0.824 \text{g/mL}} \approx 0.547 \text{mL} \] helps us find the volume as 0.547 mL.

Mass and Density Relationship

Understanding the relationship between mass and density is key to solving problems like these. Density is defined as mass per unit volume and is expressed in units like \(\text{g/mL}\) or \(\text{kg/m^3}\).

Let's break this down further:

• Mass is the quantity of matter in an object and is measured in grams (g) or kilograms (kg).
• Density is how much mass is contained in a given volume and is calculated by dividing mass by volume.

When you know the mass and density of a substance, you can always find its volume by rearranging the density formula. Remember, the more dense a substance, the less volume it will occupy for the same mass. This concept is essential in fields like chemistry and physics, where understanding the behavior of materials depends on such relationships.

Physics Formulas

Physics often involves using various formulas to describe and calculate different properties of materials. One important formula in this context is the density formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Here are some key points to remember about using physics formulas effectively:

• Always identify the known and unknown quantities before you start. This helps in selecting the right formula and makes solving the problem easier.
• Ensure that all quantities are in consistent units. For example, if mass is in grams and density in \(\text{g/mL}\), the volume will be in milliliters (mL).
• Don't forget to rearrange the formula if you need to solve for a different variable. In the given exercise, we rearranged the density formula to find volume.
• Substitute the known values accurately and perform basic arithmetic operations to find the correct answer.

This step-by-step approach not only helps in solving the problem correctly but also reinforces the core concepts behind the formulas.