Question

The element bromine at room temperature is a liquid with a density of \(3.12 \mathrm{~g} / \mathrm{mL}\). Calculate the mass of \(125 \mathrm{~mL}\) of bromine. What volume does \(85.0 \mathrm{~g}\) of bromine occupy?

Short answer

The mass of 125 mL of bromine is 390 g and the volume occupied by 85.0 g of bromine is approximately 27.24 mL.

Step-by-step solution

Find the mass of the 125 mL of bromine

We are given the density of bromine and the volume, so we can use the density formula to find the mass: \(Density = \frac{mass}{volume}\) We are given: - Density of bromine: 3.12 g/mL - Volume: 125 mL Rearrange the equation to solve for mass: \(mass = Density \times volume\) Now, plug in the given values: \(mass = 3.12 \mathrm{~g/mL} \times 125 \mathrm{~mL}\)

Calculate the mass

Now, perform the multiplication to find the mass: \(mass = 3.12 \mathrm{~g/mL} \times 125 \mathrm{~mL} = 390 \mathrm{~g}\) So, the mass of 125 mL of bromine is 390 g.

Find the volume occupied by 85 g of bromine

In this part, we are given the mass and we need to find the volume. We can use the density formula again: \(Density = \frac{mass}{volume}\) We are given: - Mass: 85.0 g - Density of bromine: 3.12 g/mL Rearrange the equation to solve for volume: \(volume = \frac{mass}{Density}\) Now, plug in the given values: \(volume = \frac{85.0 \mathrm{~g}}{3.12 \mathrm{~g/mL}}\)

Calculate the volume

Now, perform the division to find the volume: \(volume = \frac{85.0 \mathrm{~g}}{3.12 \mathrm{~g/mL}} = 27.24 \mathrm{~mL}\) So, the volume occupied by 85.0 g of bromine is approximately 27.24 mL.

Key concepts

Understanding Chemical Density

When we talk about chemical density, we're referring to how much mass a substance has in a given volume. In simple terms, it's a measure of how tightly packed the particles of a substance are. The density of chemicals is expressed in units like grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³), helping us to compare different materials. For example, a high density means the substance has more mass packed into the same amount of space, making it heavier for its size.

To visualize this, think of two containers of the same size: one filled with feathers and the other with lead. The lead-filled container is denser, thus it is much heavier, despite both containers occupying equal amounts of space. Understanding density is crucial for various fields like chemistry, material science, and even culinary arts, where it helps to determine proportions and mixtures.

The Mass-Volume Relationship

Breaking down the mass-volume relationship helps us to see the direct connection between the mass of a substance and its volume. This relationship is vital for calculations in chemistry and physics, providing a clear pathway to find one measurement when the other is known. The fundamental formula we use is:
\[Density = \frac{mass}{volume}\]
This relationship shows that if you know the density and one of the other quantities (mass or volume), you can easily compute the third. In practical terms, if you're preparing a solution and need a specific mass of a solute, knowing the density allows you to measure out the correct volume to achieve that mass. In contrast, if you're limited by volume, the density helps to determine how much mass you can fit into that space.

Solving for Mass and Volume

The process of solving for mass and volume uses the mass-volume relationship in practical situations. Here's how you can tackle such problems: First, familiarize yourself with the density equation shown above, and remember, to solve for mass, multiply density by volume. Conversely, to find volume, divide mass by density.

When applying these concepts to real-world problems, clarity in unit conversion is also crucial. Ensuring that your units for mass and volume are compatible with your density units will lead to accurate calculations. Often in science, especially chemistry, precision is key, so practicing these types of exercises strengthens your understanding and ability to work with chemical substances effectively.