Calculating the Mass of an Osmium Block
What is the mass of a block of osmium with specific dimensions?
The mass of a block of osmium that measures 1.01 cm × 0.233 cm × 0.648 cm is:
Choose the closest value from the following options:
- 3.45
- 34.5
- 6.75 × 10³
- 148
- 6.75 × 10⁻³
Answer:
The mass of the osmium block, based on the given dimensions, can be calculated as follows:
First, we need to calculate the volume of the osmium block using the given dimensions:
Volume = Length × Width × Height
Volume = 1.01 cm × 0.233 cm × 0.648 cm = 0.156 cm³
Next, we can calculate the mass of the osmium block using the density formula:
Mass = Density × Volume
Given Density of osmium = 22.6 g/cm³
Mass = 22.6 g/cm³ × 0.156 cm³ = 3.5256 g
Rounding to the appropriate number of significant figures, the mass of the osmium block is approximately 3.53 g.
Considering the answer choices provided, the closest value is 3.45 g.
Explanation:
Osmium is a dense metal with a density of 22.6 g/cm³. When calculating the mass of an osmium block, we need to first determine its volume by multiplying the length, width, and height of the block. Once we have the volume, we can then compute the mass using the formula Mass = Density × Volume.
In this specific scenario, the measurements of the osmium block are 1.01 cm × 0.233 cm × 0.648 cm. By multiplying these dimensions, we find the volume to be 0.156 cm³. When we multiply the density of osmium by this volume, we get a mass of 3.5256 g. Rounding this to the appropriate number of significant figures, we arrive at a mass of approximately 3.53 g.
Given the answer choices provided, the mass closest to this calculated value is 3.45 g. Therefore, the correct answer to the question is 3.45 g.