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Chapter 1: Problem 120

The density of osmium is reported by one source to be 22610 \(\mathrm{kg} / \mathrm{m}^{3}\). 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. The mass of the osmium block measuring \(10.0 cm \times 8.0 cm \times 9.0 cm\) is 16279.2 g, or approximately 16.3 kg.

Step by step solution

01

Convert the density from kg/m³ to g/cm³

We are given the density of osmium in kg/m³, and we need to convert it to g/cm³. To do this, we will use the conversion factors: 1 kg = 1000 g and 1 m = 100 cm. So, the conversion from kg/m³ to g/cm³ will involve the following steps: 1. Convert kg to grams: Multiply by 1000 (since 1 kg = 1000 g) 2. Convert cubic meters to cubic centimeters: Multiply by (100³) (since 1 m = 100 cm, and we are dealing with volume) Let's now do the conversion: Density in kg/m³ = 22610 kg/m³ \(Density\, in\, g/cm^3 = 22610\, \frac{kg}{m^3} \times \frac{1000\, g}{1\, kg} \times \left(\frac{100\, cm}{1\, m}\right)^3\) \(Density\, in\, g/cm^3 = 22.61\, g/cm^3\) So the density of osmium is 22.61 g/cm³.
02

Calculate the volume of the block

We are given the dimensions of the block: length = 10.0 cm width = 8.0 cm height = 9.0 cm To find the volume of the block, we simply multiply the length, width, and height: Volume = length × width × height Volume = (10.0 cm) × (8.0 cm) × (9.0 cm) Volume = 720.0 cm³
03

Calculate the mass of the block

We have the density of osmium (22.61 g/cm³) and the volume of the block (720.0 cm³). Now we can find the mass using the formula: Mass = Density × Volume Mass = (22.61 g/cm³) × (720.0 cm³) Mass = 16279.2 g So, the mass of the osmium block is 16279.2 grams, or approximately 16.3 kg.

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