Question

The mass of an empty container is \(88.25 \mathrm{~g}\). The mass of the container when filled with a liquid \((d=1.25 \mathrm{~g} / \mathrm{mL})\) is \(150.50 \mathrm{~g}\). What is the volume of the container?

Short answer

The volume of the container is 49.8 mL.

Step-by-step solution

- Determine the Mass of the Liquid

Subtract the mass of the empty container from the mass of the container filled with liquid. \[ m_{\text{liquid}} = m_{\text{filled}} - m_{\text{empty}} \]\[ m_{\text{liquid}} = 150.50 \text{ g} - 88.25 \text{ g} \]\[ m_{\text{liquid}} = 62.25 \text{ g} \]

- Use the Density Formula

The density formula is given by \( d = \frac{m}{V} \). To find the volume, rearrange the formula: \[ V = \frac{m}{d} \]

- Compute the Volume

Substitute the mass of the liquid and its density into the equation to find the volume: \[ V = \frac{62.25 \text{ g}}{1.25 \text{ g/mL}} \] \[ V = 49.8 \text{ mL} \]

Key concepts

mass and volume

Understanding the concepts of mass and volume is essential to solving density problems.
The mass of an object is a measure of the amount of matter it contains. It is usually measured in grams (g) or kilograms (kg). In the given exercise, the mass of the empty container is given as 88.25 g and the mass of the container filled with liquid is 150.50 g.
The volume of an object, on the other hand, measures the space it occupies and is usually measured in milliliters (mL) or liters (L). We are looking to find the volume of the liquid in the container using these measurements.

• Mass is related to the amount of matter - think of it like weight.
• Volume is the space that matter occupies - imagine filling a balloon with air.

With these in mind, we can better understand how to approach the problem and calculate the needed values.

density calculation

Density is a key concept that links mass and volume. It describes how much mass there is in a certain volume. The formula for density is:
\[ d = \frac{m}{V} \] Here, \( d \) is the density, \( m \) is the mass, and \( V \) is the volume. In the context of our exercise, we are given the density of the liquid as 1.25 g/mL.
Rearranging the density formula allows us to solve for volume (\( V \)) when we know the density (\( d \)) and the mass (\( m \)). The rearranged formula is:
\[ V = \frac{m}{d} \]

• Density tells us how tightly the matter is packed.
• Rearrange the density formula to solve for different variables as needed.

By applying this concept, we can calculate the volume using the given mass and density.

problem-solving steps

Solving density-related problems can be broken down into a few clear steps. Following these steps will help ensure that we arrive at the correct solution. Let's go through the steps based on the exercise provided:
Step 1: Determine the Mass of the Liquid
We first need to find the mass of the liquid itself by subtracting the mass of the empty container from the mass of the filled container:
\[ m_{\text{liquid}} = m_{\text{filled}} - m_{\text{empty}} \] Plugging in the values, we get:
\[ m_{\text{liquid}} = 150.50 \text{ g} - 88.25 \text{ g} = 62.25 \text{ g} \]
Step 2: Use the Density Formula
The next step is to use the density formula. We rearrange it to solve for volume:
\[ V = \frac{m}{d} \]
Step 3: Compute the Volume
Finally, we substitute the mass we obtained, and the given density into the formula to find the volume:
\[ V = \frac{62.25 \text{ g}}{1.25 \text{ g/mL}} = 49.8 \text{ mL} \]

• Break problems into steps to avoid errors.
• Always double-check calculations.

Following these structured steps can make solving density problems straightforward and more manageable.