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Chapter 1: Problem 29

Density is the ratio of mass to volume. Mercury has a density of $1.36 \times 10^{4} \mathrm{kg} / \mathrm{m}^{3} .$ What is the density of mercury in units of \(\mathrm{g} / \mathrm{cm}^{3} ?\)

Short Answer

Expert verified
Question: Convert the density of mercury from 1.36 x 10^4 kg/m^3 to g/cm^3. Answer: The density of mercury in units of g/cm^3 is 13.6 g/cm^3.

Step by step solution

01

Convert mass unit from \(\mathrm{kg}\) to \(\mathrm{g}\)

To convert the mass unit, we will use the conversion factor: 1 \(\mathrm{kg}\) = 1000 \(\mathrm{g}\). Multiply the given density value by 1000. \(1.36 \times 10^{4} \mathrm{kg} / \mathrm{m}^{3}\) * 1000 = \(1.36 \times 10^{7} \mathrm{g} / \mathrm{m}^{3}\).
02

Convert volume unit from \(\mathrm{m}^{3}\) to \(\mathrm{cm}^{3}\)

To convert the volume unit, we will use the conversion factor: 1 \(\mathrm{m}\) = 100 \(\mathrm{cm}\), and remembering that it's cubic, so we need to cube the conversion factor: \((1 \mathrm{m})^3 = (100 \mathrm{cm})^3\) \(1 \mathrm{m}^3 = 100^3 \mathrm{cm}^3 = 10^6 \mathrm{cm}^3\) Now, divide the density value obtained in step 1 by \(10^6\): \((1.36 \times 10^{7} \mathrm{g} / \mathrm{m}^{3}) / 10^6 = 1.36 \times 10^{1} \mathrm{g} / \mathrm{cm}^{3}\)
03

Write the final answer

The density of mercury in units of \(\mathrm{g} / \mathrm{cm}^{3}\) is: \(1.36 \times 10^{1} \mathrm{g} / \mathrm{cm}^{3} = 13.6 \mathrm{g} / \mathrm{cm}^{3}\).

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