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Chapter 1: Problem 105

The density of water is \(0.9982 \mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). Express the density of water at \(20^{\circ} \mathrm{C}\) in the following units: (a) \(\mathrm{g} / \mathrm{L} ;\) (b) \(\mathrm{kg} / \mathrm{m}^{3} ;\) (c) \(\mathrm{kg} / \mathrm{km}^{3}\).

Short Answer

Expert verified
The density of water is: (a) 998.2 g/L, (b) 998.2 kg/m³, and (c) \(9.982 * 10^{11}\) kg/km³

Step by step solution

01

Convert to Grams per Litre (g/L)

First, remember that 1 litre(I), is equal to \(1000 cm^{3}\). So, to convert the density to grams per litre, multiply the original density by the number of cubic centimetres in a litre: \(0.9982 g/cm^{3} * 1000 cm^{3}/L = 998.2 g/L\)
02

Convert to Kilograms per Cubic Meter (kg/m³)

Next, recall that 1 kilogram (kg) is equal to 1000 grams (g) and 1 meter (m) is equivalent to 100 centimeters (cm). Therefore, \(1 g = 0.001 kg\) and \(1 cm = 0.01 m\), so a cubic meter is equivalent to \(100^{3} cm^{3} = 1 000 000 cm^{3}\). The conversion therefore becomes: \(0.9982 g/cm^{3} * 0.001 kg/g * 1 000 000 cm^{3}/m^{3} = 998.2 kg/m^{3}\)
03

Convert to Kilograms per Cubic Kilometer (kg/km³)

Lastly, consider that 1 kilometer (km) is equivalent to 1000 meters (m). Therefore a cubic kilometer is equivalent to \(1000^{3} m^{3} = 1 000 000 000 m^{3}\). The conversion therefore becomes: \(998.2 kg/m^{3} * 1 000 000 000 m^{3}/km^{3} = 9.982 * 10^{11} kg/km^{3}\)

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