Question

A student weighed an empty graduated cylinder and found that it had a mass of \(25.23 \mathrm{~g}\). When filled with \(25.0 \mathrm{~mL}\) of an unknown liquid, the total mass was \(50.92 \mathrm{~g}\). What is the density of the liquid?

Short answer

1.0276 g/mL

Step-by-step solution

- Find the mass of the unknown liquid

Subtract the mass of the empty graduated cylinder from the total mass when filled with the liquid. \[ 50.92 \text{ g} - 25.23 \text{ g} = 25.69 \text{ g} \]

- Calculate the volume of the liquid

The volume of the unknown liquid is given as \(25.0 \text{ mL}\). This information is provided in the problem.

- Use the density formula

Density is calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] Substitute the mass and volume values into the formula: \[ \text{Density} = \frac{25.69 \text{ g}}{25.0 \text{ mL}} \]

- Solve for density

Calculate the value: \[ \text{Density} = 1.0276 \text{ g/mL} \]

Key concepts

Mass Measurement

Understanding how to measure mass accurately is essential in many scientific computations, including density calculations. Mass is typically measured using a balance or a scale. In this exercise, we used a balance to measure the mass of a graduated cylinder twice: when it was empty and when it was filled with an unknown liquid. By comparing these two measurements, we can determine the mass of just the liquid by subtracting the mass of the empty cylinder from the total mass. For example, if the total mass is 50.92 g and the mass of the empty cylinder is 25.23 g, the mass of the liquid is \(50.92 \text{ g} - 25.23 \text{ g} = 25.69 \text{ g}\).

Volume Measurement

Volume measurement is another crucial step in density calculation. In this exercise, we use a graduated cylinder, which is a tool specifically designed to measure liquid volumes accurately. The volume of the liquid should be read at eye level to avoid parallax error, which could lead to incorrect readings. The problem states that the volume of the unknown liquid is 25.0 mL, so there's no need for further measurement. However, in laboratory settings, you would fill the graduated cylinder to the desired mark and record the volume precisely.

Density Formula

The formula for density is one of the fundamental equations in science: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This means that density is the ratio of mass to volume. In our example, we have already calculated the mass (25.69 g) and the volume (25.0 mL). Plugging these values into the density formula gives us: \( \text{Density} = \frac{25.69 \text{ g}}{25.0 \text{ mL}} \). When we solve this, we get a density of 1.03 g/mL (rounded to two decimal places). This density tells us how much mass is packed into a specific volume and can be used for identifying the liquid.

Graduated Cylinder Use

A graduated cylinder is a common laboratory instrument used to measure liquid volumes with precision. Graduated cylinders come in various sizes and have markings along the side to indicate volume in milliliters (mL). To use it accurately:

• Place the cylinder on a flat surface.
• Pour the liquid into the cylinder and let it settle.
• Ensure your eyes are level with the surface of the liquid to avoid parallax error.
• Read the volume from the bottom of the meniscus.

In this exercise, the graduated cylinder was used to measure 25.0 mL of an unknown liquid. This accurate volume measurement is critical for correctly calculating the liquid's density. Using the graduated cylinder appropriately ensures the validity and reliability of our experimental results.