A student is determining the density of an unknown metal with a mass of 367.0 g. The student partially fills a graduated cylinder with water and measures the volume of the water by itself as 54.8 mL. The student then adds the metal to the water and measures the new volume as 87.3 mL. What is the density, in g/mL, of the metal?
The correct answer and explanation is :
To determine the density of the unknown metal, we need to use the formula for density:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Step 1: Identify the given values
- The mass of the metal is 367.0 g.
- The initial volume of water is 54.8 mL.
- The final volume of the water after adding the metal is 87.3 mL.
Step 2: Calculate the volume of the metal
The volume of the metal can be determined by the displacement of water caused by the metal. This is based on Archimedes’ principle, which states that the volume of the object submerged in water is equal to the volume of water displaced. To find the volume of the metal, subtract the initial volume of the water from the final volume:
[
\text{Volume of metal} = \text{Final volume} – \text{Initial volume}
]
[
\text{Volume of metal} = 87.3 \, \text{mL} – 54.8 \, \text{mL} = 32.5 \, \text{mL}
]
Step 3: Calculate the density
Now that we have both the mass and the volume of the metal, we can calculate its density.
[
\text{Density of metal} = \frac{\text{Mass}}{\text{Volume}} = \frac{367.0 \, \text{g}}{32.5 \, \text{mL}} = 11.3 \, \text{g/mL}
]
Final Answer:
The density of the unknown metal is 11.3 g/mL.
Explanation:
In this experiment, the principle of water displacement was used to find the volume of the metal. By measuring the change in water volume after adding the metal, we could determine the metal’s volume. Using the known mass of the metal and the calculated volume, we applied the formula for density to find the unknown metal’s density. The result indicates that the metal is relatively dense, which is typical for metals such as lead, gold, or mercury.