A chemist encounters an unknown metal. They drop the metal into a graduated cylinder containing water, and find the volume change is 4.1 mL. If the metal weighs 1.9 g, what is the density of the metal in g/mL?
The correct answer and explanation is :
To find the density of the unknown metal, we need to use the formula for density:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Step 1: Determine the mass and volume
The mass of the metal is given as 1.9 g. This is straightforward.
The volume change in the graduated cylinder is given as 4.1 mL. This represents the volume of the metal because when the metal is dropped into the water, it displaces an amount of water equal to its volume.
Step 2: Apply the density formula
Now that we have the mass and volume, we can calculate the density. The formula for density is:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{1.9 \, \text{g}}{4.1 \, \text{mL}}
]
Step 3: Perform the calculation
To find the density, divide the mass by the volume:
[
\text{Density} = \frac{1.9 \, \text{g}}{4.1 \, \text{mL}} = 0.4634 \, \text{g/mL}
]
Final Answer:
The density of the metal is 0.46 g/mL (rounded to two decimal places).
Explanation:
Density is a physical property that relates the mass of an object to its volume. In this case, the chemist dropped the metal into a graduated cylinder with water, and the water level increased by 4.1 mL. This increase represents the volume of the metal. The mass of the metal is given as 1.9 g. By using the formula for density, the density of the metal is calculated to be 0.46 g/mL.
Density is useful for identifying substances because each substance has a unique density. By comparing the density of the unknown metal to known densities of other metals, the chemist can determine what metal they are dealing with.