Question

Your boss found a piece of metal in the lab and wants you to determine what the metal is. She is pretty sure that the metal is either lead, aluminum, or silver. The lab bench has a balance and a \(100-\mathrm{mL}\) graduated cylinder with \(50 \mathrm{~mL}\) of water in it. You decide to weigh the metal and find that it has a mass of \(20.25 \mathrm{~g}\). After dropping the piece of metal into the graduated cylinder containing water, you observe that the volume increased to \(57.5 \mathrm{~mL}\). Identify the metal.

Short answer

The metal is aluminum.

Step-by-step solution

Determine the volume of the metal

Calculate the volume of the metal by subtracting the initial volume of water from the final volume of water in the graduated cylinder. Initial volume = 50 mL Final volume = 57.5 mL Volume of metal = Final volume - Initial volume Volume of metal = 57.5 mL - 50 mL = 7.5 mL

Calculate the density of the metal

Use the formula for density: density = mass/volume Where mass = 20.25 g (from the problem) and volume = 7.5 mL (from Step 1). Density = 20.25 g / 7.5 mL = 2.7 g/mL

Compare the calculated density with known densities of metals

Refer to a table of densities for lead, aluminum, and silver: - Lead: 11.34 g/mL - Aluminum: 2.7 g/mL - Silver: 10.49 g/mL Compare these values with the calculated density of 2.7 g/mL.

Identify the metal

Since the calculated density 2.7 g/mL matches the density of aluminum (2.7 g/mL), the metal is identified as aluminum.

Key concepts

mass and volume measurement

To identify an unknown metal, the first step is to measure its mass and volume. Mass can be measured using a balance. In the exercise, the metal was found to weigh 20.25 grams. Volume measurement involves a displacement method using a graduated cylinder. By noting the initial water level and the level after submerging the metal, the volume change can indicate the metal's volume. Here, the initial water volume was 50 mL, and it increased to 57.5 mL after adding the metal. The difference, 7.5 mL, is the volume of the metal.

density formula

Density is a crucial property that acts as a 'fingerprint' for substances. It is defined as the mass per unit volume. To find density, use the formula:
\(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\)
In our scenario, the mass of the metal was 20.25 g and the volume was 7.5 mL. Substituting these values into the density formula gives:
\(\text{Density} = \frac{20.25 \text{ g}}{7.5 \text{ mL}} = 2.7 \text{ g/mL}\)
The resulting density of 2.7 g/mL is then used for further identification of the metal.

identification of metals

To identify the metal, we compare the calculated density to known densities of possible candidates. The exercise hints that the metal could be lead, aluminum, or silver. Referring to standard density values:

• Lead: 11.34 g/mL
• Aluminum: 2.7 g/mL
• Silver: 10.49 g/mL

Our calculated density of 2.7 g/mL matches that of aluminum. Hence, we can confidently identify the metal as aluminum.

experimental procedure

Following a precise experimental procedure ensures accurate results. Here’s how we conducted the experiment:

• Measured the initial volume of water (50 mL) in a graduated cylinder.
• Gently submerged the metal, making sure not to splash, causing the water to rise.
• Recorded the new water level (57.5 mL), thus determining the metal's volume (7.5 mL).
• Weighed the metal on a balance to find its mass (20.25 g).
• Used these measurements to calculate the metal's density (2.7 g/mL).
• Compared the density to known values to identify the metal as aluminum.

Following these steps meticulously helps ensure reproducibility and accuracy in identifying the metal.