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Chapter 1: Problem 128

The density of osmium is reported by one source to be $22,610 \mathrm{kg} / \mathrm{m}^{3} .\( What is this density in \)\mathrm{g} / \mathrm{cm}^{3} ?$ What is the mass of a block of osmium measuring 10.0 $\mathrm{cm} \times 8.0 \mathrm{cm} \times 9.0 \mathrm{cm} ?$

Short Answer

Expert verified
The density of osmium is 22.61 g/cm³, and the mass of a block of osmium measuring 10.0 cm × 8.0 cm × 9.0 cm is 16,279.2 g.

Step by step solution

01

Conversion of units for density

First, let's convert the density of osmium from kg/m³ to g/cm³. We need to multiply the given density by the conversion factors: \(1 kg = 1000 g\) and \(1 m = 100 cm\). Density in kg/m³ = 22,610 kg/m³ To convert it to g/cm³, we have to multiply by \((1000 g/1 kg)\) and \((1 m / 100 cm)^3\): \(22,610 \frac{kg}{m^3} \times \frac{1000 g}{1 kg} \times (\frac{1 m }{100 cm})^3\)
02

Calculate the new density of Osmium

Now, let's simplify the expression we've got: \(22,610 \times \frac{1000}{1} \times \frac{1}{100^3}\) \(22,610 \times 1000 \times \frac{1}{1,000,000}\) \(22,610 \times \frac{1}{1,000}\) = 22.61 g/cm³ The density of osmium is 22.61 g/cm³.
03

Calculate the volume of the block

Now let's find the volume of the block with dimensions 10.0 cm x 8.0 cm x 9.0 cm. We can calculate the volume using the formula: Volume = Length × Width × Height Volume = 10.0 cm × 8.0 cm × 9.0 cm = 720 cm³ The volume of the block is 720 cm³.
04

Calculate the mass of the block

Finally, let's find the mass of the block using the formula: Mass = Density × Volume We know the density of osmium is 22.61 g/cm³ and the volume of the block is 720 cm³. Mass = 22.61 g/cm³ × 720 cm³ = 16,279.2 g The mass of the block of osmium is 16,279.2 g.

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Most popular questions from this chapter

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